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<h1>Macaulay2Doc : Table of Contents</h1>
<ul><li><span><span><a href="index.html" title="">Macaulay2Doc</a></span><ul><li><span><span><a href="___Copyright_spand_splicense.html" title="">Copyright and license</a></span><ul><li><span><span><a href="___Singular-__Factory.html" title="">Singular-Factory</a></span></span></li>
<li><span><span><a href="___Singular-__Libfac.html" title="">Singular-Libfac</a></span></span></li>
<li><span><span><a href="_frobby.html" title="">frobby</a></span></span></li>
<li><span><span><a href="_pari.html" title="">pari</a></span></span></li>
<li><span><span><a href="___M__P__I__R.html" title="">MPIR</a></span></span></li>
<li><span><span><a href="___M__P__F__R.html" title="">MPFR</a></span></span></li>
<li><span><span><a href="___G__C_spgarbage_spcollector.html" title="">GC garbage collector</a></span></span></li>
<li><span><span><a href="___L__A__P__A__C__K.html" title="">LAPACK</a></span></span></li>
<li><span><span><a href="___B__L__A__S.html" title="">BLAS</a></span></span></li>
<li><span><span><a href="___N__T__L_splibrary.html" title="">NTL library</a></span></span></li>
<li><span><span><a href="_4ti2.html" title="">4ti2</a></span></span></li>
<li><span><span><a href="_gfan.html" title="">gfan</a></span></span></li>
<li><span><span><a href="_normaliz.html" title="">normaliz</a></span></span></li>
</ul>
</span></li>
<li><span><span><a href="___Acknowledgements.html" title="">Acknowledgements</a></span></span></li>
<li><span><span><a href="___The_spauthors.html" title="">The authors</a></span><ul><li><span><span><a href="___Daniel_sp__R._sp__Grayson.html" title="">Daniel R. Grayson</a></span></span></li>
<li><span><span><a href="___Michael_sp__E._sp__Stillman.html" title="">Michael E. Stillman</a></span></span></li>
<li><span><span><a href="___David_sp__Eisenbud.html" title="">David Eisenbud</a></span></span></li>
</ul>
</span></li>
<li><span><span><a href="___Other_spsources_spof_spinformation_spabout_sp__Macaulay2.html" title="">Other sources of information about Macaulay2</a></span></span></li>
<li><span><span><a href="_getting_spstarted.html" title="">getting started</a></span><ul><li><span><span><a href="_checking_spyour_sp__Macaulay2_spinstallation.html" title="and bookmarking the Macaulay2 documentation">checking your Macaulay2 installation</a> -- and bookmarking the Macaulay2 documentation</span></span></li>
<li><span><span><a href="_finding_spthe_sp__Macaulay2_spfiles.html" title="">finding the Macaulay2 files</a></span></span></li>
<li><span><span><a href="_teaching_sp__M2_sphow_spto_spfind_spits_spshared_splibraries.html" title="">teaching M2 how to find its shared libraries</a></span></span></li>
<li><span><span><a href="_teaching_spyour_spshell_sphow_spto_spfind_sp__M2.html" title="">teaching your shell how to find M2</a></span></span></li>
<li><span><span><a href="_moving_spor_spcopying_spthe_sp__Macaulay2_spfiles.html" title="">moving or copying the Macaulay2 files</a></span></span></li>
<li><span><span><a href="_running_sp__Macaulay2_spin_spa_spterminal_spwindow.html" title="">running Macaulay2 in a terminal window</a></span></span></li>
<li><span><span><a href="_using_sp__Macaulay2_spwith_spemacs.html" title="">using Macaulay2 with emacs</a></span><ul><li><span><span><a href="_setting_spup_spthe_sp__Macaulay2_spemacs_spinterface.html" title="">setting up the Macaulay2 emacs interface</a></span></span></li>
<li><span><span><a href="_teaching_spemacs_sphow_spto_spfind_sp__M2-init.el.html" title="">teaching emacs how to find M2-init.el</a></span></span></li>
<li><span><span><a href="_teaching_spemacs_sphow_spto_spfind_sp__M2.html" title="">teaching emacs how to find M2</a></span></span></li>
<li><span><span><a href="_running_sp__Macaulay2_spin_spemacs.html" title="">running Macaulay2 in emacs</a></span></span></li>
<li><span><span><a href="_using_sp__Macaulay2_spwith_spemacs_spafter_spit_sphas_spbeen_spset_spup.html" title="">using Macaulay2 with emacs after it has been set up</a></span></span></li>
<li><span><span><a href="_editing_sp__Macaulay2_spcode_spwith_spemacs.html" title="">editing Macaulay2 code with emacs</a></span></span></li>
</ul>
</span></li>
<li><span><span><a href="_using_sp__Macaulay2_spwith_sp__Te__Xmacs.html" title="">using Macaulay2 with TeXmacs</a></span></span></li>
<li><span><span><a href="_a_spfirst_sp__Macaulay2_spsession.html" title="">a first Macaulay2 session</a></span></span></li>
<li><span><span><a href="_reading_spthe_spdocumentation.html" title="">reading the documentation</a></span></span></li>
<li><span><span><a href="_getting_sphelp_spor_spreporting_spbugs.html" title="">getting help or reporting bugs</a></span></span></li>
</ul>
</span></li>
<li><span><span><a href="_rings.html" title="">rings</a></span><ul><li><span><span><a href="_basic_springs_spof_spnumbers.html" title="">basic rings of numbers</a></span></span></li>
<li><span><span><a href="_integers_spmodulo_spa_spprime.html" title="">integers modulo a prime</a></span></span></li>
<li><span><span><a href="_finite_spfields.html" title="">finite fields</a></span></span></li>
<li><span><span><a href="_polynomial_springs.html" title="">polynomial rings</a></span></span></li>
<li><span><span><a href="_monoid.html" title="make or retrieve a monoid">monoid</a> -- make or retrieve a monoid</span></span></li>
<li><span><span><a href="_monomial_sporderings.html" title="">monomial orderings</a></span><ul><li><span><span><a href="_examples_spof_spspecifying_spalternate_spmonomial_sporders.html" title="">examples of specifying alternate monomial orders</a></span></span></li>
<li><span><span><a href="_monomial_sporders_spfor_spfree_spmodules.html" title="">monomial orders for free modules</a></span><ul><li><span><span><a href="___Schreyer_sporders.html" title="induced monomial order on a free module">Schreyer orders</a> -- induced monomial order on a free module</span></span></li>
</ul>
</span></li>
<li><span><span><a href="_packing_spmonomials_spfor_spefficiency.html" title="">packing monomials for efficiency</a></span></span></li>
<li><span><span><a href="___G__Rev__Lex.html" title="graded reverse lexicographical monomial order.">GRevLex</a> -- graded reverse lexicographical monomial order.</span></span></li>
<li><span><span><a href="___Lex.html" title="lexicographical monomial order.">Lex</a> -- lexicographical monomial order.</span></span></li>
<li><span><span><a href="___G__Lex.html" title="graded lexicographic ordering">GLex</a> -- graded lexicographic ordering</span></span></li>
<li><span><span><a href="___Weights.html" title="assigning weights to the variables">Weights</a> -- assigning weights to the variables</span></span></li>
<li><span><span><a href="___Eliminate.html" title="elimination order">Eliminate</a> -- elimination order</span></span></li>
<li><span><span><a href="___Group__Lex.html" title="defines a ring where some variables are inverted">GroupLex</a> -- defines a ring where some variables are inverted</span></span></li>
<li><span><span><a href="___Group__Rev__Lex.html" title="">GroupRevLex</a></span></span></li>
<li><span><span><a href="_definition_spof_spproduct_sp_lpblock_rp_sporders.html" title="">definition of product (block) orders</a></span></span></li>
<li><span><span><a href="___Rev__Lex.html" title="reverse lexicographic ordering">RevLex</a> -- reverse lexicographic ordering</span></span></li>
<li><span><span><a href="___N__C__Lex.html" title="Non-commutative lexicographical order.">NCLex</a> -- Non-commutative lexicographical order.</span></span></li>
<li><span><span><a href="___Monomial__Order.html" title="monomial ordering">MonomialOrder</a> -- monomial ordering</span></span></li>
<li><span><span><a href="_obtaining_spthe_spmonomial_sporder_spof_spa_spring.html" title="">obtaining the monomial order of a ring</a></span></span></li>
</ul>
</span></li>
<li><span><span><a href="_graded_spand_spmultigraded_sppolynomial_springs.html" title="">graded and multigraded polynomial rings</a></span></span></li>
<li><span><span><a href="_quotient_springs.html" title="">quotient rings</a></span></span></li>
<li><span><span><a href="_manipulating_sppolynomials.html" title="">manipulating polynomials</a></span></span></li>
<li><span><span><a href="_factoring_sppolynomials.html" title="">factoring polynomials</a></span></span></li>
<li><span><span><a href="_fraction_spfields.html" title="">fraction fields</a></span></span></li>
<li><span><span><a href="_finite_spfield_spextensions.html" title="">finite field extensions</a></span></span></li>
<li><span><span><a href="_exterior_spalgebras.html" title="">exterior algebras</a></span></span></li>
<li><span><span><a href="_symmetric_spalgebras.html" title="">symmetric algebras</a></span></span></li>
<li><span><span><a href="_tensor_spproducts_spof_springs.html" title="">tensor products of rings</a></span></span></li>
<li><span><span><a href="___Weyl_spalgebras.html" title="">Weyl algebras</a></span></span></li>
<li><span><span><a href="_associative_spalgebras.html" title="">associative algebras</a></span></span></li>
</ul>
</span></li>
<li><span><span><a href="_ideals.html" title="">ideals</a></span><ul><li><span><span><a href="_creating_span_spideal.html" title="">creating an ideal</a></span></span></li>
<li><span><span><a href="_ideals_spto_spand_spfrom_spmatrices.html" title="">ideals to and from matrices</a></span></span></li>
<li><span><span><a href="_ideals_spto_spand_spfrom_spmodules.html" title="">ideals to and from modules</a></span></span></li>
<li><span><span><a href="_sums_cm_spproducts_cm_spand_sppowers_spof_spideals.html" title="">sums, products, and powers of ideals</a></span></span></li>
<li><span><span><a href="_equality_spand_spcontainment.html" title="">equality and containment</a></span></span></li>
<li><span><span><a href="_extracting_spgenerators_spof_span_spideal.html" title="">extracting generators of an ideal</a></span></span></li>
<li><span><span><a href="_dimension_cm_spcodimension_cm_spand_spdegree.html" title="">dimension, codimension, and degree</a></span></span></li>
<li><span><span><a href="_intersection_spof_spideals.html" title="">intersection of ideals</a></span></span></li>
<li><span><span><a href="_ideal_spquotients_spand_spsaturation.html" title="">ideal quotients and saturation</a></span></span></li>
<li><span><span><a href="_radical_spof_span_spideal.html" title="">radical of an ideal</a></span></span></li>
<li><span><span><a href="_minimal_spprimes_spof_span_spideal.html" title="">minimal primes of an ideal</a></span></span></li>
<li><span><span><a href="_associated_spprimes_spof_span_spideal.html" title="">associated primes of an ideal</a></span></span></li>
<li><span><span><a href="_primary_spdecomposition.html" title="">primary decomposition</a></span></span></li>
</ul>
</span></li>
<li><span><span><a href="_matrices.html" title="">matrices</a></span><ul><li><span><span><a href="_inputting_spa_spmatrix.html" title="">inputting a matrix</a></span></span></li>
<li><span><span><a href="_projections_cm_spinclusions_cm_spand_sppermutations.html" title="">projections, inclusions, and permutations</a></span></span></li>
<li><span><span><a href="_random_spand_spgeneric_spmatrices.html" title="">random and generic matrices</a></span></span></li>
<li><span><span><a href="_extracting_spinformation_spabout_spa_spmatrix.html" title="">extracting information about a matrix</a></span></span></li>
<li><span><span><a href="_basic_sparithmetic_spof_spmatrices.html" title="">basic arithmetic of matrices</a></span></span></li>
<li><span><span><a href="_concatenating_spmatrices.html" title="">concatenating matrices</a></span></span></li>
<li><span><span><a href="_differentiation.html" title="">differentiation</a></span></span></li>
<li><span><span><a href="_rank_spof_spa_spmatrix.html" title="">rank of a matrix</a></span></span></li>
<li><span><span><a href="_determinants_spand_spminors.html" title="">determinants and minors</a></span></span></li>
<li><span><span><a href="___Pfaffians.html" title="">Pfaffians</a></span></span></li>
<li><span><span><a href="_exterior_sppower_spof_spa_spmatrix.html" title="">exterior power of a matrix</a></span></span></li>
<li><span><span><a href="_format_spand_spdisplay_spof_spmatrices_spin_sp__Macaulay2.html" title="">format and display of matrices in Macaulay2</a></span></span></li>
<li><span><span><a href="_importing_spand_spexporting_spmatrices.html" title="">importing and exporting matrices</a></span></span></li>
</ul>
</span></li>
<li><span><span><a href="_substitution_spand_spmaps_spbetween_springs.html" title="">substitution and maps between rings</a></span><ul><li><span><span><a href="_substitute.html" title="substituting values for variables">substitute</a> -- substituting values for variables</span></span></li>
<li><span><span><a href="_working_spwith_spmultiple_springs.html" title="">working with multiple rings</a></span></span></li>
<li><span><span><a href="_basic_spconstruction_cm_spsource_spand_sptarget_spof_spa_spring_spmap.html" title="">basic construction, source and target of a ring map</a></span></span></li>
<li><span><span><a href="_evaluation_spand_spcomposition_spof_spring_spmaps.html" title="">evaluation and composition of ring maps</a></span></span></li>
<li><span><span><a href="_kernel_spand_spimage_spof_spa_spring_spmap.html" title="">kernel and image of a ring map</a></span></span></li>
<li><span><span><a href="_graph__Ideal_lp__Ring__Map_rp.html" title="the ideal of the graph of the regular map corresponding to a ring map">graphIdeal(RingMap)</a> -- the ideal of the graph of the regular map corresponding to a ring map</span></span></li>
<li><span><span><a href="_graph__Ring_lp__Ring__Map_rp.html" title="the coordinate ring of the graph of the regular map corresponding to a ring map">graphRing(RingMap)</a> -- the coordinate ring of the graph of the regular map corresponding to a ring map</span></span></li>
</ul>
</span></li>
<li><span><span><a href="_modules.html" title="">modules</a></span><ul><li><span><span><a href="_free_spmodules.html" title="">free modules</a></span></span></li>
<li><span><span><a href="_matrices_spto_spand_spfrom_spmodules.html" title="including kernel, cokernel and image">matrices to and from modules</a> -- including kernel, cokernel and image</span></span></li>
<li><span><span><a href="_submodules_spand_spquotients.html" title="">submodules and quotients</a></span></span></li>
<li><span><span><a href="_subquotient_spmodules.html" title="the way Macaulay2 represents modules">subquotient modules</a> -- the way Macaulay2 represents modules</span></span></li>
<li><span><span><a href="_module_sphomomorphisms.html" title="">module homomorphisms</a></span></span></li>
<li><span><span><a href="_right_spmodules_spor_spleft_spmodules_qu.html" title="">right modules or left modules?</a></span></span></li>
<li><span><span><a href="___Hilbert_spfunctions_spand_spfree_spresolutions.html" title="including degree and betti numbers">Hilbert functions and free resolutions</a> -- including degree and betti numbers</span></span></li>
<li><span><span><a href="_basis.html" title="basis of all or part of a module or ring">basis</a> -- basis of all or part of a module or ring</span></span></li>
<li><span><span><a href="_exterior_sppower_spof_spa_spmodule.html" title="">exterior power of a module</a></span></span></li>
</ul>
</span></li>
<li><span><span><a href="_chain_spcomplexes.html" title="">chain complexes</a></span><ul><li><span><span><a href="_free_spresolutions_spof_spmodules.html" title="">free resolutions of modules</a></span></span></li>
<li><span><span><a href="_extracting_spinformation_spfrom_spchain_spcomplexes.html" title="">extracting information from chain complexes</a></span></span></li>
<li><span><span><a href="_making_spchain_spcomplexes_spby_sphand.html" title="">making chain complexes by hand</a></span></span></li>
<li><span><span><a href="_manipulating_spchain_spcomplexes.html" title="">manipulating chain complexes</a></span></span></li>
<li><span><span><a href="_maps_spbetween_spchain_spcomplexes.html" title="">maps between chain complexes</a></span></span></li>
</ul>
</span></li>
<li><span><span><a href="_varieties.html" title="">varieties</a></span><ul><li><span><span><a href="_coherent_spsheaves.html" title="">coherent sheaves</a></span></span></li>
<li><span><span><a href="___Variety.html" title="the class of all algebraic varieties">Variety</a> -- the class of all algebraic varieties</span></span></li>
</ul>
</span></li>
<li><span><span><a href="___Gröbner_spbases.html" title="">Gröbner bases</a></span><ul><li><span><span><a href="_what_spis_spa_sp__Groebner_spbasis_qu.html" title="">what is a Groebner basis?</a></span></span></li>
<li><span><span><a href="___Groebner_spbasis_spexamples_spand_spapplications.html" title="">Groebner basis examples and applications</a></span><ul><li><span><span><a href="_simple_sp__Groebner_spbasis_spcomputations_spover_spvarious_springs.html" title="">simple Groebner basis computations over various rings</a></span></span></li>
</ul>
</span></li>
<li><span><span><a href="_computing_sp__Groebner_spbases.html" title="">computing Groebner bases</a></span></span></li>
</ul>
</span></li>
<li><span><span><a href="_normal_spforms.html" title="">normal forms</a></span></span></li>
<li><span><span><a href="_elimination_spof_spvariables.html" title="">elimination of variables</a></span></span></li>
<li><span><span><a href="_combinatorial_spfunctions.html" title="">combinatorial functions</a></span></span></li>
<li><span><span><a href="___The_sp__Macaulay2_splanguage.html" title="">The Macaulay2 language</a></span><ul><li><span><span><a href="_variables.html" title="The variables of a complex or co-complex.">variables</a> -- The variables of a complex or co-complex.</span><ul><li><span><span><a href="_valid_spnames.html" title="">valid names</a></span></span></li>
<li><span><span><a href="_assigning_spvalues.html" title="">assigning values</a></span></span></li>
<li><span><span><a href="_local_spvariables_spin_spa_spfile.html" title="">local variables in a file</a></span></span></li>
<li><span><span><a href="_viewing_spthe_spsymbols_spdefined_spso_spfar.html" title="">viewing the symbols defined so far</a></span></span></li>
<li><span><span><a href="_subscripted_spvariables.html" title="">subscripted variables</a></span></span></li>
<li><span><span><a href="_numbered_spvariables.html" title="">numbered variables</a></span></span></li>
</ul>
</span></li>
<li><span><span><a href="_numeric_sptypes.html" title="">numeric types</a></span></span></li>
<li><span><span><a href="_strings_spand_spnets.html" title="">strings and nets</a></span><ul><li><span><span><a href="__sl_sl_sl.html" title="delineate a string with slashes">///</a> -- delineate a string with slashes</span></span></li>
<li><span><span><a href="_concatenate.html" title="join strings">concatenate</a> -- join strings</span></span></li>
<li><span><span><a href="_format.html" title="format a string or a real number">format</a> -- format a string or a real number</span></span></li>
<li><span><span><a href="_lines.html" title="split a string into lines">lines</a> -- split a string into lines</span></span></li>
<li><span><span><a href="_separate.html" title="split a string into pieces">separate</a> -- split a string into pieces</span></span></li>
<li><span><span><a href="_regular_spexpressions.html" title="">regular expressions</a></span><ul><li><span><span><a href="_match_lp__String_cm__String_rp.html" title="regular expression matching">match(String,String)</a> -- regular expression matching</span></span></li>
<li><span><span><a href="_regex.html" title="">regex</a></span></span></li>
<li><span><span><a href="_replace.html" title="replacement in strings and lists">replace</a> -- replacement in strings and lists</span></span></li>
<li><span><span><a href="_select_lp__String_cm__String_rp.html" title="select substrings matching a regular expression from a string">select(String,String)</a> -- select substrings matching a regular expression from a string</span></span></li>
<li><span><span><a href="_select_lp__String_cm__String_cm__String_rp.html" title="select substrings matching a regular expression from a string">select(String,String,String)</a> -- select substrings matching a regular expression from a string</span></span></li>
</ul>
</span></li>
<li><span><span><a href="_horizontal__Join.html" title="join nets or strings horizontally">horizontalJoin</a> -- join nets or strings horizontally</span></span></li>
<li><span><span><a href="_stack.html" title="join nets or string vertically">stack</a> -- join nets or string vertically</span></span></li>
<li><span><span><a href="_unstack.html" title="list the rows of a net">unstack</a> -- list the rows of a net</span></span></li>
<li><span><span><a href="___String.html" title="the class of all strings">String</a> -- the class of all strings</span></span></li>
<li><span><span><a href="___Net.html" title="the class of all nets and strings">Net</a> -- the class of all nets and strings</span></span></li>
</ul>
</span></li>
<li><span><span><a href="_lists_spand_spsequences.html" title="">lists and sequences</a></span><ul><li><span><span><a href="_ranges_spand_sprepetitions.html" title="">ranges and repetitions</a></span></span></li>
<li><span><span><a href="__sh_sp__Basic__List.html" title="length"># BasicList</a> -- length</span></span></li>
<li><span><span><a href="___Basic__List_sp_sh_sp__Z__Z.html" title="get element from list">BasicList # ZZ</a> -- get element from list</span></span></li>
<li><span><span><a href="___Basic__List_sp_sh_qu_sp__Z__Z.html" title="check for element in list">BasicList #? ZZ</a> -- check for element in list</span></span></li>
<li><span><span><a href="___Visible__List_sp_us_sp__Z__Z.html" title="get element from list">VisibleList _ ZZ</a> -- get element from list</span></span></li>
<li><span><span><a href="___Visible__List_sp_us_sp__List.html" title="get some entries of a list">VisibleList _ List</a> -- get some entries of a list</span></span></li>
<li><span><span><a href="_first.html" title="first element of a list">first</a> -- first element of a list</span></span></li>
<li><span><span><a href="_last.html" title="last element of a list">last</a> -- last element of a list</span></span></li>
<li><span><span><a href="_to__List.html" title="list of elements">toList</a> -- list of elements</span></span></li>
<li><span><span><a href="_to__Sequence.html" title="convert to sequence">toSequence</a> -- convert to sequence</span></span></li>
<li><span><span><a href="_sequence.html" title="make a sequence">sequence</a> -- make a sequence</span></span></li>
<li><span><span><a href="_unsequence.html" title="extract the single element from a sequence of length 1">unsequence</a> -- extract the single element from a sequence of length 1</span></span></li>
<li><span><span><a href="_append.html" title="append an element to a list">append</a> -- append an element to a list</span></span></li>
<li><span><span><a href="_between.html" title="insert something between elements of a list">between</a> -- insert something between elements of a list</span></span></li>
<li><span><span><a href="_delete.html" title="delete elements of a list">delete</a> -- delete elements of a list</span></span></li>
<li><span><span><a href="_drop.html" title="drop some elements from a list or sequence">drop</a> -- drop some elements from a list or sequence</span></span></li>
<li><span><span><a href="_flatten.html" title="flatten a list by unnesting lists">flatten</a> -- flatten a list by unnesting lists</span></span></li>
<li><span><span><a href="_fold.html" title="apply binary operator repeatedly">fold</a> -- apply binary operator repeatedly</span></span></li>
<li><span><span><a href="_join.html" title="join lists">join</a> -- join lists</span></span></li>
<li><span><span><a href="___List_sp_vb_sp__List.html" title="join lists, sequences or arrays">List | List</a> -- join lists, sequences or arrays</span></span></li>
<li><span><span><a href="_mingle.html" title="mingle elements of several lists">mingle</a> -- mingle elements of several lists</span></span></li>
<li><span><span><a href="_pack.html" title="pack elements of a list into shorter ones">pack</a> -- pack elements of a list into shorter ones</span></span></li>
<li><span><span><a href="_prepend.html" title="add an element to the beginning of a list">prepend</a> -- add an element to the beginning of a list</span></span></li>
<li><span><span><a href="_reverse_lp__Basic__List_rp.html" title="reverse a list">reverse(BasicList)</a> -- reverse a list</span></span></li>
<li><span><span><a href="_rsort.html" title="sort a list or matrix in reverse order">rsort</a> -- sort a list or matrix in reverse order</span></span></li>
<li><span><span><a href="_sort.html" title="sort a list or columns of a matrix">sort</a> -- sort a list or columns of a matrix</span></span></li>
<li><span><span><a href="_subtable.html" title="extract a subtable from a table">subtable</a> -- extract a subtable from a table</span></span></li>
<li><span><span><a href="_table.html" title="make a table (nested list)">table</a> -- make a table (nested list)</span></span></li>
<li><span><span><a href="_take.html" title="take some elements from a list">take</a> -- take some elements from a list</span></span></li>
<li><span><span><a href="_unique.html" title="eliminate duplicates from a list">unique</a> -- eliminate duplicates from a list</span></span></li>
<li><span><span><a href="_apply_lp__Basic__List_cm__Function_rp.html" title="apply a function to each element of a list">apply(BasicList,Function)</a> -- apply a function to each element of a list</span></span></li>
<li><span><span><a href="_scan_lp__Basic__List_cm__Function_rp.html" title="apply a function to each element of a list">scan(BasicList,Function)</a> -- apply a function to each element of a list</span></span></li>
<li><span><span><a href="_all_lp__Basic__List_cm__Function_rp.html" title="whether all elements of a list satisfy a specified condition">all(BasicList,Function)</a> -- whether all elements of a list satisfy a specified condition</span></span></li>
<li><span><span><a href="_any_lp__Basic__List_cm__Function_rp.html" title="whether any elements of a list satisfy a specified condition">any(BasicList,Function)</a> -- whether any elements of a list satisfy a specified condition</span></span></li>
<li><span><span><a href="_position.html" title="find first element of a list satisfying a condition">position</a> -- find first element of a list satisfying a condition</span></span></li>
<li><span><span><a href="_positions_lp__Visible__List_cm__Function_rp.html" title="which elements of a list satisfy a condition">positions(VisibleList,Function)</a> -- which elements of a list satisfy a condition</span></span></li>
<li><span><span><a href="_select_lp__Basic__List_cm__Function_rp.html" title="select elements from a list">select(BasicList,Function)</a> -- select elements from a list</span></span></li>
<li><span><span><a href="_select_lp__Z__Z_cm__Basic__List_cm__Function_rp.html" title="select a limited number of elements from a list">select(ZZ,BasicList,Function)</a> -- select a limited number of elements from a list</span></span></li>
<li><span><span><a href="___Visible__List.html" title="the class of all visible lists">VisibleList</a> -- the class of all visible lists</span><ul><li><span><span><a href="___List.html" title="the class of all lists -- {...}">List</a> -- the class of all lists -- {...}</span></span></li>
<li><span><span><a href="___Sequence.html" title="the class of all sequences -- (...)">Sequence</a> -- the class of all sequences -- (...)</span></span></li>
<li><span><span><a href="___Array.html" title="the class of all arrays -- [...]">Array</a> -- the class of all arrays -- [...]</span></span></li>
</ul>
</span></li>
<li><span><span><a href="___Basic__List.html" title="the class of all basic lists">BasicList</a> -- the class of all basic lists</span></span></li>
</ul>
</span></li>
<li><span><span><a href="_hash_sptables.html" title="">hash tables</a></span><ul><li><span><span><a href="_copy.html" title="copy an object">copy</a> -- copy an object</span></span></li>
<li><span><span><a href="_hash__Table.html" title="make a hash table">hashTable</a> -- make a hash table</span></span></li>
<li><span><span><a href="_keys.html" title="keys used in a hash table">keys</a> -- keys used in a hash table</span></span></li>
<li><span><span><a href="_values.html" title="values in a hash table">values</a> -- values in a hash table</span></span></li>
<li><span><span><a href="_pairs.html" title="list the pairs in a hash table">pairs</a> -- list the pairs in a hash table</span></span></li>
<li><span><span><a href="_mutable.html" title="whether something may be modified">mutable</a> -- whether something may be modified</span></span></li>
<li><span><span><a href="_remove.html" title="remove an entry from a hash table">remove</a> -- remove an entry from a hash table</span></span></li>
<li><span><span><a href="_apply__Keys.html" title="apply a function to each key in a hash table">applyKeys</a> -- apply a function to each key in a hash table</span></span></li>
<li><span><span><a href="_apply__Values.html" title="apply a function to each value">applyValues</a> -- apply a function to each value</span></span></li>
<li><span><span><a href="_apply__Pairs.html" title="apply a function to each pair in a hash table">applyPairs</a> -- apply a function to each pair in a hash table</span></span></li>
<li><span><span><a href="_merge_lp__Hash__Table_cm__Hash__Table_cm__Function_rp.html" title="merge hash tables">merge(HashTable,HashTable,Function)</a> -- merge hash tables</span></span></li>
<li><span><span><a href="_combine.html" title="combine hash tables">combine</a> -- combine hash tables</span></span></li>
<li><span><span><a href="_hashing.html" title="">hashing</a></span></span></li>
<li><span><span><a href="___Hash__Table.html" title="the class of all hash tables">HashTable</a> -- the class of all hash tables</span></span></li>
<li><span><span><a href="___Mutable__Hash__Table.html" title="the class of all mutable hash tables">MutableHashTable</a> -- the class of all mutable hash tables</span></span></li>
</ul>
</span></li>
<li><span><span><a href="_operators.html" title="">operators</a></span><ul><li><span><span><a href="__eq.html" title="assignment">=</a> -- assignment</span></span></li>
<li><span><span><a href="__co_eq.html" title="assignment of method or new local variable">:=</a> -- assignment of method or new local variable</span></span></li>
<li><span><span><a href="__lt-.html" title="assignment with left side evaluated"><-</a> -- assignment with left side evaluated</span></span></li>
<li><span><span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span><span><a href="_!_eq.html" title="inequality">!=</a> -- inequality</span></span></li>
<li><span><span><a href="___Thing_sp_eq_eq_eq_sp__Thing.html" title="strict equality">Thing === Thing</a> -- strict equality</span></span></li>
<li><span><span><a href="__eq!_eq.html" title="strict inequality">=!=</a> -- strict inequality</span></span></li>
<li><span><span><a href="__lt.html" title="less than"><</a> -- less than</span></span></li>
<li><span><span><a href="__lt_eq.html" title="less than or equal"><=</a> -- less than or equal</span></span></li>
<li><span><span><a href="__gt.html" title="greater than">></a> -- greater than</span></span></li>
<li><span><span><a href="__gt_eq.html" title="greater than or equal">>=</a> -- greater than or equal</span></span></li>
<li><span><span><a href="__qu.html" title="comparison operator">?</a> -- comparison operator</span></span></li>
<li><span><span><a href="_and.html" title="conjunction">and</a> -- conjunction</span></span></li>
<li><span><span><a href="_or.html" title="disjunction">or</a> -- disjunction</span></span></li>
<li><span><span><a href="_not.html" title="negation">not</a> -- negation</span></span></li>
<li><span><span><a href="___S__P__A__C__E.html" title="blank operator; often used for function application, making polynomial rings">SPACE</a> -- blank operator; often used for function application, making polynomial rings</span></span></li>
<li><span><span><a href="_-_gt.html" title="make a function">-></a> -- make a function</span></span></li>
<li><span><span><a href="__at_at.html" title="a binary operator">@@</a> -- a binary operator</span></span></li>
<li><span><span><a href="__bs_bs.html" title="a binary operator">\\</a> -- a binary operator</span></span></li>
<li><span><span><a href="__bs.html" title="a binary operator">\</a> -- a binary operator</span></span></li>
<li><span><span><a href="__us.html" title="a binary operator, used for subscripting and access to elements">_</a> -- a binary operator, used for subscripting and access to elements</span></span></li>
<li><span><span><a href="_..html" title="access to elements whose key is a symbol">.</a> -- access to elements whose key is a symbol</span></span></li>
<li><span><span><a href="_._qu.html" title="check for presence of elements whose key is a symbol">.?</a> -- check for presence of elements whose key is a symbol</span></span></li>
<li><span><span><a href="__sh.html" title="length, or access to elements">#</a> -- length, or access to elements</span></span></li>
<li><span><span><a href="__sh_qu.html" title="check for presence of elements">#?</a> -- check for presence of elements</span></span></li>
<li><span><span><a href="_!.html" title="factorial">!</a> -- factorial</span></span></li>
<li><span><span><a href="__pl.html" title="a unary or binary operator, usually used for addition">+</a> -- a unary or binary operator, usually used for addition</span></span></li>
<li><span><span><a href="_-.html" title="a unary or binary operator, usually used for negation or subtraction">-</a> -- a unary or binary operator, usually used for negation or subtraction</span></span></li>
<li><span><span><a href="__st.html" title="a binary operator, usually used for multiplication">*</a> -- a binary operator, usually used for multiplication</span></span></li>
<li><span><span><a href="__sl.html" title="a binary operator, usually used for division">/</a> -- a binary operator, usually used for division</span></span></li>
<li><span><span><a href="__sl_sl.html" title="a binary operator, usually used for quotient">//</a> -- a binary operator, usually used for quotient</span></span></li>
<li><span><span><a href="__pc.html" title="a binary operator, usually used for remainder and reduction">%</a> -- a binary operator, usually used for remainder and reduction</span></span></li>
<li><span><span><a href="_^.html" title="a binary operator, usually used for powers">^</a> -- a binary operator, usually used for powers</span></span></li>
<li><span><span><a href="__am.html" title="a binary operator">&</a> -- a binary operator</span></span></li>
<li><span><span><a href="__pl_pl.html" title="a binary operator, usually used for direct sum">++</a> -- a binary operator, usually used for direct sum</span></span></li>
<li><span><span><a href="__st_st.html" title="a binary operator, usually used for tensor product or Cartesian product">**</a> -- a binary operator, usually used for tensor product or Cartesian product</span></span></li>
<li><span><span><a href="_^_st_st.html" title="a binary operator, usually used for tensor or Cartesian power">^**</a> -- a binary operator, usually used for tensor or Cartesian power</span></span></li>
<li><span><span><a href="_~.html" title="a unary postfix operator">~</a> -- a unary postfix operator</span></span></li>
<li><span><span><a href="__lp_st_rp.html" title="a unary postfix operator, used for indicating a graded object">(*)</a> -- a unary postfix operator, used for indicating a graded object</span></span></li>
<li><span><span><a href="__co.html" title="a binary operator, uses include repetition; ideal quotients">:</a> -- a binary operator, uses include repetition; ideal quotients</span></span></li>
<li><span><span><a href="_...html" title="a binary operator, used for sequences of consecutive items">..</a> -- a binary operator, used for sequences of consecutive items</span></span></li>
<li><span><span><a href="_.._lt.html" title="a binary operator, used for sequences of consecutive items, not including the endpoint">..<</a> -- a binary operator, used for sequences of consecutive items, not including the endpoint</span></span></li>
<li><span><span><a href="__lt_lt.html" title="a binary operator (file output, ...)"><<</a> -- a binary operator (file output, ...)</span></span></li>
<li><span><span><a href="__gt_gt.html" title="a binary operator, uses include bit shifting, or attaching optional inputs to functions">>></a> -- a binary operator, uses include bit shifting, or attaching optional inputs to functions</span></span></li>
<li><span><span><a href="__vb.html" title="a binary operator, often used for horizontal concatenation">|</a> -- a binary operator, often used for horizontal concatenation</span></span></li>
<li><span><span><a href="__vb_vb.html" title="a binary operator, often used for vertical concatenation">||</a> -- a binary operator, often used for vertical concatenation</span></span></li>
<li><span><span><a href="__at.html" title="a binary operator">@</a> -- a binary operator</span></span></li>
<li><span><span><a href="_^^.html" title="a binary operator">^^</a> -- a binary operator</span></span></li>
<li><span><span><a href="__vb-.html" title="a binary operator">|-</a> -- a binary operator</span></span></li>
<li><span><span><a href="__lt_eq_eq_gt.html" title="a binary operator"><==></a> -- a binary operator</span></span></li>
<li><span><span><a href="__eq_eq_eq_gt.html" title="a binary operator">===></a> -- a binary operator</span></span></li>
<li><span><span><a href="__eq_eq_gt.html" title="a binary operator">==></a> -- a binary operator</span></span></li>
<li><span><span><a href="__lt_eq_eq_eq.html" title="a unary and binary operator"><===</a> -- a unary and binary operator</span></span></li>
<li><span><span><a href="__lt_eq_eq.html" title="a unary and binary operator"><==</a> -- a unary and binary operator</span></span></li>
<li><span><span><a href="__eq_gt.html" title="produce an Option">=></a> -- produce an Option</span></span></li>
<li><span><span><a href="__cm.html" title="the comma, used for separating entries in a list or sequence">,</a> -- the comma, used for separating entries in a list or sequence</span></span></li>
<li><span><span><a href="__se.html" title="statement separator">;</a> -- statement separator</span></span></li>
<li><span><span><a href="_precedence_spof_spoperators.html" title="">precedence of operators</a></span></span></li>
<li><span><span><a href="_operator__Attributes.html" title="">operatorAttributes</a></span></span></li>
</ul>
</span></li>
<li><span><span><a href="_conditional_spexecution.html" title="if-then-else statements">conditional execution</a> -- if-then-else statements</span></span></li>
<li><span><span><a href="_while.html" title="while loops">while</a> -- while loops</span></span></li>
<li><span><span><a href="_for.html" title="for loops">for</a> -- for loops</span></span></li>
<li><span><span><a href="_mapping_spover_splists.html" title="apply a function to each element of a list">mapping over lists</a> -- apply a function to each element of a list</span></span></li>
<li><span><span><a href="_mapping_spover_sphash_sptables.html" title="apply a function to each element of a hash table">mapping over hash tables</a> -- apply a function to each element of a hash table</span></span></li>
<li><span><span><a href="_error_sphandling.html" title="signalling and trapping errors">error handling</a> -- signalling and trapping errors</span><ul><li><span><span><a href="_error.html" title="deliver error message">error</a> -- deliver error message</span></span></li>
<li><span><span><a href="_try.html" title="catch an error">try</a> -- catch an error</span></span></li>
</ul>
</span></li>
<li><span><span><a href="_catch.html" title="catch a thrown exception">catch</a> -- catch a thrown exception</span></span></li>
<li><span><span><a href="_using_spfunctions.html" title="">using functions</a></span></span></li>
<li><span><span><a href="_using_spfunctions_spwith_spoptional_spinputs.html" title="">using functions with optional inputs</a></span></span></li>
<li><span><span><a href="_making_spfunctions.html" title="">making functions</a></span></span></li>
<li><span><span><a href="_local_spvariables_spin_spa_spfunction.html" title="">local variables in a function</a></span></span></li>
<li><span><span><a href="_making_spfunctions_spwith_spa_spvariable_spnumber_spof_sparguments.html" title="">making functions with a variable number of arguments</a></span></span></li>
<li><span><span><a href="_making_spfunctions_spwith_spmultiple_spreturn_spvalues.html" title="">making functions with multiple return values</a></span></span></li>
<li><span><span><a href="_making_spnew_spfunctions_spwith_spoptional_sparguments.html" title="">making new functions with optional arguments</a></span></span></li>
<li><span><span><a href="_what_spa_spclass_spis.html" title="">what a class is</a></span><ul><li><span><span><a href="_class.html" title="class of an object">class</a> -- class of an object</span></span></li>
<li><span><span><a href="_parent.html" title="parent type of an object">parent</a> -- parent type of an object</span></span></li>
<li><span><span><a href="_instance.html" title="whether something has a certain type">instance</a> -- whether something has a certain type</span></span></li>
<li><span><span><a href="_ancestor_lp__Type_cm__Type_rp.html" title="whether one type is an ancestor of another">ancestor(Type,Type)</a> -- whether one type is an ancestor of another</span></span></li>
</ul>
</span></li>
<li><span><span><a href="_installing_spmethods.html" title="">installing methods</a></span></span></li>
<li><span><span><a href="_binary_spmethods.html" title="">binary methods</a></span></span></li>
<li><span><span><a href="_inheritance.html" title="">inheritance</a></span></span></li>
<li><span><span><a href="_making_spnew_spclasses.html" title="">making new classes</a></span></span></li>
<li><span><span><a href="_new.html" title="new objects and new types">new</a> -- new objects and new types</span><ul><li><span><span><a href="_new__Class.html" title="set the class and parent of an object">newClass</a> -- set the class and parent of an object</span></span></li>
</ul>
</span></li>
<li><span><span><a href="_printing_spand_spformatting_spfor_spnew_spclasses.html" title="">printing and formatting for new classes</a></span></span></li>
<li><span><span><a href="_making_spa_spnew_spmethod_spfunction.html" title="">making a new method function</a></span><ul><li><span><span><a href="_method.html" title="make a new method function">method</a> -- make a new method function</span></span></li>
</ul>
</span></li>
<li><span><span><a href="_printing_spto_spthe_spscreen.html" title="">printing to the screen</a></span></span></li>
<li><span><span><a href="_reading_spfiles.html" title="">reading files</a></span></span></li>
<li><span><span><a href="_getting_spinput_spfrom_spthe_spuser.html" title="">getting input from the user</a></span></span></li>
<li><span><span><a href="_creating_spand_spwriting_spfiles.html" title="">creating and writing files</a></span></span></li>
<li><span><span><a href="_saving_sppolynomials_spand_spmatrices_spin_spfiles.html" title="">saving polynomials and matrices in files</a></span></span></li>
<li><span><span><a href="_two_spdimensional_spformatting.html" title="">two dimensional formatting</a></span></span></li>
<li><span><span><a href="_file_spmanipulation.html" title="Unix file manipulation functions">file manipulation</a> -- Unix file manipulation functions</span><ul><li><span><span><a href="_file__Exists.html" title="whether a file exists">fileExists</a> -- whether a file exists</span></span></li>
<li><span><span><a href="_is__Regular__File.html" title="whether a file is a regular file">isRegularFile</a> -- whether a file is a regular file</span></span></li>
<li><span><span><a href="_is__Directory.html" title="whether a file is a directory">isDirectory</a> -- whether a file is a directory</span></span></li>
<li><span><span><a href="_file__Time.html" title="get or set file modified time">fileTime</a> -- get or set file modified time</span></span></li>
<li><span><span><a href="_copy__File_lp__String_cm__String_rp.html" title="">copyFile(String,String)</a></span></span></li>
<li><span><span><a href="_move__File_lp__String_cm__String_rp.html" title="">moveFile(String,String)</a></span></span></li>
<li><span><span><a href="_remove__File.html" title="remove a file">removeFile</a> -- remove a file</span></span></li>
<li><span><span><a href="_find__Files.html" title="find files recursively">findFiles</a> -- find files recursively</span></span></li>
<li><span><span><a href="_symlink__File.html" title="make a symbolic link to a file">symlinkFile</a> -- make a symbolic link to a file</span></span></li>
<li><span><span><a href="_link__File_lp__String_cm__String_rp.html" title="make a new link to a file">linkFile(String,String)</a> -- make a new link to a file</span></span></li>
<li><span><span><a href="_readlink.html" title="readlink fn">readlink</a> -- readlink fn</span></span></li>
<li><span><span><a href="_mkdir.html" title="">mkdir</a></span></span></li>
<li><span><span><a href="_make__Directory_lp__String_rp.html" title="make a directory">makeDirectory(String)</a> -- make a directory</span></span></li>
<li><span><span><a href="_copy__Directory_lp__String_cm__String_rp.html" title="">copyDirectory(String,String)</a></span></span></li>
<li><span><span><a href="_remove__Directory.html" title="remove a directory">removeDirectory</a> -- remove a directory</span></span></li>
<li><span><span><a href="_symlink__Directory_lp__String_cm__String_rp.html" title="make symbolic links for all files in a directory tree">symlinkDirectory(String,String)</a> -- make symbolic links for all files in a directory tree</span></span></li>
<li><span><span><a href="_read__Directory.html" title="read the contents of a directory">readDirectory</a> -- read the contents of a directory</span></span></li>
<li><span><span><a href="_realpath.html" title="convert a filename to one passing through no symbolic links">realpath</a> -- convert a filename to one passing through no symbolic links</span></span></li>
<li><span><span><a href="_temporary__File__Name.html" title="make a temporary file name">temporaryFileName</a> -- make a temporary file name</span></span></li>
</ul>
</span></li>
<li><span><span><a href="_communicating_spwith_spprograms.html" title="">communicating with programs</a></span></span></li>
<li><span><span><a href="_using_spsockets.html" title="">using sockets</a></span></span></li>
<li><span><span><a href="_packages.html" title="">packages</a></span><ul><li><span><span><a href="_needs__Package.html" title="load a package if not already loaded">needsPackage</a> -- load a package if not already loaded</span></span></li>
<li><span><span><a href="_load__Package.html" title="load a package">loadPackage</a> -- load a package</span></span></li>
<li><span><span><a href="_install__Package.html" title="load and install a package and its documentation ">installPackage</a> -- load and install a package and its documentation </span></span></li>
<li><span><span><a href="_loaded__Packages.html" title="the list of loaded packages">loadedPackages</a> -- the list of loaded packages</span></span></li>
<li><span><span><a href="_creating_spa_sppackage.html" title="">creating a package</a></span><ul><li><span><span><a href="_an_spexample_spof_spa_sppackage.html" title="">an example of a package</a></span></span></li>
<li><span><span><a href="_new__Package_lp__String_rp.html" title="package item: start a new package">newPackage(String)</a> -- package item: start a new package</span></span></li>
<li><span><span><a href="_export.html" title="package item: export functions">export</a> -- package item: export functions</span></span></li>
<li><span><span><a href="_export__Mutable.html" title="package item: export writable variables">exportMutable</a> -- package item: export writable variables</span></span></li>
<li><span><span><a href="_begin__Documentation.html" title="package item: start documentation section">beginDocumentation</a> -- package item: start documentation section</span></span></li>
<li><span><span><a href="_document.html" title="package item: documentation node">document</a> -- package item: documentation node</span></span></li>
<li><span><span><a href="___T__E__S__T.html" title="package item: register a test of the package">TEST</a> -- package item: register a test of the package</span></span></li>
<li><span><span><a href="_writing_spdocumentation.html" title="">writing documentation</a></span></span></li>
<li><span><span><a href="_check.html" title="perform tests of a package">check</a> -- perform tests of a package</span></span></li>
<li><span><span><a href="_informing_spothers_spabout_spyour_sppackage.html" title="">informing others about your package</a></span></span></li>
</ul>
</span></li>
<li><span><span><a href="_get__Package_lp__String_rp.html" title="download a package from the repository">getPackage(String)</a> -- download a package from the repository</span></span></li>
</ul>
</span></li>
<li><span><span><a href="_system_spfacilities.html" title="">system facilities</a></span><ul><li><span><span><a href="_autoload_lp__Symbol_cm__String_rp.html" title="arrange for a function to be loaded automatically">autoload(Symbol,String)</a> -- arrange for a function to be loaded automatically</span></span></li>
<li><span><span><a href="_initialization_spfile.html" title="">initialization file</a></span></span></li>
<li><span><span><a href="_input.html" title="read Macaulay2 commands and echo">input</a> -- read Macaulay2 commands and echo</span></span></li>
<li><span><span><a href="_load.html" title="read Macaulay2 commands">load</a> -- read Macaulay2 commands</span></span></li>
<li><span><span><a href="_needs.html" title="read Macaulay2 commands if necessary">needs</a> -- read Macaulay2 commands if necessary</span></span></li>
<li><span><span><a href="_clear__Echo.html" title="turn off echoing">clearEcho</a> -- turn off echoing</span></span></li>
<li><span><span><a href="_set__Echo.html" title="turn on echoing">setEcho</a> -- turn on echoing</span></span></li>
<li><span><span><a href="_dumpdata.html" title="dump state of the system to a file">dumpdata</a> -- dump state of the system to a file</span></span></li>
<li><span><span><a href="_loaddata.html" title="load state of the system from a file">loaddata</a> -- load state of the system from a file</span></span></li>
<li><span><span><a href="_restart.html" title="restart Macaulay2">restart</a> -- restart Macaulay2</span></span></li>
<li><span><span><a href="_add__Start__Function.html" title="add a startup function">addStartFunction</a> -- add a startup function</span></span></li>
<li><span><span><a href="_add__End__Function.html" title="add an ending function">addEndFunction</a> -- add an ending function</span></span></li>
<li><span><span><a href="_top_splevel_sploop.html" title="">top level loop</a></span></span></li>
<li><span><span><a href="_alarm.html" title="set an alarm">alarm</a> -- set an alarm</span></span></li>
<li><span><span><a href="_current__Directory.html" title="current working directory">currentDirectory</a> -- current working directory</span></span></li>
<li><span><span><a href="_exec.html" title="execute another program">exec</a> -- execute another program</span></span></li>
<li><span><span><a href="_exit.html" title="exit the program">exit</a> -- exit the program</span></span></li>
<li><span><span><a href="_fork.html" title="fork the process">fork</a> -- fork the process</span></span></li>
<li><span><span><a href="_getenv.html" title="get value of environment variable">getenv</a> -- get value of environment variable</span></span></li>
<li><span><span><a href="_process__I__D.html" title="the process identifier">processID</a> -- the process identifier</span></span></li>
<li><span><span><a href="_path.html" title="list of directories to look in">path</a> -- list of directories to look in</span></span></li>
<li><span><span><a href="_quit.html" title="quit the program">quit</a> -- quit the program</span></span></li>
<li><span><span><a href="_run.html" title="run an external command">run</a> -- run an external command</span></span></li>
<li><span><span><a href="_sleep.html" title="sleep for a while">sleep</a> -- sleep for a while</span></span></li>
<li><span><span><a href="_time.html" title="time a computation">time</a> -- time a computation</span></span></li>
<li><span><span><a href="_timing.html" title="time a computation">timing</a> -- time a computation</span></span></li>
<li><span><span><a href="_wait.html" title="wait for child process">wait</a> -- wait for child process</span></span></li>
<li><span><span><a href="_command__Line.html" title="the command line arguments">commandLine</a> -- the command line arguments</span></span></li>
<li><span><span><a href="_environment.html" title="the environment variables">environment</a> -- the environment variables</span></span></li>
<li><span><span><a href="_version.html" title="information about this version of the program">version</a> -- information about this version of the program</span></span></li>
<li><span><span><a href="_collect__Garbage.html" title="collect the garbage in memory">collectGarbage</a> -- collect the garbage in memory</span></span></li>
</ul>
</span></li>
<li><span><span><a href="_debugging.html" title="">debugging</a></span></span></li>
</ul>
</span></li>
<li><span><span><a href="_packages_spprovided_spwith_sp__Macaulay2.html" title="">packages provided with Macaulay2</a></span></span></li>
<li><span><span><a href="_changes_spto_sp__Macaulay2_cm_spby_spversion.html" title="">changes to Macaulay2, by version</a></span><ul><li><span><span><a href="_changes_cm_sp1.0_spand_sp1.1.html" title="">changes, 1.0 and 1.1</a></span></span></li>
<li><span><span><a href="_changes_cm_sp1.2.html" title="">changes, 1.2</a></span></span></li>
<li><span><span><a href="_changes_cm_sp1.3.html" title="">changes, 1.3</a></span></span></li>
<li><span><span><a href="_changes_cm_sp1.3.1.html" title="">changes, 1.3.1</a></span></span></li>
<li><span><span><a href="_list_spof_spobsolete_spfunctions.html" title="">list of obsolete functions</a></span></span></li>
</ul>
</span></li>
<li><span><span><a href="_mathematical_spexamples.html" title="">mathematical examples</a></span><ul><li><span><span><a href="___Tutorial_co_sp__Elementary_spuses_spof_sp__Groebner_spbases.html" title="">Tutorial: Elementary uses of Groebner bases</a></span></span></li>
<li><span><span><a href="___Tutorial_co_sp__Canonical_sp__Embeddings_spof_sp__Plane_sp__Curves_spand_sp__Gonality.html" title="">Tutorial: Canonical Embeddings of Plane Curves and Gonality</a></span></span></li>
<li><span><span><a href="___Tutorial_co_sp__Fano_spvarieties.html" title="">Tutorial: Fano varieties</a></span></span></li>
<li><span><span><a href="___Tutorial_co_sp__Divisors.html" title="">Tutorial: Divisors</a></span></span></li>
</ul>
</span></li>
<li><span><span><a href="_basic_spcommutative_spalgebra.html" title="">basic commutative algebra</a></span><ul><li><span><span><a href="___Elementary_spuses_spof_sp__Groebner_spbases_sp__I._sp__Math_sp634_sp__Fall_sp2005.html" title="">Elementary uses of Groebner bases I. Math 634 Fall 2005</a></span></span></li>
<li><span><span><a href="_modules_spin_sp__Macaulay2.html" title="">modules in Macaulay2</a></span></span></li>
<li><span><span><a href="___M2__Singular__Book.html" title="Macaulay2 examples for the Singular book">M2SingularBook</a> -- Macaulay2 examples for the Singular book</span><ul><li><span><span><a href="___Singular_sp__Book_sp1.1.8.html" title="computation in fields">Singular Book 1.1.8</a> -- computation in fields</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp1.1.9.html" title="computation in polynomial rings">Singular Book 1.1.9</a> -- computation in polynomial rings</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp1.1.10.html" title="methods for creating ring maps">Singular Book 1.1.10</a> -- methods for creating ring maps</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp1.2.3.html" title="leading data">Singular Book 1.2.3</a> -- leading data</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp1.2.13.html" title="monomial orderings">Singular Book 1.2.13</a> -- monomial orderings</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp1.3.3.html" title="properties of ring maps">Singular Book 1.3.3</a> -- properties of ring maps</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp1.3.13.html" title="computation in quotient rings">Singular Book 1.3.13</a> -- computation in quotient rings</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp1.3.15.html" title="computing with radicals">Singular Book 1.3.15</a> -- computing with radicals</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp1.4.9.html" title="global versus local rings">Singular Book 1.4.9</a> -- global versus local rings</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp1.5.10.html" title="realization of rings">Singular Book 1.5.10</a> -- realization of rings</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp1.6.13.html" title="normal form">Singular Book 1.6.13</a> -- normal form</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp1.7.10.html" title="standard bases">Singular Book 1.7.10</a> -- standard bases</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp1.7.12.html" title="highest corner">Singular Book 1.7.12</a> -- highest corner</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp1.8.1.html" title="ideal membership">Singular Book 1.8.1</a> -- ideal membership</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp1.8.2.html" title="linear combination of ideal members">Singular Book 1.8.2</a> -- linear combination of ideal members</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp1.8.4.html" title="elimination of variables">Singular Book 1.8.4</a> -- elimination of variables</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp1.8.6.html" title="Zariski closure of the image">Singular Book 1.8.6</a> -- Zariski closure of the image</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp1.8.7.html" title="solving equations">Singular Book 1.8.7</a> -- solving equations</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp1.8.9.html" title="radical membership">Singular Book 1.8.9</a> -- radical membership</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp1.8.11.html" title="intersection of ideals">Singular Book 1.8.11</a> -- intersection of ideals</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp1.8.13.html" title="quotient of ideals">Singular Book 1.8.13</a> -- quotient of ideals</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp1.8.15.html" title="saturation">Singular Book 1.8.15</a> -- saturation</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp1.8.18.html" title="kernel of a ring map">Singular Book 1.8.18</a> -- kernel of a ring map</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp1.8.19.html" title="algebraic dependence">Singular Book 1.8.19</a> -- algebraic dependence</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp1.8.20.html" title="subalgebra membership">Singular Book 1.8.20</a> -- subalgebra membership</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp2.1.6.html" title="matrix operations">Singular Book 2.1.6</a> -- matrix operations</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp2.1.7.html" title="maps induced by Hom">Singular Book 2.1.7</a> -- maps induced by Hom</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp2.1.10.html" title="Submodules of A^n">Singular Book 2.1.10</a> -- Submodules of A^n</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp2.1.13.html" title="kernel, image and cokernel of a module homomorphism">Singular Book 2.1.13</a> -- kernel, image and cokernel of a module homomorphism</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp2.1.20.html" title="sum, intersection, module quotient">Singular Book 2.1.20</a> -- sum, intersection, module quotient</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp2.1.24.html" title="submodules, presentation of a module">Singular Book 2.1.24</a> -- submodules, presentation of a module</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp2.1.26.html" title="computation of Hom">Singular Book 2.1.26</a> -- computation of Hom</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp2.1.34.html" title="minimal presentations, prune">Singular Book 2.1.34</a> -- minimal presentations, prune</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp2.2.15.html" title="graded rings and modules">Singular Book 2.2.15</a> -- graded rings and modules</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp2.3.10.html" title="normal form">Singular Book 2.3.10</a> -- normal form</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp2.3.12.html" title="standard bases">Singular Book 2.3.12</a> -- standard bases</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp2.4.12.html" title="resolution and Betti numbers">Singular Book 2.4.12</a> -- resolution and Betti numbers</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp2.4.15.html" title="homogeneous resolution and graded Betti numbers">Singular Book 2.4.15</a> -- homogeneous resolution and graded Betti numbers</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp2.5.5.html" title="syzygies">Singular Book 2.5.5</a> -- syzygies</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp2.5.18.html" title="Schreyer resolution">Singular Book 2.5.18</a> -- Schreyer resolution</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp2.6.3.html" title="diagonal form">Singular Book 2.6.3</a> -- diagonal form</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp2.6.11.html" title="cyclic decomposition">Singular Book 2.6.11</a> -- cyclic decomposition</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp2.6.15.html" title="Jordan normal form">Singular Book 2.6.15</a> -- Jordan normal form</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp2.7.5.html" title="tensor product of maps">Singular Book 2.7.5</a> -- tensor product of maps</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp2.7.9.html" title="tensor product of modules">Singular Book 2.7.9</a> -- tensor product of modules</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp2.7.14.html" title="tensor product of rings">Singular Book 2.7.14</a> -- tensor product of rings</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp2.8.1.html" title="module membership">Singular Book 2.8.1</a> -- module membership</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp2.8.3.html" title="elimination of module components">Singular Book 2.8.3</a> -- elimination of module components</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp2.8.5.html" title="intersection of modules">Singular Book 2.8.5</a> -- intersection of modules</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp2.8.6.html" title="quotient of modules">Singular Book 2.8.6</a> -- quotient of modules</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp2.8.7.html" title="radical, zerodivisors of modules">Singular Book 2.8.7</a> -- radical, zerodivisors of modules</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp2.8.8.html" title="annihilator and Fitting ideal">Singular Book 2.8.8</a> -- annihilator and Fitting ideal</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp2.8.9.html" title="kernel of a module homomorphism">Singular Book 2.8.9</a> -- kernel of a module homomorphism</span></span></li>
<li><span><span><a href="___Singular_sp__Book_sp2.8.10.html" title="solving linear equations">Singular Book 2.8.10</a> -- solving linear equations</span></span></li>
</ul>
</span></li>
</ul>
</span></li>
<li><span><span><a href="_replacements_spfor_spcommands_spand_spscripts_spfrom_sp__Macaulay.html" title="">replacements for commands and scripts from Macaulay</a></span></span></li>
<li><span><span><a href="_how_sp__Macaulay2_spfinds_spits_spfiles.html" title="">how Macaulay2 finds its files</a></span><ul><li><span><span><a href="_current__Layout.html" title="relative locations of Macaulay2 files">currentLayout</a> -- relative locations of Macaulay2 files</span></span></li>
<li><span><span><a href="_prefix__Directory.html" title="the prefix directory">prefixDirectory</a> -- the prefix directory</span></span></li>
</ul>
</span></li>
<li><span><span><a href="___Type.html" title="the class of all types">Type</a> -- the class of all types</span></span></li>
<li><span><span><a href="___Function.html" title="the class of all functions">Function</a> -- the class of all functions</span></span></li>
</ul>
</span></li>
<li><span><span><a href="__dq.html" title="delineate a string with quotation marks">"</a> -- delineate a string with quotation marks</span></span></li>
<li><span><span><a href="__sh_sp__Hash__Table.html" title="length"># HashTable</a> -- length</span></span></li>
<li><span><span><a href="__sh_sp__Set.html" title="cardinality"># Set</a> -- cardinality</span></span></li>
<li><span><span><a href="__sh_sp__String.html" title="length"># String</a> -- length</span></span></li>
<li><span><span><a href="_-_sp__List.html" title="negation of a vector">- List</a> -- negation of a vector</span></span></li>
<li><span><span><a href="_--.html" title="comment">--</a> -- comment</span></span></li>
<li><span><span><a href="__gt_sp__Z__Z.html" title="greater than">> ZZ</a> -- greater than</span></span></li>
<li><span><span><a href="__gt_eq_sp__Z__Z.html" title="greater than or equal">>= ZZ</a> -- greater than or equal</span></span></li>
<li><span><span><a href="_^_st.html" title="a unary postfix operator, used for indicating pullback maps">^*</a> -- a unary postfix operator, used for indicating pullback maps</span></span></li>
<li><span><span><a href="__us_st.html" title="a unary postfix operator, used for indicating pushforward maps">_*</a> -- a unary postfix operator, used for indicating pushforward maps</span></span></li>
<li><span><span><a href="_abs.html" title="absolute value function">abs</a> -- absolute value function</span></span></li>
<li><span><span><a href="___Absolute__Links.html" title="name for an optional argument">AbsoluteLinks</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_accumulate.html" title="apply binary operator repeatedly">accumulate</a> -- apply binary operator repeatedly</span></span></li>
<li><span><span><a href="_accumulate_lp__Function_cm__Thing_cm__Visible__List_rp.html" title="">accumulate(Function,Thing,VisibleList)</a></span></span></li>
<li><span><span><a href="_accumulate_lp__Function_cm__Visible__List_rp.html" title="">accumulate(Function,VisibleList)</a></span></span></li>
<li><span><span><a href="_accumulate_lp__Visible__List_cm__Function_rp.html" title="">accumulate(VisibleList,Function)</a></span></span></li>
<li><span><span><a href="_accumulate_lp__Visible__List_cm__Thing_cm__Function_rp.html" title="">accumulate(VisibleList,Thing,Function)</a></span></span></li>
<li><span><span><a href="_acos.html" title="arccosine">acos</a> -- arccosine</span></span></li>
<li><span><span><a href="_acosh.html" title="inverse hyperbolic cosine">acosh</a> -- inverse hyperbolic cosine</span></span></li>
<li><span><span><a href="_acot.html" title="compute the inverse cotangent">acot</a> -- compute the inverse cotangent</span></span></li>
<li><span><span><a href="_add__Hook.html" title="add a hook function to an object for later processing">addHook</a> -- add a hook function to an object for later processing</span></span></li>
<li><span><span><a href="_add__Hook_lp__Hash__Table_cm__Thing_cm__Function_rp.html" title="add a hook function to an object for later processing">addHook(HashTable,Thing,Function)</a> -- add a hook function to an object for later processing</span></span></li>
<li><span><span><a href="_add__Hook_lp__Symbol_cm__Function_rp.html" title="add a hook function to an object for later processing">addHook(Symbol,Function)</a> -- add a hook function to an object for later processing</span></span></li>
<li><span><span><a href="___Adjacent.html" title="the class of all adjacent expression pairs">Adjacent</a> -- the class of all adjacent expression pairs</span></span></li>
<li><span><span><a href="_adjoint_lp__Matrix_cm__Module_cm__Module_rp.html" title="an adjoint map">adjoint(Matrix,Module,Module)</a> -- an adjoint map</span></span></li>
<li><span><span><a href="_adjoint1_lp__Matrix_cm__Module_cm__Module_rp.html" title="an adjoint map">adjoint1(Matrix,Module,Module)</a> -- an adjoint map</span></span></li>
<li><span><span><a href="___Affine__Variety.html" title="the class of all affine varieties">AffineVariety</a> -- the class of all affine varieties</span></span></li>
<li><span><span><a href="___Affine__Variety_sp_st_st_sp__Ring.html" title="a binary operator, usually used for tensor product or Cartesian product">AffineVariety ** Ring</a> -- a binary operator, usually used for tensor product or Cartesian product</span></span></li>
<li><span><span><a href="___After__Eval.html" title="top level method applied after evaluation">AfterEval</a> -- top level method applied after evaluation</span></span></li>
<li><span><span><a href="___After__No__Print.html" title="top level method applied after not printing">AfterNoPrint</a> -- top level method applied after not printing</span></span></li>
<li><span><span><a href="___After__Print.html" title="top level method applied after printing">AfterPrint</a> -- top level method applied after printing</span></span></li>
<li><span><span><a href="_agm.html" title="arithmetic-geometric mean">agm</a> -- arithmetic-geometric mean</span></span></li>
<li><span><span><a href="___Algorithm.html" title="name for an optional argument">Algorithm</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="___Alignment.html" title="name for an optional argument">Alignment</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_all.html" title="whether all elements satisfy a specified condition">all</a> -- whether all elements satisfy a specified condition</span></span></li>
<li><span><span><a href="_all_lp__Basic__List_cm__Basic__List_cm__Function_rp.html" title="whether all corresponding elements of a pair of lists satisfy a condition">all(BasicList,BasicList,Function)</a> -- whether all corresponding elements of a pair of lists satisfy a condition</span></span></li>
<li><span><span><a href="_all_lp__Hash__Table_cm__Function_rp.html" title="whether all key/value pairs in a hash table satisfy a specified condition">all(HashTable,Function)</a> -- whether all key/value pairs in a hash table satisfy a specified condition</span></span></li>
<li><span><span><a href="_ambient.html" title="ambient free module of a subquotient, or ambient ring">ambient</a> -- ambient free module of a subquotient, or ambient ring</span></span></li>
<li><span><span><a href="_ambient_lp__Affine__Variety_rp.html" title="">ambient(AffineVariety)</a></span></span></li>
<li><span><span><a href="_ambient_lp__Coherent__Sheaf_rp.html" title="">ambient(CoherentSheaf)</a></span></span></li>
<li><span><span><a href="_ambient_lp__Galois__Field_rp.html" title="corresponding quotient ring">ambient(GaloisField)</a> -- corresponding quotient ring</span></span></li>
<li><span><span><a href="_ambient_lp__Graded__Module_rp.html" title="">ambient(GradedModule)</a></span></span></li>
<li><span><span><a href="_ambient_lp__Matrix_rp.html" title="">ambient(Matrix)</a></span></span></li>
<li><span><span><a href="_ambient_lp__Module_rp.html" title="ambient free module">ambient(Module)</a> -- ambient free module</span></span></li>
<li><span><span><a href="_ambient_lp__Projective__Variety_rp.html" title="">ambient(ProjectiveVariety)</a></span></span></li>
<li><span><span><a href="_ambient_lp__Ring_rp.html" title="ambient polynomial ring">ambient(Ring)</a> -- ambient polynomial ring</span></span></li>
<li><span><span><a href="_ancestors.html" title="the ancestors of something">ancestors</a> -- the ancestors of something</span></span></li>
<li><span><span><a href="_annihilator.html" title="the annihilator ideal">annihilator</a> -- the annihilator ideal</span></span></li>
<li><span><span><a href="_annihilator_spof_spa_spmodule.html" title="">annihilator of a module</a></span></span></li>
<li><span><span><a href="_any.html" title="whether any elements satisfy a specified condition">any</a> -- whether any elements satisfy a specified condition</span></span></li>
<li><span><span><a href="_any_lp__Basic__List_cm__Basic__List_cm__Function_rp.html" title="whether any corresponding elements of a pair of lists satisfy a condition">any(BasicList,BasicList,Function)</a> -- whether any corresponding elements of a pair of lists satisfy a condition</span></span></li>
<li><span><span><a href="_any_lp__Hash__Table_cm__Function_rp.html" title="whether all key/value pairs in a hash table satisfy a specified condition">any(HashTable,Function)</a> -- whether all key/value pairs in a hash table satisfy a specified condition</span></span></li>
<li><span><span><a href="_append_lp__Basic__List_cm__Thing_rp.html" title="append an element to a list">append(BasicList,Thing)</a> -- append an element to a list</span></span></li>
<li><span><span><a href="_application__Directory.html" title="the path to the user's application directory">applicationDirectory</a> -- the path to the user's application directory</span></span></li>
<li><span><span><a href="_application__Directory__Suffix.html" title="suffix that determines the user's application directory">applicationDirectorySuffix</a> -- suffix that determines the user's application directory</span></span></li>
<li><span><span><a href="_apply.html" title="apply a function to each element">apply</a> -- apply a function to each element</span></span></li>
<li><span><span><a href="_apply_lp__Basic__List_cm__Basic__List_cm__Function_rp.html" title="apply a function to pairs of elements, one from each list">apply(BasicList,BasicList,Function)</a> -- apply a function to pairs of elements, one from each list</span></span></li>
<li><span><span><a href="_apply_lp__Z__Z_cm__Function_rp.html" title="apply a function to {0,..., n-1}">apply(ZZ,Function)</a> -- apply a function to {0,..., n-1}</span></span></li>
<li><span><span><a href="_apply__Table.html" title="apply a function to elements of a table">applyTable</a> -- apply a function to elements of a table</span></span></li>
<li><span><span><a href="_apropos_lp__String_rp.html" title="symbols matching a pattern">apropos(String)</a> -- symbols matching a pattern</span></span></li>
<li><span><span><a href="_argument.html" title="specify the function in a scripted functor for an argument">argument</a> -- specify the function in a scripted functor for an argument</span></span></li>
<li><span><span><a href="___Ascending.html" title="">Ascending</a></span></span></li>
<li><span><span><a href="_ascii.html" title="ASCII character conversion">ascii</a> -- ASCII character conversion</span></span></li>
<li><span><span><a href="_ascii_lp__List_rp.html" title="ASCII character conversion">ascii(List)</a> -- ASCII character conversion</span></span></li>
<li><span><span><a href="_ascii_lp__String_rp.html" title="ASCII character conversion">ascii(String)</a> -- ASCII character conversion</span></span></li>
<li><span><span><a href="_asin.html" title="arcsine">asin</a> -- arcsine</span></span></li>
<li><span><span><a href="_asinh.html" title="inverse hyperbolic sine">asinh</a> -- inverse hyperbolic sine</span></span></li>
<li><span><span><a href="_assert.html" title="assert something is true">assert</a> -- assert something is true</span></span></li>
<li><span><span><a href="_associated__Primes.html" title="find the associated primes of an ideal">associatedPrimes</a> -- find the associated primes of an ideal</span></span></li>
<li><span><span><a href="_associated__Primes_lp..._cm_sp__Strategy_sp_eq_gt_sp..._rp.html" title="">associatedPrimes(..., Strategy => ...)</a></span></span></li>
<li><span><span><a href="___Associative__Expression.html" title="the class of associative expressions">AssociativeExpression</a> -- the class of associative expressions</span></span></li>
<li><span><span><a href="_atan.html" title="compute the arctangent">atan</a> -- compute the arctangent</span></span></li>
<li><span><span><a href="_atan_lp__R__R_rp.html" title="compute the arctangent of a number ">atan(RR)</a> -- compute the arctangent of a number </span></span></li>
<li><span><span><a href="_atan2_lp__R__R_cm__R__R_rp.html" title="compute an angle of a certain triangle">atan2(RR,RR)</a> -- compute an angle of a certain triangle</span></span></li>
<li><span><span><a href="_at__End__Of__File_lp__File_rp.html" title="test for end of file">atEndOfFile(File)</a> -- test for end of file</span></span></li>
<li><span><span><a href="_backtrace.html" title="whether a backtrace is displayed following an error message">backtrace</a> -- whether a backtrace is displayed following an error message</span></span></li>
<li><span><span><a href="_backup__File__Regexp.html" title="a regular expression for recognizing names of backup files">backupFileRegexp</a> -- a regular expression for recognizing names of backup files</span></span></li>
<li><span><span><a href="___Bag.html" title="the class of all bags">Bag</a> -- the class of all bags</span></span></li>
<li><span><span><a href="___Bareiss.html" title="">Bareiss</a></span></span></li>
<li><span><span><a href="_base__Filename.html" title="the base part of a filename or path">baseFilename</a> -- the base part of a filename or path</span></span></li>
<li><span><span><a href="_base__Name.html" title="the base name of a generator">baseName</a> -- the base name of a generator</span></span></li>
<li><span><span><a href="_base__Rings.html" title="store the list of base rings of a ring">baseRings</a> -- store the list of base rings of a ring</span></span></li>
<li><span><span><a href="___Base__Row.html" title="name for an optional argument">BaseRow</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="___Basis__Element__Limit.html" title="name for an optional argument">BasisElementLimit</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="___Bayer.html" title="a Strategy option value for saturate">Bayer</a> -- a Strategy option value for saturate</span></span></li>
<li><span><span><a href="___Before__Print.html" title="top level method applied before printing results">BeforePrint</a> -- top level method applied before printing results</span></span></li>
<li><span><span><a href="_benchmark.html" title="accurate timing of execution">benchmark</a> -- accurate timing of execution</span></span></li>
<li><span><span><a href="___Bessel__J.html" title="Bessel function of the first kind">BesselJ</a> -- Bessel function of the first kind</span></span></li>
<li><span><span><a href="___Bessel__Y.html" title="Bessel function of the second kind">BesselY</a> -- Bessel function of the second kind</span></span></li>
<li><span><span><a href="_betti.html" title="display degrees">betti</a> -- display degrees</span></span></li>
<li><span><span><a href="_betti_lp..._cm_sp__Weights_sp_eq_gt_sp..._rp.html" title="">betti(..., Weights => ...)</a></span></span></li>
<li><span><span><a href="_betti_lp__Betti__Tally_rp.html" title="view and set the weights of a betti display">betti(BettiTally)</a> -- view and set the weights of a betti display</span></span></li>
<li><span><span><a href="_betti_lp__Graded__Module_rp.html" title="display of degrees in a graded module">betti(GradedModule)</a> -- display of degrees in a graded module</span></span></li>
<li><span><span><a href="_betti_lp__Groebner__Basis_rp.html" title="diagram of the degrees of a groebner basis">betti(GroebnerBasis)</a> -- diagram of the degrees of a groebner basis</span></span></li>
<li><span><span><a href="_betti_lp__Ideal_rp.html" title="gives the degrees of generators.">betti(Ideal)</a> -- gives the degrees of generators.</span></span></li>
<li><span><span><a href="_betti_lp__Matrix_rp.html" title="display of the degrees of a map">betti(Matrix)</a> -- display of the degrees of a map</span></span></li>
<li><span><span><a href="_betti_lp__Module_rp.html" title="show the degrees of the generators and relations of a module or a coherent sheaf">betti(Module)</a> -- show the degrees of the generators and relations of a module or a coherent sheaf</span></span></li>
<li><span><span><a href="___Betti__Tally.html" title="the class of all Betti tallies">BettiTally</a> -- the class of all Betti tallies</span></span></li>
<li><span><span><a href="_between_lp__Thing_cm__Visible__List_rp.html" title="insert something between elements of a list">between(Thing,VisibleList)</a> -- insert something between elements of a list</span></span></li>
<li><span><span><a href="___Binary__Operation.html" title="the class of all binary operation expressions">BinaryOperation</a> -- the class of all binary operation expressions</span></span></li>
<li><span><span><a href="___Binomial.html" title="name for an optional argument">Binomial</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_binomial.html" title="binomial coefficient">binomial</a> -- binomial coefficient</span></span></li>
<li><span><span><a href="___Boolean.html" title="the class of Boolean values">Boolean</a> -- the class of Boolean values</span></span></li>
<li><span><span><a href="_borel_lp__Matrix_rp.html" title="make a Borel fixed submodule">borel(Matrix)</a> -- make a Borel fixed submodule</span></span></li>
<li><span><span><a href="___Boxes.html" title="name for an optional argument">Boxes</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_break.html" title="break from a loop">break</a> -- break from a loop</span></span></li>
<li><span><span><a href="_cache.html" title="a key under which to store cache tables">cache</a> -- a key under which to store cache tables</span></span></li>
<li><span><span><a href="___Cache__Example__Output.html" title="name for an optional argument">CacheExampleOutput</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="___Cache__Function.html" title="the class of cache functions">CacheFunction</a> -- the class of cache functions</span></span></li>
<li><span><span><a href="___Cache__Table.html" title="hash tables for caching">CacheTable</a> -- hash tables for caching</span></span></li>
<li><span><span><a href="_cache__Value.html" title="cache values of functions in their arguments">cacheValue</a> -- cache values of functions in their arguments</span></span></li>
<li><span><span><a href="_capture_lp__String_rp.html" title="evaluate Macaulay2 code and capture the output (under development)">capture(String)</a> -- evaluate Macaulay2 code and capture the output (under development)</span></span></li>
<li><span><span><a href="___C__C.html" title="the class of all complex numbers">CC</a> -- the class of all complex numbers</span></span></li>
<li><span><span><a href="_ceiling.html" title="ceiling function">ceiling</a> -- ceiling function</span></span></li>
<li><span><span><a href="___Center.html" title="value for an optional argument">Center</a> -- value for an optional argument</span></span></li>
<li><span><span><a href="_center__String.html" title="center a string or net">centerString</a> -- center a string or net</span></span></li>
<li><span><span><a href="___Certification.html" title="name for an optional argument">Certification</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="___Chain__Complex.html" title="the class of all chain complexes">ChainComplex</a> -- the class of all chain complexes</span></span></li>
<li><span><span><a href="_chain__Complex.html" title="make a chain complex">chainComplex</a> -- make a chain complex</span></span></li>
<li><span><span><a href="___Chain__Complex_sp_st_st_sp__Chain__Complex.html" title="tensor product">ChainComplex ** ChainComplex</a> -- tensor product</span></span></li>
<li><span><span><a href="___Chain__Complex_sp_st_st_sp__Chain__Complex__Map.html" title="tensor product">ChainComplex ** ChainComplexMap</a> -- tensor product</span></span></li>
<li><span><span><a href="___Chain__Complex_sp_st_st_sp__Graded__Module.html" title="tensor product">ChainComplex ** GradedModule</a> -- tensor product</span></span></li>
<li><span><span><a href="___Chain__Complex_sp_st_st_sp__Ring.html" title="a binary operator, usually used for tensor product or Cartesian product">ChainComplex ** Ring</a> -- a binary operator, usually used for tensor product or Cartesian product</span></span></li>
<li><span><span><a href="___Chain__Complex_sp_pl_pl_sp__Chain__Complex.html" title="direct sum">ChainComplex ++ ChainComplex</a> -- direct sum</span></span></li>
<li><span><span><a href="___Chain__Complex_sp^_sp__Z__Z.html" title="access member, cohomological degree">ChainComplex ^ ZZ</a> -- access member, cohomological degree</span></span></li>
<li><span><span><a href="___Chain__Complex_sp_us_sp__Z__Z.html" title="component">ChainComplex _ ZZ</a> -- component</span></span></li>
<li><span><span><a href="___Chain__Complex_sp_us_sp__Z__Z_sp_eq_sp__Thing.html" title="install component of chain complex">ChainComplex _ ZZ = Thing</a> -- install component of chain complex</span></span></li>
<li><span><span><a href="___Chain__Complex_sp__Array.html" title="degree shift">ChainComplex Array</a> -- degree shift</span></span></li>
<li><span><span><a href="_chain__Complex_lp__Graded__Module_rp.html" title="make a chain complex from a graded module">chainComplex(GradedModule)</a> -- make a chain complex from a graded module</span></span></li>
<li><span><span><a href="_chain__Complex_lp__List_rp.html" title="make a chain complex">chainComplex(List)</a> -- make a chain complex</span></span></li>
<li><span><span><a href="_chain__Complex_lp__Matrix_rp.html" title="make a small chain complex">chainComplex(Matrix)</a> -- make a small chain complex</span></span></li>
<li><span><span><a href="_chain__Complex_lp__Ring_rp.html" title="make an empty chain complex over a ring">chainComplex(Ring)</a> -- make an empty chain complex over a ring</span></span></li>
<li><span><span><a href="___Chain__Complex__Map.html" title="the class of all maps between chain complexes">ChainComplexMap</a> -- the class of all maps between chain complexes</span></span></li>
<li><span><span><a href="___Chain__Complex__Map_sp_st_st_sp__Chain__Complex.html" title="tensor product">ChainComplexMap ** ChainComplex</a> -- tensor product</span></span></li>
<li><span><span><a href="___Chain__Complex__Map_sp_st_st_sp__Chain__Complex__Map.html" title="tensor product">ChainComplexMap ** ChainComplexMap</a> -- tensor product</span></span></li>
<li><span><span><a href="___Chain__Complex__Map_sp^_sp__Z__Z.html" title="iterated composition">ChainComplexMap ^ ZZ</a> -- iterated composition</span></span></li>
<li><span><span><a href="___Chain__Complex__Map_sp_us_sp__Z__Z.html" title="component map">ChainComplexMap _ ZZ</a> -- component map</span></span></li>
<li><span><span><a href="___Chain__Complex__Map_sp_us_sp__Z__Z_sp_eq_sp__Thing.html" title="install component of chain complex map">ChainComplexMap _ ZZ = Thing</a> -- install component of chain complex map</span></span></li>
<li><span><span><a href="___Chain__Complex__Map_sp__Array.html" title="degree shift">ChainComplexMap Array</a> -- degree shift</span></span></li>
<li><span><span><a href="___Change__Matrix.html" title="name for an optional argument">ChangeMatrix</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_char.html" title="computes the characteristic of the ring or field">char</a> -- computes the characteristic of the ring or field</span></span></li>
<li><span><span><a href="_characters.html" title="get characters from a string">characters</a> -- get characters from a string</span></span></li>
<li><span><span><a href="___Check__Documentation.html" title="name for an optional argument">CheckDocumentation</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_clean.html" title="Set to zero elements that are approximately zero">clean</a> -- Set to zero elements that are approximately zero</span></span></li>
<li><span><span><a href="_clear__All.html" title="forget everything">clearAll</a> -- forget everything</span></span></li>
<li><span><span><a href="_clear__Output.html" title="forget output values">clearOutput</a> -- forget output values</span></span></li>
<li><span><span><a href="_close.html" title="close a file">close</a> -- close a file</span></span></li>
<li><span><span><a href="_close__In.html" title="close an input file">closeIn</a> -- close an input file</span></span></li>
<li><span><span><a href="_close__Out.html" title="close an output file">closeOut</a> -- close an output file</span></span></li>
<li><span><span><a href="___Closest__Fit.html" title="name for an optional argument">ClosestFit</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_code.html" title="display source code">code</a> -- display source code</span></span></li>
<li><span><span><a href="_codim.html" title="compute the codimension">codim</a> -- compute the codimension</span></span></li>
<li><span><span><a href="_codim_lp__Coherent__Sheaf_rp.html" title="codimension of the support of a coherent sheaf on a projective variety">codim(CoherentSheaf)</a> -- codimension of the support of a coherent sheaf on a projective variety</span></span></li>
<li><span><span><a href="_codim_lp__Ideal_rp.html" title="compute the codimension">codim(Ideal)</a> -- compute the codimension</span></span></li>
<li><span><span><a href="_codim_lp__Ideal_cm_sp__Generic_sp_eq_gt_sp..._rp.html" title="">codim(Ideal, Generic => ...)</a></span></span></li>
<li><span><span><a href="_codim_lp__Module_rp.html" title="codimension of the support of a module">codim(Module)</a> -- codimension of the support of a module</span></span></li>
<li><span><span><a href="_codim_lp__Monomial__Ideal_rp.html" title="compute the codimension">codim(MonomialIdeal)</a> -- compute the codimension</span></span></li>
<li><span><span><a href="_codim_lp__Projective__Variety_rp.html" title="codimension of the projective variety">codim(ProjectiveVariety)</a> -- codimension of the projective variety</span></span></li>
<li><span><span><a href="_codim_lp__Quotient__Ring_rp.html" title="compute the codimension">codim(QuotientRing)</a> -- compute the codimension</span></span></li>
<li><span><span><a href="___Codimension__Limit.html" title="name for an optional argument">CodimensionLimit</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_coefficient.html" title="coefficient of a monomial">coefficient</a> -- coefficient of a monomial</span></span></li>
<li><span><span><a href="___Coefficient__Ring.html" title="name for an optional argument">CoefficientRing</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_coefficient__Ring.html" title="get the coefficient ring">coefficientRing</a> -- get the coefficient ring</span></span></li>
<li><span><span><a href="_coefficients.html" title="monomials and their coefficients">coefficients</a> -- monomials and their coefficients</span></span></li>
<li><span><span><a href="_coefficients_lp..._cm_sp__Monomials_sp_eq_gt_sp..._rp.html" title="specify monomials">coefficients(..., Monomials => ...)</a> -- specify monomials</span></span></li>
<li><span><span><a href="_coefficients_lp..._cm_sp__Variables_sp_eq_gt_sp..._rp.html" title="take coefficients using these variables">coefficients(..., Variables => ...)</a> -- take coefficients using these variables</span></span></li>
<li><span><span><a href="___Cofactor.html" title="">Cofactor</a></span></span></li>
<li><span><span><a href="___Coherent__Sheaf.html" title="the class of all coherent sheaves">CoherentSheaf</a> -- the class of all coherent sheaves</span></span></li>
<li><span><span><a href="___Coherent__Sheaf_sp_lp_st_rp.html" title="sum of twists">CoherentSheaf (*)</a> -- sum of twists</span></span></li>
<li><span><span><a href="___Coherent__Sheaf_sp_st_st_sp__Coherent__Sheaf.html" title="tensor produce of coherent sheaves">CoherentSheaf ** CoherentSheaf</a> -- tensor produce of coherent sheaves</span></span></li>
<li><span><span><a href="___Coherent__Sheaf_sp_pl_pl_sp__Coherent__Sheaf.html" title="direct sum of coherent sheaves">CoherentSheaf ++ CoherentSheaf</a> -- direct sum of coherent sheaves</span></span></li>
<li><span><span><a href="___Coherent__Sheaf_sp_sl_sp__Coherent__Sheaf.html" title="quotient of coherent sheaves">CoherentSheaf / CoherentSheaf</a> -- quotient of coherent sheaves</span></span></li>
<li><span><span><a href="___Coherent__Sheaf_sp^_sp__Z__Z.html" title="direct sum">CoherentSheaf ^ ZZ</a> -- direct sum</span></span></li>
<li><span><span><a href="___Coherent__Sheaf_sp^_st_st_sp__Z__Z.html" title="tensor power">CoherentSheaf ^** ZZ</a> -- tensor power</span></span></li>
<li><span><span><a href="___Coherent__Sheaf_sp__Z__Z.html" title="canonical twist of a coherent sheaf">CoherentSheaf ZZ</a> -- canonical twist of a coherent sheaf</span></span></li>
<li><span><span><a href="_cohomology.html" title="general cohomology functor">cohomology</a> -- general cohomology functor</span></span></li>
<li><span><span><a href="_cohomology_lp..._cm_sp__Degree_sp_eq_gt_sp..._rp.html" title="">cohomology(..., Degree => ...)</a></span></span></li>
<li><span><span><a href="_coimage.html" title="coimage of a map">coimage</a> -- coimage of a map</span></span></li>
<li><span><span><a href="_cokernel.html" title="cokernel of a map of modules, graded modules, or chaincomplexes">cokernel</a> -- cokernel of a map of modules, graded modules, or chaincomplexes</span></span></li>
<li><span><span><a href="_column__Add.html" title="add a multiple of one column to another">columnAdd</a> -- add a multiple of one column to another</span></span></li>
<li><span><span><a href="_columnate.html" title="arrange strings in columns">columnate</a> -- arrange strings in columns</span></span></li>
<li><span><span><a href="_column__Mult.html" title="multiply a column by a ring element">columnMult</a> -- multiply a column by a ring element</span></span></li>
<li><span><span><a href="_column__Permute.html" title="permute some columns">columnPermute</a> -- permute some columns</span></span></li>
<li><span><span><a href="_column__Swap.html" title="interchange columns">columnSwap</a> -- interchange columns</span></span></li>
<li><span><span><a href="___Command.html" title="the class of all commands">Command</a> -- the class of all commands</span></span></li>
<li><span><span><a href="_command__Interpreter.html" title="the top level command interpreter">commandInterpreter</a> -- the top level command interpreter</span></span></li>
<li><span><span><a href="_commonest.html" title="the most common elements of a list or tally">commonest</a> -- the most common elements of a list or tally</span></span></li>
<li><span><span><a href="_common__Ring.html" title="find smallest containing ring">commonRing</a> -- find smallest containing ring</span></span></li>
<li><span><span><a href="_comodule.html" title="submodule to quotient module">comodule</a> -- submodule to quotient module</span></span></li>
<li><span><span><a href="_compact__Matrix__Form.html" title="global flag for compact printing">compactMatrixForm</a> -- global flag for compact printing</span></span></li>
<li><span><span><a href="_comparison_spoperators.html" title="">comparison operators</a></span></span></li>
<li><span><span><a href="___Compiled__Function.html" title="the class of all compiled functions">CompiledFunction</a> -- the class of all compiled functions</span></span></li>
<li><span><span><a href="___Compiled__Function__Body.html" title="the class of all compiled function bodies">CompiledFunctionBody</a> -- the class of all compiled function bodies</span></span></li>
<li><span><span><a href="___Compiled__Function__Closure.html" title="the class of all compiled function closures">CompiledFunctionClosure</a> -- the class of all compiled function closures</span></span></li>
<li><span><span><a href="___Complement.html" title="">Complement</a></span></span></li>
<li><span><span><a href="_complement_lp__Matrix_rp.html" title="find the minimal generators for cokernel of a matrix (low level form)">complement(Matrix)</a> -- find the minimal generators for cokernel of a matrix (low level form)</span></span></li>
<li><span><span><a href="_complete.html" title="">complete</a></span></span></li>
<li><span><span><a href="_complete_lp__Chain__Complex_rp.html" title="complete the internal parts">complete(ChainComplex)</a> -- complete the internal parts</span></span></li>
<li><span><span><a href="___Complete__Intersection.html" title="name for an optional argument">CompleteIntersection</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="___Complex__Field.html" title="the class of all complex fields">ComplexField</a> -- the class of all complex fields</span></span></li>
<li><span><span><a href="_component_spexample.html" title="">component example</a></span></span></li>
<li><span><span><a href="_components.html" title="list the components of a direct sum">components</a> -- list the components of a direct sum</span></span></li>
<li><span><span><a href="_components_lp__Chain__Complex_rp.html" title="list the components of a direct sum">components(ChainComplex)</a> -- list the components of a direct sum</span></span></li>
<li><span><span><a href="_compositions.html" title="compositions of an integer">compositions</a> -- compositions of an integer</span></span></li>
<li><span><span><a href="_compress.html" title="extract nonzero columns from a matrix">compress</a> -- extract nonzero columns from a matrix</span></span></li>
<li><span><span><a href="_computing_spresolutions.html" title="">computing resolutions</a></span></span></li>
<li><span><span><a href="_computing_spsyzygies.html" title="">computing syzygies</a></span></span></li>
<li><span><span><a href="_cone.html" title="mapping cone of a chain map">cone</a> -- mapping cone of a chain map</span></span></li>
<li><span><span><a href="_cone_lp__Chain__Complex__Map_rp.html" title="mapping cone of a chain map">cone(ChainComplexMap)</a> -- mapping cone of a chain map</span></span></li>
<li><span><span><a href="_conjugate.html" title="complex conjugate">conjugate</a> -- complex conjugate</span></span></li>
<li><span><span><a href="_conjugate_lp__C__C_rp.html" title="complex conjugate">conjugate(CC)</a> -- complex conjugate</span></span></li>
<li><span><span><a href="_conjugate_lp__Partition_rp.html" title="conjugate a partition">conjugate(Partition)</a> -- conjugate a partition</span></span></li>
<li><span><span><a href="_connection__Count.html" title="the number of connections">connectionCount</a> -- the number of connections</span></span></li>
<li><span><span><a href="___Constant.html" title="">Constant</a></span></span></li>
<li><span><span><a href="_constructing_spmaps_spbetween_spmodules.html" title="">constructing maps between modules</a></span></span></li>
<li><span><span><a href="_content_lp__Ring__Element_rp.html" title="the content of a polynomial">content(RingElement)</a> -- the content of a polynomial</span></span></li>
<li><span><span><a href="_continue.html" title="continue with the next iteration of a loop">continue</a> -- continue with the next iteration of a loop</span></span></li>
<li><span><span><a href="_contract.html" title="contract one matrix by another">contract</a> -- contract one matrix by another</span></span></li>
<li><span><span><a href="_contract_sq_lp__Matrix_cm__Matrix_rp.html" title="contract a matrix by a matrix, the dual notion">contract'(Matrix,Matrix)</a> -- contract a matrix by a matrix, the dual notion</span></span></li>
<li><span><span><a href="_contract_lp__Matrix_cm__Matrix_rp.html" title="contract a matrix by a matrix">contract(Matrix,Matrix)</a> -- contract a matrix by a matrix</span></span></li>
<li><span><span><a href="_conventions_spfor_spdocumentation.html" title="">conventions for documentation</a></span></span></li>
<li><span><span><a href="_copy__Directory_lp..._cm_sp__Update__Only_sp_eq_gt_sp..._rp.html" title="">copyDirectory(..., UpdateOnly => ...)</a></span></span></li>
<li><span><span><a href="___C__O__P__Y__I__N__G.html" title="the Macaulay2 license agreement">COPYING</a> -- the Macaulay2 license agreement</span></span></li>
<li><span><span><a href="_copyright.html" title="a string containing the copyright notice for Macaulay2">copyright</a> -- a string containing the copyright notice for Macaulay2</span></span></li>
<li><span><span><a href="___Core.html" title="the core part of Macaulay2">Core</a> -- the core part of Macaulay2</span></span></li>
<li><span><span><a href="_cos.html" title="compute the cosine">cos</a> -- compute the cosine</span></span></li>
<li><span><span><a href="_cosh.html" title="compute the hyperbolic cosine">cosh</a> -- compute the hyperbolic cosine</span></span></li>
<li><span><span><a href="_cot.html" title="cotangent">cot</a> -- cotangent</span></span></li>
<li><span><span><a href="_cotangent__Sheaf.html" title="cotangent sheaf of a projective variety">cotangentSheaf</a> -- cotangent sheaf of a projective variety</span></span></li>
<li><span><span><a href="_cotangent__Sheaf_lp__Projective__Variety_rp.html" title="cotangent sheaf of a projective variety">cotangentSheaf(ProjectiveVariety)</a> -- cotangent sheaf of a projective variety</span></span></li>
<li><span><span><a href="_cotangent__Sheaf_lp__Z__Z_cm__Projective__Variety_rp.html" title="exterior powers of the cotangent sheaf of a projective variety">cotangentSheaf(ZZ,ProjectiveVariety)</a> -- exterior powers of the cotangent sheaf of a projective variety</span></span></li>
<li><span><span><a href="_coth.html" title="hyperbolic cotangent">coth</a> -- hyperbolic cotangent</span></span></li>
<li><span><span><a href="_cover.html" title="get the covering free module">cover</a> -- get the covering free module</span></span></li>
<li><span><span><a href="_cover_lp__Matrix_rp.html" title="get the covering free module">cover(Matrix)</a> -- get the covering free module</span></span></li>
<li><span><span><a href="_cover_lp__Module_rp.html" title="get the covering free module">cover(Module)</a> -- get the covering free module</span></span></li>
<li><span><span><a href="_cover__Map_lp__Module_rp.html" title="the surjective map from a free module to a module corresponding to the generators">coverMap(Module)</a> -- the surjective map from a free module to a module corresponding to the generators</span></span></li>
<li><span><span><a href="_cpu__Time.html" title="seconds of cpu time used since Macaulay2 began">cpuTime</a> -- seconds of cpu time used since Macaulay2 began</span></span></li>
<li><span><span><a href="_csc.html" title="cosecant">csc</a> -- cosecant</span></span></li>
<li><span><span><a href="_csch.html" title="hyperbolic cosecant">csch</a> -- hyperbolic cosecant</span></span></li>
<li><span><span><a href="_current.html" title="the pseudocode that produced an error">current</a> -- the pseudocode that produced an error</span></span></li>
<li><span><span><a href="_current__File__Directory.html" title="the directory containing the current input file">currentFileDirectory</a> -- the directory containing the current input file</span></span></li>
<li><span><span><a href="_current__File__Name.html" title="the current source file">currentFileName</a> -- the current source file</span></span></li>
<li><span><span><a href="_current__Line__Number.html" title="current line number of the current input file">currentLineNumber</a> -- current line number of the current input file</span></span></li>
<li><span><span><a href="_current__Package.html" title="the current package">currentPackage</a> -- the current package</span></span></li>
<li><span><span><a href="_current__Time.html" title="get the current time">currentTime</a> -- get the current time</span></span></li>
<li><span><span><a href="___Database.html" title="the class of all database files">Database</a> -- the class of all database files</span></span></li>
<li><span><span><a href="___Database_sp_sh_sp__String.html" title="get value from database">Database # String</a> -- get value from database</span></span></li>
<li><span><span><a href="___Database_sp_sh_qu_sp__String.html" title="check for value in database">Database #? String</a> -- check for value in database</span></span></li>
<li><span><span><a href="_dd.html" title="differential in a chain complex">dd</a> -- differential in a chain complex</span></span></li>
<li><span><span><a href="_debug.html" title="open private dictionary of a package">debug</a> -- open private dictionary of a package</span></span></li>
<li><span><span><a href="_debug__Error.html" title="a function to debug">debugError</a> -- a function to debug</span></span></li>
<li><span><span><a href="___Debugging__Mode.html" title="name for an optional argument">DebuggingMode</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_debugging__Mode.html" title="whether to enter the debugger when an error occurs">debuggingMode</a> -- whether to enter the debugger when an error occurs</span></span></li>
<li><span><span><a href="_debug__Level.html" title="current level debugging">debugLevel</a> -- current level debugging</span></span></li>
<li><span><span><a href="___Decompose.html" title="name for an optional argument">Decompose</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_deep__Splice.html" title="remove subsequences">deepSplice</a> -- remove subsequences</span></span></li>
<li><span><span><a href="_default.html" title="default member of a family">default</a> -- default member of a family</span></span></li>
<li><span><span><a href="_default__Precision.html" title="default precision of numbers">defaultPrecision</a> -- default precision of numbers</span></span></li>
<li><span><span><a href="___Degree.html" title="">Degree</a></span></span></li>
<li><span><span><a href="_degree.html" title="">degree</a></span></span></li>
<li><span><span><a href="_degree_lp__Ideal_rp.html" title="">degree(Ideal)</a></span></span></li>
<li><span><span><a href="_degree_lp__Matrix_rp.html" title="">degree(Matrix)</a></span></span></li>
<li><span><span><a href="_degree_lp__Module_rp.html" title="">degree(Module)</a></span></span></li>
<li><span><span><a href="_degree_lp__Projective__Hilbert__Polynomial_rp.html" title="">degree(ProjectiveHilbertPolynomial)</a></span></span></li>
<li><span><span><a href="_degree_lp__Projective__Variety_rp.html" title="">degree(ProjectiveVariety)</a></span></span></li>
<li><span><span><a href="_degree_lp__Ring_rp.html" title="">degree(Ring)</a></span></span></li>
<li><span><span><a href="_degree_lp__Ring__Element_rp.html" title="">degree(RingElement)</a></span></span></li>
<li><span><span><a href="_degree_lp__Ring__Element_cm__Ring__Element_rp.html" title="degree with respect to a variable">degree(RingElement,RingElement)</a> -- degree with respect to a variable</span></span></li>
<li><span><span><a href="_degree__Length.html" title="the number of degrees">degreeLength</a> -- the number of degrees</span></span></li>
<li><span><span><a href="___Degree__Lift.html" title="name for an optional argument">DegreeLift</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="___Degree__Limit.html" title="name for an optional argument">DegreeLimit</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="___Degree__Map.html" title="name for an optional argument">DegreeMap</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="___Degree__Order.html" title="sort primarily by degree">DegreeOrder</a> -- sort primarily by degree</span></span></li>
<li><span><span><a href="___Degree__Rank.html" title="name for an optional argument">DegreeRank</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="___Degrees.html" title="name for an optional argument">Degrees</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_degrees.html" title="degrees of generators">degrees</a> -- degrees of generators</span></span></li>
<li><span><span><a href="_degrees_lp__Matrix_rp.html" title="degrees of target and source">degrees(Matrix)</a> -- degrees of target and source</span></span></li>
<li><span><span><a href="_degrees_lp__Ring_rp.html" title="degrees of generators">degrees(Ring)</a> -- degrees of generators</span></span></li>
<li><span><span><a href="_degrees__Monoid.html" title="get the monoid of degrees">degreesMonoid</a> -- get the monoid of degrees</span></span></li>
<li><span><span><a href="_degrees__Ring.html" title="the ring of degrees">degreesRing</a> -- the ring of degrees</span></span></li>
<li><span><span><a href="_degrees__Ring_lp__List_rp.html" title="the ring of degrees">degreesRing(List)</a> -- the ring of degrees</span></span></li>
<li><span><span><a href="_degrees__Ring_lp__Ring_rp.html" title="the ring of degrees">degreesRing(Ring)</a> -- the ring of degrees</span></span></li>
<li><span><span><a href="_demark.html" title="insert a string between elements of a list of strings">demark</a> -- insert a string between elements of a list of strings</span></span></li>
<li><span><span><a href="_denominator.html" title="denominator of a fraction">denominator</a> -- denominator of a fraction</span></span></li>
<li><span><span><a href="___Dense.html" title="name for an optional argument">Dense</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="___Density.html" title="name for an optional argument">Density</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_depth.html" title="depth of a net">depth</a> -- depth of a net</span></span></li>
<li><span><span><a href="___Descending.html" title="specify descending order">Descending</a> -- specify descending order</span></span></li>
<li><span><span><a href="___Descent.html" title="">Descent</a></span></span></li>
<li><span><span><a href="_describe.html" title="real description">describe</a> -- real description</span></span></li>
<li><span><span><a href="___Description.html" title="name for an optional argument">Description</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_determinant.html" title="determinant of a matrix">determinant</a> -- determinant of a matrix</span></span></li>
<li><span><span><a href="_determinant_lp..._cm_sp__Strategy_sp_eq_gt_sp..._rp.html" title="choose between Bareiss and Cofactor algorithms">determinant(..., Strategy => ...)</a> -- choose between Bareiss and Cofactor algorithms</span></span></li>
<li><span><span><a href="___Developer_sqs_sp__Corner.html" title="">Developer's Corner</a></span><ul><li><span><span><a href="_engine.html" title="">engine</a></span></span></li>
</ul>
</span></li>
<li><span><span><a href="_diagonal__Matrix.html" title="make a diagonal matrix">diagonalMatrix</a> -- make a diagonal matrix</span></span></li>
<li><span><span><a href="_diagonal__Matrix_lp__Matrix_rp.html" title="make a diagonal matrix from entries of a matrix">diagonalMatrix(Matrix)</a> -- make a diagonal matrix from entries of a matrix</span></span></li>
<li><span><span><a href="_diagonal__Matrix_lp__Ring_cm__Z__Z_cm__Z__Z_cm__List_rp.html" title="make a diagonal matrix from a list">diagonalMatrix(Ring,ZZ,ZZ,List)</a> -- make a diagonal matrix from a list</span></span></li>
<li><span><span><a href="___Dictionary.html" title="the class of all dictionaries">Dictionary</a> -- the class of all dictionaries</span></span></li>
<li><span><span><a href="_dictionary.html" title="determine the dictionary to which a symbol belongs">dictionary</a> -- determine the dictionary to which a symbol belongs</span></span></li>
<li><span><span><a href="_dictionary__Path.html" title="">dictionaryPath</a></span></span></li>
<li><span><span><a href="_diff.html" title="differentiate or take difference">diff</a> -- differentiate or take difference</span><ul><li><span><span><a href="_diff_lp__Ring__Element_cm__Ring__Element_rp.html" title="differentiation">diff(RingElement,RingElement)</a> -- differentiation</span></span></li>
<li><span><span><a href="_diff_lp__Ring__Element_cm__Matrix_rp.html" title="differentiate each entry of a matrix">diff(RingElement,Matrix)</a> -- differentiate each entry of a matrix</span></span></li>
<li><span><span><a href="_diff_lp__Matrix_cm__Ring__Element_rp.html" title="differentiation">diff(Matrix,RingElement)</a> -- differentiation</span></span></li>
<li><span><span><a href="_diff_lp__Matrix_cm__Matrix_rp.html" title="differentiate a matrix by a matrix">diff(Matrix,Matrix)</a> -- differentiate a matrix by a matrix</span></span></li>
<li><span><span><a href="_diff_lp__Projective__Hilbert__Polynomial_rp.html" title="">diff(ProjectiveHilbertPolynomial)</a></span></span></li>
<li><span><span><a href="_diff_lp__Projective__Hilbert__Polynomial_cm__Z__Z_rp.html" title="">diff(ProjectiveHilbertPolynomial,ZZ)</a></span></span></li>
</ul>
</span></li>
<li><span><span><a href="_diff_spand_spcontract.html" title="">diff and contract</a></span></span></li>
<li><span><span><a href="_diff_sq_lp__Matrix_cm__Matrix_rp.html" title="differentiate a matrix by a matrix, the dual notion">diff'(Matrix,Matrix)</a> -- differentiate a matrix by a matrix, the dual notion</span></span></li>
<li><span><span><a href="_difference.html" title="difference">difference</a> -- difference</span></span></li>
<li><span><span><a href="_dim.html" title="compute the Krull dimension">dim</a> -- compute the Krull dimension</span></span></li>
<li><span><span><a href="_dim_lp__Affine__Variety_rp.html" title="dimension of the affine variety">dim(AffineVariety)</a> -- dimension of the affine variety</span></span></li>
<li><span><span><a href="_dim_lp__Ideal_rp.html" title="compute the Krull dimension">dim(Ideal)</a> -- compute the Krull dimension</span></span></li>
<li><span><span><a href="_dim_lp__Module_rp.html" title="compute the Krull dimension">dim(Module)</a> -- compute the Krull dimension</span></span></li>
<li><span><span><a href="_dim_lp__Projective__Hilbert__Polynomial_rp.html" title="the degree of the Hilbert polynomial">dim(ProjectiveHilbertPolynomial)</a> -- the degree of the Hilbert polynomial</span></span></li>
<li><span><span><a href="_dim_lp__Projective__Variety_rp.html" title="dimension of the projective variety">dim(ProjectiveVariety)</a> -- dimension of the projective variety</span></span></li>
<li><span><span><a href="_dim_lp__Ring_rp.html" title="compute the Krull dimension">dim(Ring)</a> -- compute the Krull dimension</span></span></li>
<li><span><span><a href="_direct__Sum.html" title="direct sum of modules or maps">directSum</a> -- direct sum of modules or maps</span></span></li>
<li><span><span><a href="_disassemble.html" title="disassemble pseudocode or a function">disassemble</a> -- disassemble pseudocode or a function</span></span></li>
<li><span><span><a href="_dismiss.html" title="dismiss a package">dismiss</a> -- dismiss a package</span></span></li>
<li><span><span><a href="___Divide.html" title="the class of all divide expressions">Divide</a> -- the class of all divide expressions</span></span></li>
<li><span><span><a href="_divide__By__Variable.html" title="divide all columns by a (power of a) variable">divideByVariable</a> -- divide all columns by a (power of a) variable</span></span></li>
<li><span><span><a href="___Divide__Conquer.html" title="name for an optional argument">DivideConquer</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_division_spin_sppolynomial_springs_spwith_spmonomials_spless_spthan_sp1.html" title="">division in polynomial rings with monomials less than 1</a></span></span></li>
<li><span><span><a href="_do.html" title="loop control">do</a> -- loop control</span></span></li>
<li><span><span><a href="_document_lp..._cm_sp__Base__Function_sp_eq_gt_sp..._rp.html" title="function for a documented feature">document(..., BaseFunction => ...)</a> -- function for a documented feature</span></span></li>
<li><span><span><a href="_document_lp..._cm_sp__Caveat_sp_eq_gt_sp..._rp.html" title="warnings">document(..., Caveat => ...)</a> -- warnings</span></span></li>
<li><span><span><a href="_document_lp..._cm_sp__Consequences_sp_eq_gt_sp..._rp.html" title="side-effects of a function">document(..., Consequences => ...)</a> -- side-effects of a function</span></span></li>
<li><span><span><a href="_document_lp..._cm_sp__Inputs_sp_eq_gt_sp..._rp.html" title="inputs for a function">document(..., Inputs => ...)</a> -- inputs for a function</span></span></li>
<li><span><span><a href="_document_lp..._cm_sp__Key_sp_eq_gt_sp..._rp.html" title="key of a documentation node">document(..., Key => ...)</a> -- key of a documentation node</span></span></li>
<li><span><span><a href="_document_lp..._cm_sp__Outputs_sp_eq_gt_sp..._rp.html" title="outputs for a function">document(..., Outputs => ...)</a> -- outputs for a function</span></span></li>
<li><span><span><a href="_document_lp..._cm_sp__See__Also_sp_eq_gt_sp..._rp.html" title="crossreferences in documentation">document(..., SeeAlso => ...)</a> -- crossreferences in documentation</span></span></li>
<li><span><span><a href="_document_lp..._cm_sp__Subnodes_sp_eq_gt_sp..._rp.html" title="a menu of documentation nodes">document(..., Subnodes => ...)</a> -- a menu of documentation nodes</span></span></li>
<li><span><span><a href="_documentation_spkeys.html" title="">documentation keys</a></span></span></li>
<li><span><span><a href="___Document__Tag.html" title="the class of all document tags">DocumentTag</a> -- the class of all document tags</span></span></li>
<li><span><span><a href="_drop_lp__Basic__List_cm__List_rp.html" title="">drop(BasicList,List)</a></span></span></li>
<li><span><span><a href="_drop_lp__Basic__List_cm__Z__Z_rp.html" title="">drop(BasicList,ZZ)</a></span></span></li>
<li><span><span><a href="_dual.html" title="dual module or map">dual</a> -- dual module or map</span></span></li>
<li><span><span><a href="_dual_lp__Chain__Complex_rp.html" title="dual">dual(ChainComplex)</a> -- dual</span></span></li>
<li><span><span><a href="_dual_lp__Chain__Complex__Map_rp.html" title="dual of a chain complex">dual(ChainComplexMap)</a> -- dual of a chain complex</span></span></li>
<li><span><span><a href="_dual_lp__Coherent__Sheaf_rp.html" title="dual coherent sheaf">dual(CoherentSheaf)</a> -- dual coherent sheaf</span></span></li>
<li><span><span><a href="_dual_lp__Matrix_rp.html" title="dual of a map">dual(Matrix)</a> -- dual of a map</span></span></li>
<li><span><span><a href="_dual_lp__Module_rp.html" title="dual module">dual(Module)</a> -- dual module</span></span></li>
<li><span><span><a href="_dual_lp__Monomial__Ideal_rp.html" title="the Alexander dual of a monomial ideal">dual(MonomialIdeal)</a> -- the Alexander dual of a monomial ideal</span></span></li>
<li><span><span><a href="_dual_lp__Monomial__Ideal_cm_sp__Strategy_sp_eq_gt_sp..._rp.html" title="">dual(MonomialIdeal, Strategy => ...)</a></span></span></li>
<li><span><span><a href="_dual_lp__Monomial__Ideal_cm__List_rp.html" title="the Alexander dual">dual(MonomialIdeal,List)</a> -- the Alexander dual</span></span></li>
<li><span><span><a href="_dual_lp__Monomial__Ideal_cm__Ring__Element_rp.html" title="the Alexander dual">dual(MonomialIdeal,RingElement)</a> -- the Alexander dual</span></span></li>
<li><span><span><a href="_eagon__Northcott_lp__Matrix_rp.html" title="Eagon-Northcott complex of a matrix of linear forms">eagonNorthcott(Matrix)</a> -- Eagon-Northcott complex of a matrix of linear forms</span></span></li>
<li><span><span><a href="_echo__Off.html" title="turn off echoing">echoOff</a> -- turn off echoing</span></span></li>
<li><span><span><a href="_echo__On.html" title="turn on echoing">echoOn</a> -- turn on echoing</span></span></li>
<li><span><span><a href="_edit.html" title="edit source code">edit</a> -- edit source code</span></span></li>
<li><span><span><a href="_eigenvalues.html" title="find eigenvalues of a matrix">eigenvalues</a> -- find eigenvalues of a matrix</span></span></li>
<li><span><span><a href="_eigenvalues_lp..._cm_sp__Hermitian_sp_eq_gt_sp..._rp.html" title="Hermitian=>true means assume the matrix is symmetric or Hermitian">eigenvalues(..., Hermitian => ...)</a> -- Hermitian=>true means assume the matrix is symmetric or Hermitian</span></span></li>
<li><span><span><a href="_eigenvectors.html" title="find eigenvectors of a matrix over RR or CC">eigenvectors</a> -- find eigenvectors of a matrix over RR or CC</span></span></li>
<li><span><span><a href="_eigenvectors_lp..._cm_sp__Hermitian_sp_eq_gt_sp..._rp.html" title="Hermitian=>true means assume the matrix is symmetric or Hermitian">eigenvectors(..., Hermitian => ...)</a> -- Hermitian=>true means assume the matrix is symmetric or Hermitian</span></span></li>
<li><span><span><a href="_eint.html" title="exponential integral">eint</a> -- exponential integral</span></span></li>
<li><span><span><a href="_elements.html" title="list of elements">elements</a> -- list of elements</span></span></li>
<li><span><span><a href="_else.html" title="condition testing">else</a> -- condition testing</span></span></li>
<li><span><span><a href="_encap__Directory.html" title="encapsulated installation directory">encapDirectory</a> -- encapsulated installation directory</span></span></li>
<li><span><span><a href="___Encapsulate.html" title="name for an optional argument">Encapsulate</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="___Encapsulate__Directory.html" title="name for an optional argument">EncapsulateDirectory</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="___End.html" title="module of endomorphisms">End</a> -- module of endomorphisms</span></span></li>
<li><span><span><a href="_end.html" title="stop loading a file">end</a> -- stop loading a file</span></span></li>
<li><span><span><a href="_endl.html" title="end an output line">endl</a> -- end an output line</span></span></li>
<li><span><span><a href="_end__Package_lp__String_rp.html" title="end a new package">endPackage(String)</a> -- end a new package</span></span></li>
<li><span><span><a href="___Engine.html" title="specify whether a ring is handled by the engine">Engine</a> -- specify whether a ring is handled by the engine</span></span></li>
<li><span><span><a href="_engine__Debug__Level.html" title="current engine debugging level">engineDebugLevel</a> -- current engine debugging level</span></span></li>
<li><span><span><a href="___Engine__Ring.html" title="the class of rings handled by the engine">EngineRing</a> -- the class of rings handled by the engine</span></span></li>
<li><span><span><a href="_entries.html" title="lists the entries of a matrix">entries</a> -- lists the entries of a matrix</span></span></li>
<li><span><span><a href="_entries_lp__Vector_rp.html" title="lists the entries of a vector">entries(Vector)</a> -- lists the entries of a vector</span></span></li>
<li><span><span><a href="_epkg.html" title="">epkg</a></span></span></li>
<li><span><span><a href="_equality_spand_spcontainment_spof_spmodules.html" title="">equality and containment of modules</a></span></span></li>
<li><span><span><a href="___Equation.html" title="the class of all equation expressions">Equation</a> -- the class of all equation expressions</span></span></li>
<li><span><span><a href="_erase.html" title="remove a global symbol">erase</a> -- remove a global symbol</span></span></li>
<li><span><span><a href="_erf.html" title="error function">erf</a> -- error function</span></span></li>
<li><span><span><a href="_erfc.html" title="complementary error function">erfc</a> -- complementary error function</span></span></li>
<li><span><span><a href="_error__Depth.html" title="set the error printing depth">errorDepth</a> -- set the error printing depth</span></span></li>
<li><span><span><a href="_euler.html" title="Euler characteristic">euler</a> -- Euler characteristic</span></span></li>
<li><span><span><a href="_euler_lp__Coherent__Sheaf_rp.html" title="Euler characteristic of coherent sheaf">euler(CoherentSheaf)</a> -- Euler characteristic of coherent sheaf</span></span></li>
<li><span><span><a href="_euler_lp__Ideal_rp.html" title="Euler characteristic">euler(Ideal)</a> -- Euler characteristic</span></span></li>
<li><span><span><a href="_euler_lp__Module_rp.html" title="Euler characteristic">euler(Module)</a> -- Euler characteristic</span></span></li>
<li><span><span><a href="_euler_lp__Projective__Hilbert__Polynomial_rp.html" title="constant term of the Hilbert polynomial">euler(ProjectiveHilbertPolynomial)</a> -- constant term of the Hilbert polynomial</span></span></li>
<li><span><span><a href="_euler_lp__Projective__Variety_rp.html" title="topological Euler characteristic of a (smooth) projective variety">euler(ProjectiveVariety)</a> -- topological Euler characteristic of a (smooth) projective variety</span></span></li>
<li><span><span><a href="_euler_lp__Ring_rp.html" title="Euler characteristic">euler(Ring)</a> -- Euler characteristic</span></span></li>
<li><span><span><a href="___Euler__Constant.html" title="the Euler-Mascheroni constant">EulerConstant</a> -- the Euler-Mascheroni constant</span></span></li>
<li><span><span><a href="_eulers.html" title="list the sectional Euler characteristics">eulers</a> -- list the sectional Euler characteristics</span></span></li>
<li><span><span><a href="_eulers_lp__Coherent__Sheaf_rp.html" title="list the sectional Euler characteristics">eulers(CoherentSheaf)</a> -- list the sectional Euler characteristics</span></span></li>
<li><span><span><a href="_eulers_lp__Ideal_rp.html" title="list the sectional Euler characteristics">eulers(Ideal)</a> -- list the sectional Euler characteristics</span></span></li>
<li><span><span><a href="_eulers_lp__Ring_rp.html" title="list the sectional Euler characteristics">eulers(Ring)</a> -- list the sectional Euler characteristics</span></span></li>
<li><span><span><a href="_even.html" title="tell whether an integer is even">even</a> -- tell whether an integer is even</span></span></li>
<li><span><span><a href="___E__X__A__M__P__L__E.html" title="hypertext EXAMPLE item">EXAMPLE</a> -- hypertext EXAMPLE item</span></span></li>
<li><span><span><a href="_examples.html" title="list the examples in documentation">examples</a> -- list the examples in documentation</span></span></li>
<li><span><span><a href="___Exclude.html" title="name for an optional argument">Exclude</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_exp.html" title="exponential function">exp</a> -- exponential function</span></span></li>
<li><span><span><a href="_expm1.html" title="exponential minus 1">expm1</a> -- exponential minus 1</span></span></li>
<li><span><span><a href="_exponents.html" title="list the exponents in a polynomial">exponents</a> -- list the exponents in a polynomial</span></span></li>
<li><span><span><a href="___Expression.html" title="the class of all expressions">Expression</a> -- the class of all expressions</span></span></li>
<li><span><span><a href="_expression.html" title="convert to an expression">expression</a> -- convert to an expression</span></span></li>
<li><span><span><a href="___Ext.html" title="compute an Ext module">Ext</a> -- compute an Ext module</span></span></li>
<li><span><span><a href="___Ext_lp__Module_cm__Module_rp.html" title="total Ext module">Ext(Module,Module)</a> -- total Ext module</span></span></li>
<li><span><span><a href="___Ext^__Z__Z_lp__Coherent__Sheaf_cm__Coherent__Sheaf_rp.html" title="global Ext">Ext^ZZ(CoherentSheaf,CoherentSheaf)</a> -- global Ext</span></span></li>
<li><span><span><a href="___Ext^__Z__Z_lp__Coherent__Sheaf_cm__Sum__Of__Twists_rp.html" title="global Ext">Ext^ZZ(CoherentSheaf,SumOfTwists)</a> -- global Ext</span></span></li>
<li><span><span><a href="___Ext^__Z__Z_lp__Matrix_cm__Module_rp.html" title="map between Ext modules">Ext^ZZ(Matrix,Module)</a> -- map between Ext modules</span></span></li>
<li><span><span><a href="___Ext^__Z__Z_lp__Module_cm__Matrix_rp.html" title="map between Ext modules">Ext^ZZ(Module,Matrix)</a> -- map between Ext modules</span></span></li>
<li><span><span><a href="___Ext^__Z__Z_lp__Module_cm__Module_rp.html" title="Ext module">Ext^ZZ(Module,Module)</a> -- Ext module</span></span></li>
<li><span><span><a href="_extend.html" title="extend a module map to a chain map, if possible">extend</a> -- extend a module map to a chain map, if possible</span></span></li>
<li><span><span><a href="_extend_lp__Chain__Complex_cm__Chain__Complex_cm__Matrix_rp.html" title="extend a module map to a chain map, if possible">extend(ChainComplex,ChainComplex,Matrix)</a> -- extend a module map to a chain map, if possible</span></span></li>
<li><span><span><a href="_exterior__Power.html" title="exterior power">exteriorPower</a> -- exterior power</span></span></li>
<li><span><span><a href="_exterior__Power_lp..._cm_sp__Strategy_sp_eq_gt_sp..._rp.html" title="choose between Bareiss and Cofactor algorithms">exteriorPower(..., Strategy => ...)</a> -- choose between Bareiss and Cofactor algorithms</span></span></li>
<li><span><span><a href="_exterior__Power_lp__Z__Z_cm__Coherent__Sheaf_rp.html" title="exterior power">exteriorPower(ZZ,CoherentSheaf)</a> -- exterior power</span></span></li>
<li><span><span><a href="_exterior__Power_lp__Z__Z_cm__Matrix_rp.html" title="exterior power of a matrix">exteriorPower(ZZ,Matrix)</a> -- exterior power of a matrix</span></span></li>
<li><span><span><a href="_exterior__Power_lp__Z__Z_cm__Module_rp.html" title="exterior power of a module">exteriorPower(ZZ,Module)</a> -- exterior power of a module</span></span></li>
<li><span><span><a href="_extracting_spelements.html" title="">extracting elements</a></span></span></li>
<li><span><span><a href="_factor.html" title="factor a ring element or a ZZ-module">factor</a> -- factor a ring element or a ZZ-module</span></span></li>
<li><span><span><a href="_factor_lp__Module_rp.html" title="factor a ZZ-module">factor(Module)</a> -- factor a ZZ-module</span></span></li>
<li><span><span><a href="_factor_lp__Ring__Element_rp.html" title="factor a ring element">factor(RingElement)</a> -- factor a ring element</span></span></li>
<li><span><span><a href="_false.html" title="">false</a></span></span></li>
<li><span><span><a href="___Fano.html" title="Fano scheme">Fano</a> -- Fano scheme</span></span></li>
<li><span><span><a href="___Fano_lp__Z__Z_cm__Ideal_rp.html" title="Fano scheme">Fano(ZZ,Ideal)</a> -- Fano scheme</span></span></li>
<li><span><span><a href="___Fano_lp__Z__Z_cm__Ideal_cm__Ring_rp.html" title="Fano scheme">Fano(ZZ,Ideal,Ring)</a> -- Fano scheme</span></span></li>
<li><span><span><a href="___File.html" title="the class of all files">File</a> -- the class of all files</span></span></li>
<li><span><span><a href="___File_sp_lt_lt_sp__Thing.html" title="print to a file">File << Thing</a> -- print to a file</span></span></li>
<li><span><span><a href="_file__Dictionaries.html" title="local dictionaries for loaded files">fileDictionaries</a> -- local dictionaries for loaded files</span></span></li>
<li><span><span><a href="_file__Exit__Hooks.html" title="a list of hooks (functions) to execute when the current file has been loaded">fileExitHooks</a> -- a list of hooks (functions) to execute when the current file has been loaded</span></span></li>
<li><span><span><a href="_file__Length.html" title="the length of a file">fileLength</a> -- the length of a file</span></span></li>
<li><span><span><a href="_file__Mode.html" title="set or get file mode">fileMode</a> -- set or get file mode</span></span></li>
<li><span><span><a href="_file__Mode_lp__File_rp.html" title="get file mode">fileMode(File)</a> -- get file mode</span></span></li>
<li><span><span><a href="_file__Mode_lp__String_rp.html" title="get file mode">fileMode(String)</a> -- get file mode</span></span></li>
<li><span><span><a href="_file__Mode_lp__Z__Z_cm__File_rp.html" title="set file mode">fileMode(ZZ,File)</a> -- set file mode</span></span></li>
<li><span><span><a href="_file__Mode_lp__Z__Z_cm__String_rp.html" title="set file mode">fileMode(ZZ,String)</a> -- set file mode</span></span></li>
<li><span><span><a href="___File__Name.html" title="name for an optional argument">FileName</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="___File__Position.html" title="the class of all file positions">FilePosition</a> -- the class of all file positions</span></span></li>
<li><span><span><a href="_fill__Matrix.html" title="fill a mutable matrix with random numbers">fillMatrix</a> -- fill a mutable matrix with random numbers</span></span></li>
<li><span><span><a href="_finding_spyour_spfiles_spunder_spcygwin.html" title="">finding your files under cygwin</a></span></span></li>
<li><span><span><a href="___Find__One.html" title="find a primitive element">FindOne</a> -- find a primitive element</span></span></li>
<li><span><span><a href="_find__Synonyms_lp__Symbol_rp.html" title="find synonyms of symbols">findSynonyms(Symbol)</a> -- find synonyms of symbols</span></span></li>
<li><span><span><a href="_fine_spcontrol_spof_spa_sp__Groebner_spbasis_spcomputation.html" title="">fine control of a Groebner basis computation</a></span></span></li>
<li><span><span><a href="___First.html" title="name for an optional argument">First</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_firstkey.html" title="get the first key">firstkey</a> -- get the first key</span></span></li>
<li><span><span><a href="_fitting__Ideal.html" title="Fitting ideal of a module">fittingIdeal</a> -- Fitting ideal of a module</span></span></li>
<li><span><span><a href="_flag__Lookup.html" title="flag a symbol">flagLookup</a> -- flag a symbol</span></span></li>
<li><span><span><a href="___Flat__Monoid.html" title="">FlatMonoid</a></span></span></li>
<li><span><span><a href="_flatten_lp__Matrix_rp.html" title="puts the columns of a matrix into a single row">flatten(Matrix)</a> -- puts the columns of a matrix into a single row</span></span></li>
<li><span><span><a href="_flatten__Ring.html" title="write a ring as a (quotient) of a polynomial ring over ZZ or a prime field">flattenRing</a> -- write a ring as a (quotient) of a polynomial ring over ZZ or a prime field</span></span></li>
<li><span><span><a href="_flip_lp__Module_cm__Module_rp.html" title="matrix of commutativity of tensor product">flip(Module,Module)</a> -- matrix of commutativity of tensor product</span></span></li>
<li><span><span><a href="_floor.html" title="floor function">floor</a> -- floor function</span></span></li>
<li><span><span><a href="_flush.html" title="flush output to file">flush</a> -- flush output to file</span></span></li>
<li><span><span><a href="_fold_lp__Function_cm__Thing_cm__Visible__List_rp.html" title="">fold(Function,Thing,VisibleList)</a></span></span></li>
<li><span><span><a href="_fold_lp__Function_cm__Visible__List_rp.html" title="">fold(Function,VisibleList)</a></span></span></li>
<li><span><span><a href="_fold_lp__Visible__List_cm__Function_rp.html" title="">fold(VisibleList,Function)</a></span></span></li>
<li><span><span><a href="_fold_lp__Visible__List_cm__Thing_cm__Function_rp.html" title="">fold(VisibleList,Thing,Function)</a></span></span></li>
<li><span><span><a href="___Follow__Links.html" title="name for an optional argument">FollowLinks</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_force__G__B.html" title="declare that the columns of a matrix are a Gröbner basis">forceGB</a> -- declare that the columns of a matrix are a Gröbner basis</span></span></li>
<li><span><span><a href="_force__G__B_lp..._cm_sp__Change__Matrix_sp_eq_gt_sp..._rp.html" title="inform Macaulay2 about the change of basis matrix from GB to generators">forceGB(..., ChangeMatrix => ...)</a> -- inform Macaulay2 about the change of basis matrix from GB to generators</span></span></li>
<li><span><span><a href="_force__G__B_lp..._cm_sp__Minimal__Matrix_sp_eq_gt_sp..._rp.html" title="specify the minimal generator matrix">forceGB(..., MinimalMatrix => ...)</a> -- specify the minimal generator matrix</span></span></li>
<li><span><span><a href="_force__G__B_lp..._cm_sp__Syzygy__Matrix_sp_eq_gt_sp..._rp.html" title="specify the syzygy matrix">forceGB(..., SyzygyMatrix => ...)</a> -- specify the syzygy matrix</span></span></li>
<li><span><span><a href="___Forest__Node.html" title="a type of basic list used to represent a forest, i.e., a list of rooted trees">ForestNode</a> -- a type of basic list used to represent a forest, i.e., a list of rooted trees</span></span></li>
<li><span><span><a href="___Format.html" title="name for an optional argument">Format</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_frac.html" title="construct a fraction field">frac</a> -- construct a fraction field</span></span></li>
<li><span><span><a href="_fraction.html" title="">fraction</a></span></span></li>
<li><span><span><a href="___Fraction__Field.html" title="the class of all fraction fields">FractionField</a> -- the class of all fraction fields</span></span></li>
<li><span><span><a href="_frames.html" title="get the frames associated to a closure">frames</a> -- get the frames associated to a closure</span></span></li>
<li><span><span><a href="_from.html" title="loop control">from</a> -- loop control</span></span></li>
<li><span><span><a href="_from__Dual.html" title="ideal from inverse system">fromDual</a> -- ideal from inverse system</span></span></li>
<li><span><span><a href="___Function_sp_at_at_sp__Function.html" title="composition of functions">Function @@ Function</a> -- composition of functions</span></span></li>
<li><span><span><a href="___Function_sp_us_sp__Thing.html" title="attach the first argument to a function of two or more arguments">Function _ Thing</a> -- attach the first argument to a function of two or more arguments</span></span></li>
<li><span><span><a href="_function_spdocumentation_sptemplate.html" title="">function documentation template</a></span></span></li>
<li><span><span><a href="_function_spname_spdocumentation_sptemplate.html" title="">function name documentation template</a></span></span></li>
<li><span><span><a href="___Function_sp__Thing.html" title="function application">Function Thing</a> -- function application</span></span></li>
<li><span><span><a href="___Function__Application.html" title="the class of all function application expressions">FunctionApplication</a> -- the class of all function application expressions</span></span></li>
<li><span><span><a href="___Function__Body.html" title="the class of function bodies">FunctionBody</a> -- the class of function bodies</span></span></li>
<li><span><span><a href="_function__Body.html" title="get the body of a function">functionBody</a> -- get the body of a function</span></span></li>
<li><span><span><a href="___Function__Closure.html" title="the class of all function closures">FunctionClosure</a> -- the class of all function closures</span></span></li>
<li><span><span><a href="___Galois__Field.html" title="the class of all Galois fields">GaloisField</a> -- the class of all Galois fields</span></span></li>
<li><span><span><a href="___Gamma.html" title="Gamma function">Gamma</a> -- Gamma function</span></span></li>
<li><span><span><a href="_gb.html" title="compute a Gröbner basis">gb</a> -- compute a Gröbner basis</span></span></li>
<li><span><span><a href="___G__B__Degrees.html" title="name for an optional argument">GBDegrees</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_gb__Remove.html" title="remove Gröbner basis">gbRemove</a> -- remove Gröbner basis</span></span></li>
<li><span><span><a href="_gb__Snapshot.html" title="the Gröbner basis matrix as so far computed">gbSnapshot</a> -- the Gröbner basis matrix as so far computed</span></span></li>
<li><span><span><a href="_gb__Trace.html" title="provide tracing output during various computations in the engine.">gbTrace</a> -- provide tracing output during various computations in the engine.</span></span></li>
<li><span><span><a href="___G__C_sperror_spmessages.html" title="">GC error messages</a></span></span></li>
<li><span><span><a href="_gcd.html" title="greatest common divisor">gcd</a> -- greatest common divisor</span></span></li>
<li><span><span><a href="_gcd__Coefficients.html" title="gcd with coefficients">gcdCoefficients</a> -- gcd with coefficients</span></span></li>
<li><span><span><a href="_genera.html" title="list of the successive linear sectional arithmetic genera">genera</a> -- list of the successive linear sectional arithmetic genera</span></span></li>
<li><span><span><a href="_genera_lp__Coherent__Sheaf_rp.html" title="list of the successive linear sectional arithmetic genera">genera(CoherentSheaf)</a> -- list of the successive linear sectional arithmetic genera</span></span></li>
<li><span><span><a href="_genera_lp__Ideal_rp.html" title="list of the successive linear sectional arithmetic genera">genera(Ideal)</a> -- list of the successive linear sectional arithmetic genera</span></span></li>
<li><span><span><a href="_genera_lp__Projective__Variety_rp.html" title="list of the successive linear sectional arithmetic genera">genera(ProjectiveVariety)</a> -- list of the successive linear sectional arithmetic genera</span></span></li>
<li><span><span><a href="_genera_lp__Ring_rp.html" title="list of the successive linear sectional arithmetic genera">genera(Ring)</a> -- list of the successive linear sectional arithmetic genera</span></span></li>
<li><span><span><a href="___General__Ordered__Monoid.html" title="the class of all ordered free commutative monoids">GeneralOrderedMonoid</a> -- the class of all ordered free commutative monoids</span></span></li>
<li><span><span><a href="_generate__Assertions.html" title="generate assert statements from experimental input">generateAssertions</a> -- generate assert statements from experimental input</span></span></li>
<li><span><span><a href="_generator.html" title="provide a single generator">generator</a> -- provide a single generator</span></span></li>
<li><span><span><a href="_generators.html" title="provide matrix or list of generators">generators</a> -- provide matrix or list of generators</span></span></li>
<li><span><span><a href="_generators_spof_spideals_spand_spmodules.html" title="">generators of ideals and modules</a></span></span></li>
<li><span><span><a href="_generators_lp__General__Ordered__Monoid_rp.html" title="list of generators">generators(GeneralOrderedMonoid)</a> -- list of generators</span></span></li>
<li><span><span><a href="_generators_lp__Groebner__Basis_rp.html" title="the generator matrix of a Gröbner basis">generators(GroebnerBasis)</a> -- the generator matrix of a Gröbner basis</span></span></li>
<li><span><span><a href="_generators_lp__Ideal_rp.html" title="the generator matrix of an ideal">generators(Ideal)</a> -- the generator matrix of an ideal</span></span></li>
<li><span><span><a href="_generators_lp__Module_rp.html" title="the generator matrix of a module">generators(Module)</a> -- the generator matrix of a module</span></span></li>
<li><span><span><a href="_generators_lp__Ring_rp.html" title="the list of generators of a ring">generators(Ring)</a> -- the list of generators of a ring</span></span></li>
<li><span><span><a href="___Generic.html" title="name for an optional argument">Generic</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_generic__Matrix.html" title="make a generic matrix of variables">genericMatrix</a> -- make a generic matrix of variables</span></span></li>
<li><span><span><a href="_generic__Skew__Matrix.html" title="make a generic skew symmetric matrix of variables">genericSkewMatrix</a> -- make a generic skew symmetric matrix of variables</span></span></li>
<li><span><span><a href="_generic__Symmetric__Matrix.html" title="make a generic symmetric matrix">genericSymmetricMatrix</a> -- make a generic symmetric matrix</span></span></li>
<li><span><span><a href="_genus.html" title="arithmetic genus">genus</a> -- arithmetic genus</span></span></li>
<li><span><span><a href="_genus_lp__Coherent__Sheaf_rp.html" title="arithmetic genus">genus(CoherentSheaf)</a> -- arithmetic genus</span></span></li>
<li><span><span><a href="_genus_lp__Projective__Variety_rp.html" title="arithmetic genus">genus(ProjectiveVariety)</a> -- arithmetic genus</span></span></li>
<li><span><span><a href="_genus_lp__Ring_rp.html" title="arithmetic genus">genus(Ring)</a> -- arithmetic genus</span></span></li>
<li><span><span><a href="_get.html" title="get the contents of a file">get</a> -- get the contents of a file</span></span></li>
<li><span><span><a href="_getc.html" title="get a byte">getc</a> -- get a byte</span></span></li>
<li><span><span><a href="_get__Change__Matrix.html" title="get the change of basis matrix">getChangeMatrix</a> -- get the change of basis matrix</span></span></li>
<li><span><span><a href="_get__Global__Symbol.html" title="create a global symbol in a global dictionary">getGlobalSymbol</a> -- create a global symbol in a global dictionary</span></span></li>
<li><span><span><a href="_get__Net__File.html" title="get the sequence of completed lines (nets) from a net file">getNetFile</a> -- get the sequence of completed lines (nets) from a net file</span></span></li>
<li><span><span><a href="_get__Non__Unit.html" title="retrieve a previously discovered non-unit">getNonUnit</a> -- retrieve a previously discovered non-unit</span></span></li>
<li><span><span><a href="_get__Symbol.html" title="make a global symbol from a string">getSymbol</a> -- make a global symbol from a string</span></span></li>
<li><span><span><a href="_get__W__W__W.html" title="get a web page">getWWW</a> -- get a web page</span></span></li>
<li><span><span><a href="___G__F.html" title="make a finite field">GF</a> -- make a finite field</span></span></li>
<li><span><span><a href="_global.html" title="get a global symbol">global</a> -- get a global symbol</span></span></li>
<li><span><span><a href="_global__Assign.html" title="global assignment, in function form">globalAssign</a> -- global assignment, in function form</span></span></li>
<li><span><span><a href="_global__Assign__Function.html" title="the standard method for the global assignment hook">globalAssignFunction</a> -- the standard method for the global assignment hook</span></span></li>
<li><span><span><a href="___Global__Assign__Hook.html" title="hook for assignment to global variables">GlobalAssignHook</a> -- hook for assignment to global variables</span></span></li>
<li><span><span><a href="_global__Assignment.html" title="install standard global assignment method">globalAssignment</a> -- install standard global assignment method</span></span></li>
<li><span><span><a href="_global__Assignment__Hooks.html" title="assignment hooks for global symbols">globalAssignmentHooks</a> -- assignment hooks for global symbols</span></span></li>
<li><span><span><a href="___Global__Dictionary.html" title="the class of all global dictionaries">GlobalDictionary</a> -- the class of all global dictionaries</span></span></li>
<li><span><span><a href="_global__Release__Function.html" title="the standard method for the global variable release hook">globalReleaseFunction</a> -- the standard method for the global variable release hook</span></span></li>
<li><span><span><a href="___Global__Release__Hook.html" title="">GlobalReleaseHook</a></span></span></li>
<li><span><span><a href="_graded_spmodules.html" title="">graded modules</a></span></span></li>
<li><span><span><a href="___Graded__Module.html" title="the class of all graded modules">GradedModule</a> -- the class of all graded modules</span></span></li>
<li><span><span><a href="_graded__Module.html" title="make a graded module">gradedModule</a> -- make a graded module</span></span></li>
<li><span><span><a href="___Graded__Module_sp_st_st_sp__Chain__Complex.html" title="tensor product">GradedModule ** ChainComplex</a> -- tensor product</span></span></li>
<li><span><span><a href="___Graded__Module_sp_st_st_sp__Graded__Module.html" title="a binary operator, usually used for tensor product or Cartesian product">GradedModule ** GradedModule</a> -- a binary operator, usually used for tensor product or Cartesian product</span></span></li>
<li><span><span><a href="___Graded__Module_sp_st_st_sp__Module.html" title="a binary operator, usually used for tensor product or Cartesian product">GradedModule ** Module</a> -- a binary operator, usually used for tensor product or Cartesian product</span></span></li>
<li><span><span><a href="___Graded__Module_sp__Array.html" title="degree shift">GradedModule Array</a> -- degree shift</span></span></li>
<li><span><span><a href="___Graded__Module__Map.html" title="the class of all maps between graded modules">GradedModuleMap</a> -- the class of all maps between graded modules</span></span></li>
<li><span><span><a href="_graded__Module__Map.html" title="make a map of graded modules">gradedModuleMap</a> -- make a map of graded modules</span></span></li>
<li><span><span><a href="___Graded__Module__Map_sp_vb_sp__Graded__Module__Map.html" title="a binary operator, often used for horizontal concatenation">GradedModuleMap | GradedModuleMap</a> -- a binary operator, often used for horizontal concatenation</span></span></li>
<li><span><span><a href="___Graded__Module__Map_sp_vb_vb_sp__Graded__Module__Map.html" title="a binary operator, often used for vertical concatenation">GradedModuleMap || GradedModuleMap</a> -- a binary operator, often used for vertical concatenation</span></span></li>
<li><span><span><a href="___Grassmannian_lp__Z__Z_cm__Z__Z_rp.html" title="the Grassmannian of linear subspaces of a vector space">Grassmannian(ZZ,ZZ)</a> -- the Grassmannian of linear subspaces of a vector space</span></span></li>
<li><span><span><a href="___Groebner__Basis.html" title="the class of all Gröbner bases">GroebnerBasis</a> -- the class of all Gröbner bases</span></span></li>
<li><span><span><a href="_groebner__Basis.html" title="Gröbner basis, as a matrix">groebnerBasis</a> -- Gröbner basis, as a matrix</span></span></li>
<li><span><span><a href="___Groebner__Basis__Options.html" title="">GroebnerBasisOptions</a></span></span></li>
<li><span><span><a href="_group__I__D.html" title="the process group identifier">groupID</a> -- the process group identifier</span></span></li>
<li><span><span><a href="_handle__Interrupts.html" title="">handleInterrupts</a></span></span></li>
<li><span><span><a href="_handling_sphypertext.html" title="">handling hypertext</a></span></span></li>
<li><span><span><a href="___Hard__Degree__Limit.html" title="compute only up to this degree">HardDegreeLimit</a> -- compute only up to this degree</span></span></li>
<li><span><span><a href="_hash.html" title="hash code of an object">hash</a> -- hash code of an object</span></span></li>
<li><span><span><a href="___Hash__Table_sp_sh_sp__Thing.html" title="get value from hash table">HashTable # Thing</a> -- get value from hash table</span></span></li>
<li><span><span><a href="___Hash__Table_sp_sh_qu_sp__Thing.html" title="check for value in hash table">HashTable #? Thing</a> -- check for value in hash table</span></span></li>
<li><span><span><a href="___Header__Type.html" title="a class of lists with abbreviated constructors">HeaderType</a> -- a class of lists with abbreviated constructors</span></span></li>
<li><span><span><a href="___Heading.html" title="name for an optional argument">Heading</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="___Headline.html" title="make a headline for a documentation node">Headline</a> -- make a headline for a documentation node</span></span></li>
<li><span><span><a href="___Heft.html" title="name for an optional argument">Heft</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_heft.html" title="heft vector of ring, module, graded module, or resolution">heft</a> -- heft vector of ring, module, graded module, or resolution</span></span></li>
<li><span><span><a href="_heft_spvectors.html" title="">heft vectors</a></span></span></li>
<li><span><span><a href="___Height.html" title="name for an optional argument">Height</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_height.html" title="height of a net">height</a> -- height of a net</span></span></li>
<li><span><span><a href="_height_lp__File_rp.html" title="get window height">height(File)</a> -- get window height</span></span></li>
<li><span><span><a href="_help.html" title="help command">help</a> -- help command</span></span></li>
<li><span><span><a href="___Hermitian.html" title="name for an optional argument">Hermitian</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="___H__H.html" title="general homology and cohomology functor">HH</a> -- general homology and cohomology functor</span></span></li>
<li><span><span><a href="_hh.html" title="Hodge numbers of a smooth projective variety">hh</a> -- Hodge numbers of a smooth projective variety</span></span></li>
<li><span><span><a href="___H__H_sp__Chain__Complex.html" title="homology of a chain complex">HH ChainComplex</a> -- homology of a chain complex</span></span></li>
<li><span><span><a href="___H__H_sp__Chain__Complex__Map.html" title="homology of a chain complex map">HH ChainComplexMap</a> -- homology of a chain complex map</span></span></li>
<li><span><span><a href="___H__H^__Z__Z_sp__Chain__Complex.html" title="cohomology of a chain complex">HH^ZZ ChainComplex</a> -- cohomology of a chain complex</span></span></li>
<li><span><span><a href="___H__H^__Z__Z_sp__Chain__Complex__Map.html" title="cohomology of a chain complex map">HH^ZZ ChainComplexMap</a> -- cohomology of a chain complex map</span></span></li>
<li><span><span><a href="___H__H^__Z__Z_sp__Coherent__Sheaf.html" title="cohomology of a coherent sheaf on a projective variety">HH^ZZ CoherentSheaf</a> -- cohomology of a coherent sheaf on a projective variety</span></span></li>
<li><span><span><a href="___H__H^__Z__Z_sp__Module.html" title="local cohomology of a module">HH^ZZ Module</a> -- local cohomology of a module</span></span></li>
<li><span><span><a href="___H__H^__Z__Z_sp__Sheaf__Of__Rings.html" title="cohomology of a sheaf of rings on a projective variety">HH^ZZ SheafOfRings</a> -- cohomology of a sheaf of rings on a projective variety</span></span></li>
<li><span><span><a href="___H__H^__Z__Z_sp__Sum__Of__Twists.html" title="coherent sheaf cohomology module">HH^ZZ SumOfTwists</a> -- coherent sheaf cohomology module</span></span></li>
<li><span><span><a href="___H__H_us__Z__Z_sp__Chain__Complex.html" title="homology of a chain complex">HH_ZZ ChainComplex</a> -- homology of a chain complex</span></span></li>
<li><span><span><a href="___H__H_us__Z__Z_sp__Chain__Complex__Map.html" title="homology of a chain complex map">HH_ZZ ChainComplexMap</a> -- homology of a chain complex map</span></span></li>
<li><span><span><a href="___H__H_us__Z__Z_sp__Sequence.html" title="">HH_ZZ Sequence</a></span></span></li>
<li><span><span><a href="___Hilbert.html" title="name for an optional argument">Hilbert</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_hilbert__Function.html" title="the Hilbert function">hilbertFunction</a> -- the Hilbert function</span></span></li>
<li><span><span><a href="_hilbert__Polynomial.html" title="compute the Hilbert polynomial">hilbertPolynomial</a> -- compute the Hilbert polynomial</span></span></li>
<li><span><span><a href="_hilbert__Polynomial_lp..._cm_sp__Projective_sp_eq_gt_sp..._rp.html" title="choose how to display the Hilbert polynomial">hilbertPolynomial(..., Projective => ...)</a> -- choose how to display the Hilbert polynomial</span></span></li>
<li><span><span><a href="_hilbert__Polynomial_lp__Coherent__Sheaf_rp.html" title="compute the Hilbert polynomial of the coherent sheaf">hilbertPolynomial(CoherentSheaf)</a> -- compute the Hilbert polynomial of the coherent sheaf</span></span></li>
<li><span><span><a href="_hilbert__Polynomial_lp__Ideal_rp.html" title="compute the Hilbert polynomial of the quotient of the ambient ring by the ideal">hilbertPolynomial(Ideal)</a> -- compute the Hilbert polynomial of the quotient of the ambient ring by the ideal</span></span></li>
<li><span><span><a href="_hilbert__Polynomial_lp__Module_rp.html" title="compute the Hilbert polynomial of the module">hilbertPolynomial(Module)</a> -- compute the Hilbert polynomial of the module</span></span></li>
<li><span><span><a href="_hilbert__Polynomial_lp__Projective__Variety_rp.html" title="compute the Hilbert polynomial of the projective variety">hilbertPolynomial(ProjectiveVariety)</a> -- compute the Hilbert polynomial of the projective variety</span></span></li>
<li><span><span><a href="_hilbert__Polynomial_lp__Ring_rp.html" title="compute the Hilbert polynomial of the ring">hilbertPolynomial(Ring)</a> -- compute the Hilbert polynomial of the ring</span></span></li>
<li><span><span><a href="_hilbert__Series.html" title="compute the Hilbert series">hilbertSeries</a> -- compute the Hilbert series</span></span></li>
<li><span><span><a href="_hilbert__Series_lp..._cm_sp__Order_sp_eq_gt_sp..._rp.html" title="display the truncated power series expansion">hilbertSeries(..., Order => ...)</a> -- display the truncated power series expansion</span></span></li>
<li><span><span><a href="_hilbert__Series_lp..._cm_sp__Reduce_sp_eq_gt_sp..._rp.html" title="reduce the Hilbert series">hilbertSeries(..., Reduce => ...)</a> -- reduce the Hilbert series</span></span></li>
<li><span><span><a href="_hilbert__Series_lp__Ideal_rp.html" title="compute the Hilbert series of the quotient of the ambient ring by the ideal">hilbertSeries(Ideal)</a> -- compute the Hilbert series of the quotient of the ambient ring by the ideal</span></span></li>
<li><span><span><a href="_hilbert__Series_lp__Module_rp.html" title="compute the Hilbert series of the module">hilbertSeries(Module)</a> -- compute the Hilbert series of the module</span></span></li>
<li><span><span><a href="_hilbert__Series_lp__Polynomial__Ring_rp.html" title="compute the Hilbert series of a ring">hilbertSeries(PolynomialRing)</a> -- compute the Hilbert series of a ring</span></span></li>
<li><span><span><a href="_hilbert__Series_lp__Projective__Hilbert__Polynomial_rp.html" title="compute the Hilbert series of a projective Hilbert polynomial">hilbertSeries(ProjectiveHilbertPolynomial)</a> -- compute the Hilbert series of a projective Hilbert polynomial</span></span></li>
<li><span><span><a href="_hilbert__Series_lp__Projective__Variety_rp.html" title="compute the Hilbert series of a projective variety">hilbertSeries(ProjectiveVariety)</a> -- compute the Hilbert series of a projective variety</span></span></li>
<li><span><span><a href="_hold.html" title="hold something in a holder expression">hold</a> -- hold something in a holder expression</span></span></li>
<li><span><span><a href="___Holder.html" title="the class of all holder expressions">Holder</a> -- the class of all holder expressions</span></span></li>
<li><span><span><a href="___Hom.html" title="module of homomorphisms">Hom</a> -- module of homomorphisms</span></span></li>
<li><span><span><a href="___Hom_lp__Coherent__Sheaf_cm__Coherent__Sheaf_rp.html" title="global Hom">Hom(CoherentSheaf,CoherentSheaf)</a> -- global Hom</span></span></li>
<li><span><span><a href="___Hom_lp__Matrix_cm__Module_rp.html" title="induced map on Hom modules">Hom(Matrix,Module)</a> -- induced map on Hom modules</span></span></li>
<li><span><span><a href="___Hom_lp__Module_cm__Chain__Complex_rp.html" title="">Hom(Module,ChainComplex)</a></span></span></li>
<li><span><span><a href="___Hom_lp__Module_cm__Module_rp.html" title="module of homomorphisms">Hom(Module,Module)</a> -- module of homomorphisms</span></span></li>
<li><span><span><a href="_home__Directory.html" title="the home directory of the user">homeDirectory</a> -- the home directory of the user</span></span></li>
<li><span><span><a href="___Homogeneous.html" title="">Homogeneous</a></span></span></li>
<li><span><span><a href="_homogenize.html" title="homogenize with respect to a variable">homogenize</a> -- homogenize with respect to a variable</span></span></li>
<li><span><span><a href="_homology.html" title="general homology functor">homology</a> -- general homology functor</span></span></li>
<li><span><span><a href="_homology_lp__Matrix_cm__Matrix_rp.html" title="homology of a pair of maps">homology(Matrix,Matrix)</a> -- homology of a pair of maps</span></span></li>
<li><span><span><a href="_homomorphism.html" title="get the homomorphism from element of Hom">homomorphism</a> -- get the homomorphism from element of Hom</span></span></li>
<li><span><span><a href="_homomorphisms_sp_lpmaps_rp_spbetween_spmodules.html" title="including elements of modules">homomorphisms (maps) between modules</a> -- including elements of modules</span></span></li>
<li><span><span><a href="___Horizontal__Space.html" title="name for an optional argument">HorizontalSpace</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_html.html" title="convert hypertext to html format">html</a> -- convert hypertext to html format</span></span></li>
<li><span><span><a href="_http__Headers_lp__String_rp.html" title="prepend http headers to a string">httpHeaders(String)</a> -- prepend http headers to a string</span></span></li>
<li><span><span><a href="_hypertext.html" title="prepare hypertext for display">hypertext</a> -- prepare hypertext for display</span></span></li>
<li><span><span><a href="_hypertext_splist_spformat.html" title="">hypertext list format</a></span></span></li>
<li><span><span><a href="_id.html" title="identity map">id</a> -- identity map</span></span></li>
<li><span><span><a href="___Ideal.html" title="the class of all ideals">Ideal</a> -- the class of all ideals</span></span></li>
<li><span><span><a href="_ideal.html" title="make an ideal">ideal</a> -- make an ideal</span></span></li>
<li><span><span><a href="___Ideal_sp_st_sp__Ideal.html" title="product of ideals">Ideal * Ideal</a> -- product of ideals</span></span></li>
<li><span><span><a href="___Ideal_sp_pl_sp__Ideal.html" title="sum of ideals">Ideal + Ideal</a> -- sum of ideals</span></span></li>
<li><span><span><a href="___Ideal_sp_sl_sp__Function.html" title="apply a function to generators of an ideal">Ideal / Function</a> -- apply a function to generators of an ideal</span></span></li>
<li><span><span><a href="___Ideal_sp_sl_sp__Ideal.html" title="quotient module">Ideal / Ideal</a> -- quotient module</span></span></li>
<li><span><span><a href="___Ideal_sp^_sp__Z__Z.html" title="power">Ideal ^ ZZ</a> -- power</span></span></li>
<li><span><span><a href="___Ideal_sp_us_st.html" title="get the list of generators of an ideal">Ideal _*</a> -- get the list of generators of an ideal</span></span></li>
<li><span><span><a href="_ideal_lp__List_rp.html" title="make an ideal">ideal(List)</a> -- make an ideal</span></span></li>
<li><span><span><a href="_ideal_lp__Matrix_rp.html" title="make an ideal">ideal(Matrix)</a> -- make an ideal</span></span></li>
<li><span><span><a href="_ideal_lp__Module_rp.html" title="converts a module to an ideal">ideal(Module)</a> -- converts a module to an ideal</span></span></li>
<li><span><span><a href="_ideal_lp__Monomial__Ideal_rp.html" title="converts a monomial ideal to an ideal">ideal(MonomialIdeal)</a> -- converts a monomial ideal to an ideal</span></span></li>
<li><span><span><a href="_ideal_lp__Ring_rp.html" title="returns the defining ideal">ideal(Ring)</a> -- returns the defining ideal</span></span></li>
<li><span><span><a href="_ideal_lp__Ring__Element_rp.html" title="make an ideal">ideal(RingElement)</a> -- make an ideal</span></span></li>
<li><span><span><a href="_ideal_lp__Variety_rp.html" title="returns the defining ideal">ideal(Variety)</a> -- returns the defining ideal</span></span></li>
<li><span><span><a href="_identity.html" title="the identity function">identity</a> -- the identity function</span></span></li>
<li><span><span><a href="_if.html" title="condition testing">if</a> -- condition testing</span></span></li>
<li><span><span><a href="___Ignore__Example__Errors.html" title="name for an optional argument">IgnoreExampleErrors</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_ii.html" title="the square root of -1">ii</a> -- the square root of -1</span></span></li>
<li><span><span><a href="_image.html" title="image of a map">image</a> -- image of a map</span></span></li>
<li><span><span><a href="_imaginary__Part.html" title="imaginary part">imaginaryPart</a> -- imaginary part</span></span></li>
<li><span><span><a href="___Immutable__Type.html" title="the class of immutable types">ImmutableType</a> -- the class of immutable types</span></span></li>
<li><span><span><a href="_in.html" title="a keyword used in for-loops">in</a> -- a keyword used in for-loops</span></span></li>
<li><span><span><a href="_incomparable.html" title="a result indicating incomparability">incomparable</a> -- a result indicating incomparability</span></span></li>
<li><span><span><a href="_independent__Sets.html" title="some size-maximal independent subsets of variables modulo an ideal">independentSets</a> -- some size-maximal independent subsets of variables modulo an ideal</span></span></li>
<li><span><span><a href="_indeterminate.html" title="an indeterminate number">indeterminate</a> -- an indeterminate number</span></span></li>
<li><span><span><a href="___Indeterminate__Number.html" title="the class of all indeterminate numbers">IndeterminateNumber</a> -- the class of all indeterminate numbers</span></span></li>
<li><span><span><a href="_index.html" title="numeric index of a ring variable">index</a> -- numeric index of a ring variable</span></span></li>
<li><span><span><a href="_index__Components.html" title="specify keys for components of a direct sum">indexComponents</a> -- specify keys for components of a direct sum</span></span></li>
<li><span><span><a href="___Indexed__Variable.html" title="the class of all indexed variables">IndexedVariable</a> -- the class of all indexed variables</span></span></li>
<li><span><span><a href="___Indexed__Variable_sp.._sp__Indexed__Variable.html" title="sequences of consecutive indexed variables">IndexedVariable .. IndexedVariable</a> -- sequences of consecutive indexed variables</span></span></li>
<li><span><span><a href="___Indexed__Variable_sp.._lt_sp__Indexed__Variable.html" title="sequences of consecutive indexed variables">IndexedVariable ..< IndexedVariable</a> -- sequences of consecutive indexed variables</span></span></li>
<li><span><span><a href="___Indexed__Variable_sp_us_sp__Ring.html" title="get a ring variable by name">IndexedVariable _ Ring</a> -- get a ring variable by name</span></span></li>
<li><span><span><a href="___Indexed__Variable__Table.html" title="">IndexedVariableTable</a></span></span></li>
<li><span><span><a href="_indices.html" title="indices of a polynomial; also components for a direct sum">indices</a> -- indices of a polynomial; also components for a direct sum</span></span></li>
<li><span><span><a href="_indices_lp__Hash__Table_rp.html" title="preferred indices of a direct sum">indices(HashTable)</a> -- preferred indices of a direct sum</span></span></li>
<li><span><span><a href="_indices_lp__Ring__Element_rp.html" title="indices of variables occurring in a polynomial">indices(RingElement)</a> -- indices of variables occurring in a polynomial</span></span></li>
<li><span><span><a href="_induced__Map.html" title="compute an induced map">inducedMap</a> -- compute an induced map</span></span></li>
<li><span><span><a href="_induced__Map_lp..._cm_sp__Degree_sp_eq_gt_sp..._rp.html" title="specify the degree of a map">inducedMap(..., Degree => ...)</a> -- specify the degree of a map</span></span></li>
<li><span><span><a href="_induced__Map_lp..._cm_sp__Verify_sp_eq_gt_sp..._rp.html" title="">inducedMap(..., Verify => ...)</a></span></span></li>
<li><span><span><a href="_induced__Map_lp__Module_cm__Module_rp.html" title="compute the map induced by the identity">inducedMap(Module,Module)</a> -- compute the map induced by the identity</span></span></li>
<li><span><span><a href="_induced__Map_lp__Module_cm__Module_cm__Matrix_rp.html" title="compute the induced map">inducedMap(Module,Module,Matrix)</a> -- compute the induced map</span></span></li>
<li><span><span><a href="_induces__Well__Defined__Map.html" title="whether a map is well defined">inducesWellDefinedMap</a> -- whether a map is well defined</span></span></li>
<li><span><span><a href="___Inexact__Field.html" title="the class of inexact fields">InexactField</a> -- the class of inexact fields</span></span></li>
<li><span><span><a href="___Inexact__Field__Family.html" title="the class of all families of inexact fields">InexactFieldFamily</a> -- the class of all families of inexact fields</span></span></li>
<li><span><span><a href="___Inexact__Number.html" title="">InexactNumber</a></span></span></li>
<li><span><span><a href="___Inexact__Number_sq.html" title="">InexactNumber'</a></span></span></li>
<li><span><span><a href="___Infinite__Number.html" title="the class of all infinite numbers">InfiniteNumber</a> -- the class of all infinite numbers</span></span></li>
<li><span><span><a href="_infinity.html" title="infinity">infinity</a> -- infinity</span></span></li>
<li><span><span><a href="_info.html" title="convert hypertext to info format">info</a> -- convert hypertext to info format</span></span></li>
<li><span><span><a href="_info__Help.html" title="view online doc with info">infoHelp</a> -- view online doc with info</span></span></li>
<li><span><span><a href="_information_spabout_spa_spmap_spof_spmodules.html" title="">information about a map of modules</a></span></span></li>
<li><span><span><a href="___Inhomogeneous.html" title="">Inhomogeneous</a></span></span></li>
<li><span><span><a href="_initial_sphelp.html" title="">initial help</a></span></span></li>
<li><span><span><a href="_insert_lp__Z__Z_cm__Thing_cm__Visible__List_rp.html" title="copy a list, inserting an element">insert(ZZ,Thing,VisibleList)</a> -- copy a list, inserting an element</span></span></li>
<li><span><span><a href="_install__Assignment__Method.html" title="install methods assignment to the value of an operator">installAssignmentMethod</a> -- install methods assignment to the value of an operator</span></span></li>
<li><span><span><a href="_install__Hilbert__Function.html" title="install a Hilbert function without computation">installHilbertFunction</a> -- install a Hilbert function without computation</span></span></li>
<li><span><span><a href="_install__Method.html" title="install methods">installMethod</a> -- install methods</span></span></li>
<li><span><span><a href="___Install__Prefix.html" title="name for an optional argument">InstallPrefix</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_instances_lp__Type_rp.html" title="">instances(Type)</a></span></span></li>
<li><span><span><a href="_integrate.html" title="numerical integration">integrate</a> -- numerical integration</span></span></li>
<li><span><span><a href="_interpreter__Depth.html" title="nesting depth of the interpreter">interpreterDepth</a> -- nesting depth of the interpreter</span></span></li>
<li><span><span><a href="_intersect.html" title="compute an intersection">intersect</a> -- compute an intersection</span></span></li>
<li><span><span><a href="___Intersection.html" title="value for an optional argument">Intersection</a> -- value for an optional argument</span></span></li>
<li><span><span><a href="_inverse.html" title="compute the inverse">inverse</a> -- compute the inverse</span></span></li>
<li><span><span><a href="_inverse_spsystems.html" title="">inverse systems</a></span></span></li>
<li><span><span><a href="_inverse_lp__Matrix_rp.html" title="compute the inverse">inverse(Matrix)</a> -- compute the inverse</span></span></li>
<li><span><span><a href="___Inverse__Method.html" title="compute reciprocals">InverseMethod</a> -- compute reciprocals</span></span></li>
<li><span><span><a href="_inverse__Permutation.html" title="inverse permutation">inversePermutation</a> -- inverse permutation</span></span></li>
<li><span><span><a href="___Inverses.html" title="name for an optional argument">Inverses</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="___Invoking_spthe_spprogram.html" title="">Invoking the program</a></span></span></li>
<li><span><span><a href="_irreducible__Characteristic__Series.html" title="irreducible characteristic series of an ideal">irreducibleCharacteristicSeries</a> -- irreducible characteristic series of an ideal</span></span></li>
<li><span><span><a href="_is__Affine__Ring.html" title="whether something is an affine ring">isAffineRing</a> -- whether something is an affine ring</span></span></li>
<li><span><span><a href="_is__A__Number.html" title="whether a number is a number">isANumber</a> -- whether a number is a number</span></span></li>
<li><span><span><a href="_is__Borel.html" title="whether an ideal is fixed by upper triangular changes of coordinates">isBorel</a> -- whether an ideal is fixed by upper triangular changes of coordinates</span></span></li>
<li><span><span><a href="_is__Commutative.html" title="whether a ring is commutative">isCommutative</a> -- whether a ring is commutative</span></span></li>
<li><span><span><a href="_is__Constant.html" title="whether a ring element is constant">isConstant</a> -- whether a ring element is constant</span></span></li>
<li><span><span><a href="_is__Direct__Sum.html" title="whether something is a direct sum">isDirectSum</a> -- whether something is a direct sum</span></span></li>
<li><span><span><a href="_is__Field.html" title="whether something is a field">isField</a> -- whether something is a field</span></span></li>
<li><span><span><a href="_is__Finite.html" title="whether a number is finite">isFinite</a> -- whether a number is finite</span></span></li>
<li><span><span><a href="_is__Free__Module.html" title="whether something is a free module">isFreeModule</a> -- whether something is a free module</span></span></li>
<li><span><span><a href="_is__Global__Symbol.html" title="whether a global symbol with a given name exists">isGlobalSymbol</a> -- whether a global symbol with a given name exists</span></span></li>
<li><span><span><a href="_is__Homogeneous.html" title="whether something is homogeneous (graded)">isHomogeneous</a> -- whether something is homogeneous (graded)</span></span></li>
<li><span><span><a href="_is__Ideal.html" title="whether something is an ideal">isIdeal</a> -- whether something is an ideal</span></span></li>
<li><span><span><a href="_is__Infinite.html" title="whether a number is infinite">isInfinite</a> -- whether a number is infinite</span></span></li>
<li><span><span><a href="_is__Injective.html" title="whether a map is injective">isInjective</a> -- whether a map is injective</span></span></li>
<li><span><span><a href="_is__Input__File_lp__File_rp.html" title="whether a file is open for input">isInputFile(File)</a> -- whether a file is open for input</span></span></li>
<li><span><span><a href="_is__Isomorphism.html" title="whether a map is an isomorphism">isIsomorphism</a> -- whether a map is an isomorphism</span></span></li>
<li><span><span><a href="_is__Listener_lp__File_rp.html" title="whether a file is open for listening">isListener(File)</a> -- whether a file is open for listening</span></span></li>
<li><span><span><a href="_is__Module.html" title="whether something is a module">isModule</a> -- whether something is a module</span></span></li>
<li><span><span><a href="_is__Monomial__Ideal.html" title="whether something is a monomial ideal">isMonomialIdeal</a> -- whether something is a monomial ideal</span></span></li>
<li><span><span><a href="_is__Open.html" title="whether a file or database is open">isOpen</a> -- whether a file or database is open</span></span></li>
<li><span><span><a href="_is__Output__File_lp__File_rp.html" title="whether a file is open for output">isOutputFile(File)</a> -- whether a file is open for output</span></span></li>
<li><span><span><a href="_is__Polynomial__Ring.html" title="whether someting is a polynomial ring">isPolynomialRing</a> -- whether someting is a polynomial ring</span></span></li>
<li><span><span><a href="_is__Prime.html" title="whether a integer, polynomial, or ideal is prime">isPrime</a> -- whether a integer, polynomial, or ideal is prime</span></span></li>
<li><span><span><a href="_is__Primitive.html" title="whether an element is a primitive element of a finite field">isPrimitive</a> -- whether an element is a primitive element of a finite field</span></span></li>
<li><span><span><a href="_is__Pseudoprime_lp__Z__Z_rp.html" title="whether an integer is a pseudoprime">isPseudoprime(ZZ)</a> -- whether an integer is a pseudoprime</span></span></li>
<li><span><span><a href="_is__Quotient__Module.html" title="whether something is evidently a quotient of a free module">isQuotientModule</a> -- whether something is evidently a quotient of a free module</span></span></li>
<li><span><span><a href="_is__Quotient__Of.html" title="whether one thing is a quotient of another">isQuotientOf</a> -- whether one thing is a quotient of another</span></span></li>
<li><span><span><a href="_is__Quotient__Of_lp__Ring_cm__Ring_rp.html" title="whether one ring is a quotient of another">isQuotientOf(Ring,Ring)</a> -- whether one ring is a quotient of another</span></span></li>
<li><span><span><a href="_is__Quotient__Of_lp__Type_cm__Ring_rp.html" title="whether one ring is a quotient of a ring of a given type">isQuotientOf(Type,Ring)</a> -- whether one ring is a quotient of a ring of a given type</span></span></li>
<li><span><span><a href="_is__Quotient__Ring.html" title="whether something is a quotient ring">isQuotientRing</a> -- whether something is a quotient ring</span></span></li>
<li><span><span><a href="_is__Ready_lp__File_rp.html" title="whether a file has data available for reading">isReady(File)</a> -- whether a file has data available for reading</span></span></li>
<li><span><span><a href="_is__Real.html" title="whether a number is real">isReal</a> -- whether a number is real</span></span></li>
<li><span><span><a href="_is__Ring.html" title="whether something is a ring">isRing</a> -- whether something is a ring</span></span></li>
<li><span><span><a href="_is__Skew__Commutative.html" title="whether a ring has skew commuting variables">isSkewCommutative</a> -- whether a ring has skew commuting variables</span></span></li>
<li><span><span><a href="_is__Sorted_lp__Visible__List_rp.html" title="whether a list is sorted">isSorted(VisibleList)</a> -- whether a list is sorted</span></span></li>
<li><span><span><a href="_is__Square__Free.html" title="whether something is square free monomial ideal">isSquareFree</a> -- whether something is square free monomial ideal</span></span></li>
<li><span><span><a href="_is__Submodule.html" title="whether a module is evidently a submodule of a free module">isSubmodule</a> -- whether a module is evidently a submodule of a free module</span></span></li>
<li><span><span><a href="_is__Subquotient_lp__Module_cm__Module_rp.html" title="check whether a module is a subquotient of another">isSubquotient(Module,Module)</a> -- check whether a module is a subquotient of another</span></span></li>
<li><span><span><a href="_is__Subset.html" title="whether one object is a subset of another">isSubset</a> -- whether one object is a subset of another</span></span></li>
<li><span><span><a href="_is__Subset_lp__Ideal_cm__Ideal_rp.html" title="whether one object is a subset of another">isSubset(Ideal,Ideal)</a> -- whether one object is a subset of another</span></span></li>
<li><span><span><a href="_is__Subset_lp__Module_cm__Module_rp.html" title="whether one object is a subset of another">isSubset(Module,Module)</a> -- whether one object is a subset of another</span></span></li>
<li><span><span><a href="_is__Subset_lp__Set_cm__Set_rp.html" title="whether one object is a subset of another">isSubset(Set,Set)</a> -- whether one object is a subset of another</span></span></li>
<li><span><span><a href="_is__Surjective.html" title="whether a map is surjective">isSurjective</a> -- whether a map is surjective</span></span></li>
<li><span><span><a href="_is__Table.html" title="whether something is a rectangular list of lists">isTable</a> -- whether something is a rectangular list of lists</span></span></li>
<li><span><span><a href="_is__Unit.html" title="whether a ring element is a unit">isUnit</a> -- whether a ring element is a unit</span></span></li>
<li><span><span><a href="_is__Well__Defined.html" title="whether a map is well defined">isWellDefined</a> -- whether a map is well defined</span></span></li>
<li><span><span><a href="___Iterate.html" title="a Strategy option value for saturate">Iterate</a> -- a Strategy option value for saturate</span></span></li>
<li><span><span><a href="_jacobian.html" title="the Jacobian matrix of partial derivatives">jacobian</a> -- the Jacobian matrix of partial derivatives</span></span></li>
<li><span><span><a href="_jacobian_lp__Ideal_rp.html" title="the Jacobian matrix of the generators of an ideal">jacobian(Ideal)</a> -- the Jacobian matrix of the generators of an ideal</span></span></li>
<li><span><span><a href="_jacobian_lp__Matrix_rp.html" title="the matrix of partial derivatives of polynomials in a matrix">jacobian(Matrix)</a> -- the matrix of partial derivatives of polynomials in a matrix</span></span></li>
<li><span><span><a href="_jacobian_lp__Ring_rp.html" title="the Jacobian matrix of the polynomials defining a quotient ring">jacobian(Ring)</a> -- the Jacobian matrix of the polynomials defining a quotient ring</span></span></li>
<li><span><span><a href="___Join.html" title="name for an optional argument">Join</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="___Keep__Zeroes.html" title="name for an optional argument">KeepZeroes</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_kernel.html" title="kernel of a ringmap, matrix, or chain complex">kernel</a> -- kernel of a ringmap, matrix, or chain complex</span></span></li>
<li><span><span><a href="_kernel_lp..._cm_sp__Subring__Limit_sp_eq_gt_sp..._rp.html" title="">kernel(..., SubringLimit => ...)</a></span></span></li>
<li><span><span><a href="_kernel_lp__Chain__Complex__Map_rp.html" title="kernel of a chain complex map">kernel(ChainComplexMap)</a> -- kernel of a chain complex map</span></span></li>
<li><span><span><a href="_kernel_lp__Matrix_rp.html" title="kernel of a matrix">kernel(Matrix)</a> -- kernel of a matrix</span></span></li>
<li><span><span><a href="_kernel_lp__Ring__Map_rp.html" title="kernel of a ringmap">kernel(RingMap)</a> -- kernel of a ringmap</span></span></li>
<li><span><span><a href="_keys_lp__Hash__Table_rp.html" title="keys used in a hash table">keys(HashTable)</a> -- keys used in a hash table</span></span></li>
<li><span><span><a href="___Keyword.html" title="the class of all keywords">Keyword</a> -- the class of all keywords</span></span></li>
<li><span><span><a href="_kill.html" title="kill a process">kill</a> -- kill a process</span></span></li>
<li><span><span><a href="_koszul.html" title="Koszul complex or specific matrix in the Koszul complex">koszul</a> -- Koszul complex or specific matrix in the Koszul complex</span></span></li>
<li><span><span><a href="_koszul_lp__Matrix_rp.html" title="the Koszul complex">koszul(Matrix)</a> -- the Koszul complex</span></span></li>
<li><span><span><a href="_koszul_lp__Z__Z_cm__Matrix_rp.html" title="a differential in a Koszul complex">koszul(ZZ,Matrix)</a> -- a differential in a Koszul complex</span></span></li>
<li><span><span><a href="_lcm.html" title="least common multiple">lcm</a> -- least common multiple</span></span></li>
<li><span><span><a href="_lcm_lp__Monomial__Ideal_rp.html" title="least common multiple of all minimal generators">lcm(MonomialIdeal)</a> -- least common multiple of all minimal generators</span></span></li>
<li><span><span><a href="_lead__Coefficient.html" title="the leading coefficient">leadCoefficient</a> -- the leading coefficient</span></span></li>
<li><span><span><a href="_lead__Component.html" title="the leading component of a vector or matrix">leadComponent</a> -- the leading component of a vector or matrix</span></span></li>
<li><span><span><a href="_lead__Monomial.html" title="the leading monomial">leadMonomial</a> -- the leading monomial</span></span></li>
<li><span><span><a href="_lead__Term.html" title="get the greatest term">leadTerm</a> -- get the greatest term</span></span></li>
<li><span><span><a href="_lead__Term_lp__Ideal_rp.html" title="get the ideal of greatest terms">leadTerm(Ideal)</a> -- get the ideal of greatest terms</span></span></li>
<li><span><span><a href="_lead__Term_lp__Matrix_rp.html" title="get the greatest term of each column">leadTerm(Matrix)</a> -- get the greatest term of each column</span></span></li>
<li><span><span><a href="_lead__Term_lp__Ring__Element_rp.html" title="get the greatest term">leadTerm(RingElement)</a> -- get the greatest term</span></span></li>
<li><span><span><a href="_lead__Term_lp__Z__Z_cm__Ideal_rp.html" title="get the ideal of lead polynomials">leadTerm(ZZ,Ideal)</a> -- get the ideal of lead polynomials</span></span></li>
<li><span><span><a href="_lead__Term_lp__Z__Z_cm__Matrix_rp.html" title="get the matrix of lead polynomials of each column">leadTerm(ZZ,Matrix)</a> -- get the matrix of lead polynomials of each column</span></span></li>
<li><span><span><a href="_lead__Term_lp__Z__Z_cm__Ring__Element_rp.html" title="get the lead polynomials using part of the monomial order">leadTerm(ZZ,RingElement)</a> -- get the lead polynomials using part of the monomial order</span></span></li>
<li><span><span><a href="___Left.html" title="value for an optional argument">Left</a> -- value for an optional argument</span></span></li>
<li><span><span><a href="_left_spshift.html" title="">left shift</a></span></span></li>
<li><span><span><a href="_length.html" title="length">length</a> -- length</span></span></li>
<li><span><span><a href="_length_lp__Chain__Complex_rp.html" title="length of a chain complex or graded module">length(ChainComplex)</a> -- length of a chain complex or graded module</span></span></li>
<li><span><span><a href="_length_lp__Dictionary_rp.html" title="length of a dictionary">length(Dictionary)</a> -- length of a dictionary</span></span></li>
<li><span><span><a href="_length_lp__Graded__Module_rp.html" title="length of a graded module">length(GradedModule)</a> -- length of a graded module</span></span></li>
<li><span><span><a href="_length_lp__Module_rp.html" title="length">length(Module)</a> -- length</span></span></li>
<li><span><span><a href="_length_lp__String_rp.html" title="length of a string">length(String)</a> -- length of a string</span></span></li>
<li><span><span><a href="_length_lp__Visible__List_rp.html" title="length of a visible list">length(VisibleList)</a> -- length of a visible list</span></span></li>
<li><span><span><a href="___Length__Limit.html" title="stop when the resolution reaches this length">LengthLimit</a> -- stop when the resolution reaches this length</span></span></li>
<li><span><span><a href="_lift.html" title="lift to another ring">lift</a> -- lift to another ring</span></span></li>
<li><span><span><a href="_liftable.html" title="whether lifting to another ring is possible">liftable</a> -- whether lifting to another ring is possible</span></span></li>
<li><span><span><a href="___Limit.html" title="name for an optional argument">Limit</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="___Linear.html" title="a Strategy option value for saturate">Linear</a> -- a Strategy option value for saturate</span></span></li>
<li><span><span><a href="_line__Number.html" title="current line number">lineNumber</a> -- current line number</span></span></li>
<li><span><span><a href="_list.html" title="loop control">list</a> -- loop control</span></span></li>
<li><span><span><a href="___List_sp_pl_sp__List.html" title="sum of two vectors">List + List</a> -- sum of two vectors</span></span></li>
<li><span><span><a href="___List_sp-_sp__List.html" title="difference of two vectors">List - List</a> -- difference of two vectors</span></span></li>
<li><span><span><a href="___List_sp.._sp__List.html" title="rectangular sequences of consecutive lists and sequences">List .. List</a> -- rectangular sequences of consecutive lists and sequences</span></span></li>
<li><span><span><a href="___List_sp.._lt_sp__List.html" title="rectangular sequences of consecutive lists and sequences">List ..< List</a> -- rectangular sequences of consecutive lists and sequences</span></span></li>
<li><span><span><a href="___List_sp_sl_sp__Thing.html" title="vector division">List / Thing</a> -- vector division</span></span></li>
<li><span><span><a href="_list__Form.html" title="convert to list form">listForm</a> -- convert to list form</span></span></li>
<li><span><span><a href="_list__Local__Symbols.html" title="display of local symbols and their values">listLocalSymbols</a> -- display of local symbols and their values</span></span></li>
<li><span><span><a href="_list__Symbols.html" title="compact display of symbols and their values">listSymbols</a> -- compact display of symbols and their values</span></span></li>
<li><span><span><a href="_list__User__Symbols.html" title="display the user's symbols">listUserSymbols</a> -- display the user's symbols</span></span></li>
<li><span><span><a href="_lngamma.html" title="logarithm of the Gamma function">lngamma</a> -- logarithm of the Gamma function</span></span></li>
<li><span><span><a href="_load__Depth.html" title="the load depth">loadDepth</a> -- the load depth</span></span></li>
<li><span><span><a href="___Load__Documentation.html" title="when loading a package, load the documentation, too">LoadDocumentation</a> -- when loading a package, load the documentation, too</span></span></li>
<li><span><span><a href="_loaded__Files.html" title="">loadedFiles</a></span></span></li>
<li><span><span><a href="___Local.html" title="name for an optional argument">Local</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_local.html" title="get a local symbol">local</a> -- get a local symbol</span></span></li>
<li><span><span><a href="_local__Dictionaries.html" title="get local dictionaries">localDictionaries</a> -- get local dictionaries</span></span></li>
<li><span><span><a href="___Local__Dictionary.html" title="the class of all local dictionaries">LocalDictionary</a> -- the class of all local dictionaries</span></span></li>
<li><span><span><a href="_locate.html" title="locate source code">locate</a> -- locate source code</span></span></li>
<li><span><span><a href="_log.html" title="logarithm function">log</a> -- logarithm function</span></span></li>
<li><span><span><a href="_log1p.html" title="logarithm of 1+x">log1p</a> -- logarithm of 1+x</span></span></li>
<li><span><span><a href="___Long__Polynomial.html" title="">LongPolynomial</a></span></span></li>
<li><span><span><a href="_lookup.html" title="look up methods">lookup</a> -- look up methods</span></span></li>
<li><span><span><a href="_lookup__Count.html" title="reference count for a symbol">lookupCount</a> -- reference count for a symbol</span></span></li>
<li><span><span><a href="___Lower__Bound.html" title="the class of lower bound objects">LowerBound</a> -- the class of lower bound objects</span></span></li>
<li><span><span><a href="___L__Udecomposition.html" title="LU decomposition">LUdecomposition</a> -- LU decomposition</span></span></li>
<li><span><span><a href="___Make__Documentation.html" title="name for an optional argument">MakeDocumentation</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_make__Document__Tag.html" title="convert a documentation key to a documentation tag">makeDocumentTag</a> -- convert a documentation key to a documentation tag</span></span></li>
<li><span><span><a href="___Make__Info.html" title="name for an optional argument">MakeInfo</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="___Make__Links.html" title="name for an optional argument">MakeLinks</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_make__Package__Index.html" title="">makePackageIndex</a></span></span></li>
<li><span><span><a href="_making_spmodules_spfrom_spmatrices.html" title="">making modules from matrices</a></span></span></li>
<li><span><span><a href="_manipulating_spmodules.html" title="">manipulating modules</a></span></span></li>
<li><span><span><a href="___Manipulator.html" title="the class of all file manipulators">Manipulator</a> -- the class of all file manipulators</span></span></li>
<li><span><span><a href="_map.html" title="make a map">map</a> -- make a map</span><ul><li><span><span><a href="_map_lp__Module_cm__Module_cm__Function_rp.html" title="create a matrix by specifying a function that gives each entry">map(Module,Module,Function)</a> -- create a matrix by specifying a function that gives each entry</span></span></li>
<li><span><span><a href="_map_lp__Module_cm__Module_cm__List_rp.html" title="create a matrix by giving a sparse or dense list of entries">map(Module,Module,List)</a> -- create a matrix by giving a sparse or dense list of entries</span></span></li>
<li><span><span><a href="_map_lp__Module_cm__Module_cm__Ring__Element_rp.html" title="construct the map induced by multiplication by a ring element on the generators">map(Module,Module,RingElement)</a> -- construct the map induced by multiplication by a ring element on the generators</span></span></li>
<li><span><span><a href="_map_lp__Module_cm__Module_cm__Matrix_rp.html" title="create the matrix induced on generators by a given matrix">map(Module,Module,Matrix)</a> -- create the matrix induced on generators by a given matrix</span></span></li>
<li><span><span><a href="_map_lp__Module_cm__Z__Z_cm__Function_rp.html" title="create a matrix from a free module by specifying a function that gives each entry">map(Module,ZZ,Function)</a> -- create a matrix from a free module by specifying a function that gives each entry</span></span></li>
<li><span><span><a href="_map_lp__Module_cm__Nothing_cm__List_rp.html" title="create a matrix by giving a doubly nested list of ring elements">map(Module,Nothing,List)</a> -- create a matrix by giving a doubly nested list of ring elements</span></span></li>
<li><span><span><a href="_map_lp__Module_cm__Z__Z_cm__List_rp.html" title="create a matrix by giving a sparse or dense list of entries">map(Module,ZZ,List)</a> -- create a matrix by giving a sparse or dense list of entries</span></span></li>
<li><span><span><a href="_map_lp__Module_cm__Nothing_cm__Matrix_rp.html" title="recast a matrix to have a new target, and a free module as source">map(Module,Nothing,Matrix)</a> -- recast a matrix to have a new target, and a free module as source</span></span></li>
<li><span><span><a href="_map_lp__Matrix_rp.html" title="make a matrix with a different degree">map(Matrix)</a> -- make a matrix with a different degree</span></span></li>
<li><span><span><a href="_map_lp__Module_cm__Module_cm__Ring__Map_cm__Matrix_rp.html" title="homomorphism of modules over different rings">map(Module,Module,RingMap,Matrix)</a> -- homomorphism of modules over different rings</span></span></li>
<li><span><span><a href="_map_lp__Ring_cm__Ring_rp.html" title="make a ring map, using the names of the variables">map(Ring,Ring)</a> -- make a ring map, using the names of the variables</span></span></li>
<li><span><span><a href="_map_lp__Ring_cm__Ring_cm__List_rp.html" title="make a ring map">map(Ring,Ring,List)</a> -- make a ring map</span></span></li>
<li><span><span><a href="_map_lp__Ring_cm__Ring_cm__Matrix_rp.html" title="make a ring map">map(Ring,Ring,Matrix)</a> -- make a ring map</span></span></li>
<li><span><span><a href="_map_lp__Chain__Complex_cm__Chain__Complex_cm__Chain__Complex__Map_rp.html" title="">map(ChainComplex,ChainComplex,ChainComplexMap)</a></span></span></li>
<li><span><span><a href="_map_lp__Chain__Complex_cm__Chain__Complex_cm__Function_rp.html" title="make a map of chain complexes">map(ChainComplex,ChainComplex,Function)</a> -- make a map of chain complexes</span></span></li>
</ul>
</span></li>
<li><span><span><a href="_map_lp..._cm_sp__Degree_sp_eq_gt_sp..._rp.html" title="set the degree of a map">map(..., Degree => ...)</a> -- set the degree of a map</span></span></li>
<li><span><span><a href="_map_lp__Module_rp.html" title="identity map">map(Module)</a> -- identity map</span></span></li>
<li><span><span><a href="_map_lp__Ring_cm__Matrix_rp.html" title="make a ring map">map(Ring,Matrix)</a> -- make a ring map</span></span></li>
<li><span><span><a href="_maps_spbetween_spmodules.html" title="">maps between modules</a></span></span></li>
<li><span><span><a href="_marked__G__B_lp__Matrix_cm__Matrix_rp.html" title="make a marked Gröbner basis">markedGB(Matrix,Matrix)</a> -- make a marked Gröbner basis</span></span></li>
<li><span><span><a href="_math__M__L.html" title="convert to MathML format">mathML</a> -- convert to MathML format</span></span></li>
<li><span><span><a href="___Matrix.html" title="the class of all matrices">Matrix</a> -- the class of all matrices</span></span></li>
<li><span><span><a href="_matrix.html" title="make a matrix">matrix</a> -- make a matrix</span></span></li>
<li><span><span><a href="___Matrix_sp_pc_sp__Groebner__Basis.html" title="calculate the normal form of ring elements and matrices using a (partially computed) Gröbner basis">Matrix % GroebnerBasis</a> -- calculate the normal form of ring elements and matrices using a (partially computed) Gröbner basis</span></span></li>
<li><span><span><a href="___Matrix_sp_st_sp__Matrix.html" title="matrix multiplication">Matrix * Matrix</a> -- matrix multiplication</span></span></li>
<li><span><span><a href="___Matrix_sp_st_st_sp__Matrix.html" title="tensor product">Matrix ** Matrix</a> -- tensor product</span></span></li>
<li><span><span><a href="___Matrix_sp_st_st_sp__Module.html" title="tensor product">Matrix ** Module</a> -- tensor product</span></span></li>
<li><span><span><a href="___Matrix_sp_st_st_sp__Ring.html" title="tensor product">Matrix ** Ring</a> -- tensor product</span></span></li>
<li><span><span><a href="___Matrix_sp_st_st_sp__Ring__Element.html" title="a binary operator, usually used for tensor product or Cartesian product">Matrix ** RingElement</a> -- a binary operator, usually used for tensor product or Cartesian product</span></span></li>
<li><span><span><a href="___Matrix_sp_pl_pl_sp__Matrix.html" title="direct sum of maps">Matrix ++ Matrix</a> -- direct sum of maps</span></span></li>
<li><span><span><a href="___Matrix_sp_sl_sl_sp__Matrix.html" title="factor a map through another">Matrix // Matrix</a> -- factor a map through another</span></span></li>
<li><span><span><a href="___Matrix_sp^_sp__Array.html" title="component of map corresponding to summand of target">Matrix ^ Array</a> -- component of map corresponding to summand of target</span></span></li>
<li><span><span><a href="___Matrix_sp^_sp__List.html" title="select rows">Matrix ^ List</a> -- select rows</span></span></li>
<li><span><span><a href="___Matrix_sp^_sp__Z__Z.html" title="power">Matrix ^ ZZ</a> -- power</span></span></li>
<li><span><span><a href="___Matrix_sp_us_sp__Array.html" title="component of map corresponding to summand of source">Matrix _ Array</a> -- component of map corresponding to summand of source</span></span></li>
<li><span><span><a href="___Matrix_sp_us_sp__List.html" title="select columns">Matrix _ List</a> -- select columns</span></span></li>
<li><span><span><a href="___Matrix_sp_us_sp__Sequence.html" title="get entry of matrix">Matrix _ Sequence</a> -- get entry of matrix</span></span></li>
<li><span><span><a href="___Matrix_sp_vb_sp__Matrix.html" title="join matrices horizontally">Matrix | Matrix</a> -- join matrices horizontally</span></span></li>
<li><span><span><a href="___Matrix_sp_vb_vb_sp__Matrix.html" title="join matrices vertically">Matrix || Matrix</a> -- join matrices vertically</span></span></li>
<li><span><span><a href="_matrix_lp__List_rp.html" title="create a matrix from a doubly-nested list of ring elements or matrices">matrix(List)</a> -- create a matrix from a doubly-nested list of ring elements or matrices</span></span></li>
<li><span><span><a href="_matrix_lp__Matrix_rp.html" title="the matrix between generators">matrix(Matrix)</a> -- the matrix between generators</span></span></li>
<li><span><span><a href="_matrix_lp__Mutable__Matrix_rp.html" title="make a matrix from a mutable one">matrix(MutableMatrix)</a> -- make a matrix from a mutable one</span></span></li>
<li><span><span><a href="_matrix_lp__Ring_cm__List_rp.html" title="create a matrix from a doubly nested list of ring elements or matrices">matrix(Ring,List)</a> -- create a matrix from a doubly nested list of ring elements or matrices</span></span></li>
<li><span><span><a href="_matrix_lp__Ring__Map_rp.html" title="the matrix associated to a ring map">matrix(RingMap)</a> -- the matrix associated to a ring map</span></span></li>
<li><span><span><a href="_matrix_lp__Vector_rp.html" title="">matrix(Vector)</a></span></span></li>
<li><span><span><a href="___Matrix__Expression.html" title="the class of all matrix expressions">MatrixExpression</a> -- the class of all matrix expressions</span></span></li>
<li><span><span><a href="_max.html" title="maximum of elements of a list">max</a> -- maximum of elements of a list</span></span></li>
<li><span><span><a href="_max_lp__Graded__Module_rp.html" title="maximum of elements of a list">max(GradedModule)</a> -- maximum of elements of a list</span></span></li>
<li><span><span><a href="_max__Exponent.html" title="">maxExponent</a></span></span></li>
<li><span><span><a href="___Maximal__Rank.html" title="name for an optional argument">MaximalRank</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_max__Position.html" title="position of largest element">maxPosition</a> -- position of largest element</span></span></li>
<li><span><span><a href="___Max__Reduction__Count.html" title="name for an optional argument">MaxReductionCount</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_member.html" title="test membership in a list or set">member</a> -- test membership in a list or set</span></span></li>
<li><span><span><a href="_memoize.html" title="record results of function evaluation for future use">memoize</a> -- record results of function evaluation for future use</span></span></li>
<li><span><span><a href="_merge__Pairs.html" title="merge sorted lists of pairs">mergePairs</a> -- merge sorted lists of pairs</span></span></li>
<li><span><span><a href="___Method__Function.html" title="a type of method function">MethodFunction</a> -- a type of method function</span></span></li>
<li><span><span><a href="___Method__Function__With__Options.html" title="a type of method function">MethodFunctionWithOptions</a> -- a type of method function</span></span></li>
<li><span><span><a href="_method__Options_lp__Function_rp.html" title="recover the options used when a method function was created">methodOptions(Function)</a> -- recover the options used when a method function was created</span></span></li>
<li><span><span><a href="_methods.html" title="list methods">methods</a> -- list methods</span></span></li>
<li><span><span><a href="_methods_spfor_spnormal_spforms_spand_spremainder.html" title="calculate the normal form of ring elements and matrices">methods for normal forms and remainder</a> -- calculate the normal form of ring elements and matrices</span></span></li>
<li><span><span><a href="_min.html" title="minimum of elements of a list">min</a> -- minimum of elements of a list</span></span></li>
<li><span><span><a href="_min_lp__Graded__Module_rp.html" title="minimum of elements of a list">min(GradedModule)</a> -- minimum of elements of a list</span></span></li>
<li><span><span><a href="_min__Exponent.html" title="">minExponent</a></span></span></li>
<li><span><span><a href="_mingens.html" title="minimal generator matrix">mingens</a> -- minimal generator matrix</span></span></li>
<li><span><span><a href="_mingens_lp__Groebner__Basis_rp.html" title="(partially constructed) minimal generator matrix">mingens(GroebnerBasis)</a> -- (partially constructed) minimal generator matrix</span></span></li>
<li><span><span><a href="_mingens_lp__Module_rp.html" title="minimal generator matrix">mingens(Module)</a> -- minimal generator matrix</span></span></li>
<li><span><span><a href="_minimal_sppresentations_spand_spgenerators.html" title="">minimal presentations and generators</a></span></span></li>
<li><span><span><a href="___Minimal__Generators.html" title="">MinimalGenerators</a></span></span></li>
<li><span><span><a href="___Minimal__Matrix.html" title="name for an optional argument">MinimalMatrix</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_minimal__Presentation.html" title="compute a minimal presentation">minimalPresentation</a> -- compute a minimal presentation</span></span></li>
<li><span><span><a href="_minimal__Presentation_lp__Ideal_rp.html" title="compute a minimal presentation of the quotient ring defined by an ideal">minimalPresentation(Ideal)</a> -- compute a minimal presentation of the quotient ring defined by an ideal</span></span></li>
<li><span><span><a href="_minimal__Presentation_lp__Matrix_rp.html" title="minimally present source and target of a matrix">minimalPresentation(Matrix)</a> -- minimally present source and target of a matrix</span></span></li>
<li><span><span><a href="_minimal__Presentation_lp__Module_rp.html" title="minimal presentation of a module">minimalPresentation(Module)</a> -- minimal presentation of a module</span></span></li>
<li><span><span><a href="_minimal__Presentation_lp__Ring_rp.html" title="compute a minimal presentation of a quotient ring">minimalPresentation(Ring)</a> -- compute a minimal presentation of a quotient ring</span></span></li>
<li><span><span><a href="_minimal__Primes.html" title="minimal associated primes of an ideal">minimalPrimes</a> -- minimal associated primes of an ideal</span></span></li>
<li><span><span><a href="___Minimize.html" title="name for an optional argument">Minimize</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_minimize__Filename.html" title="minimize a file name">minimizeFilename</a> -- minimize a file name</span></span></li>
<li><span><span><a href="_minors_lp..._cm_sp__Strategy_sp_eq_gt_sp..._rp.html" title="choose between Bareiss and Cofactor algorithms">minors(..., Strategy => ...)</a> -- choose between Bareiss and Cofactor algorithms</span></span></li>
<li><span><span><a href="_minors_lp__Z__Z_cm__Matrix_rp.html" title="ideal generated by minors">minors(ZZ,Matrix)</a> -- ideal generated by minors</span></span></li>
<li><span><span><a href="_min__Position.html" title="position of smallest element">minPosition</a> -- position of smallest element</span></span></li>
<li><span><span><a href="___Minus.html" title="the class of all minus expressions">Minus</a> -- the class of all minus expressions</span></span></li>
<li><span><span><a href="_minus.html" title="additive inverse">minus</a> -- additive inverse</span></span></li>
<li><span><span><a href="_mod.html" title="reduce modulo an integer">mod</a> -- reduce modulo an integer</span></span></li>
<li><span><span><a href="___Module.html" title="the class of all modules">Module</a> -- the class of all modules</span></span></li>
<li><span><span><a href="_module.html" title="make or get a module">module</a> -- make or get a module</span></span></li>
<li><span><span><a href="___Module_sp_st_st_sp__Module.html" title="tensor product">Module ** Module</a> -- tensor product</span></span></li>
<li><span><span><a href="___Module_sp_st_st_sp__Ring.html" title="tensor product">Module ** Ring</a> -- tensor product</span></span></li>
<li><span><span><a href="___Module_sp_pl_sp__Module.html" title="sum of submodules">Module + Module</a> -- sum of submodules</span></span></li>
<li><span><span><a href="___Module_sp_pl_pl_sp__Module.html" title="direct sum of modules">Module ++ Module</a> -- direct sum of modules</span></span></li>
<li><span><span><a href="___Module_sp_sl_sp__Module.html" title="quotient module">Module / Module</a> -- quotient module</span></span></li>
<li><span><span><a href="___Module_sp^_sp__Array.html" title="projection onto summand">Module ^ Array</a> -- projection onto summand</span></span></li>
<li><span><span><a href="___Module_sp^_sp__List.html" title="projection onto summand">Module ^ List</a> -- projection onto summand</span></span></li>
<li><span><span><a href="___Module_sp^_sp__Z__Z.html" title="direct sum">Module ^ ZZ</a> -- direct sum</span></span></li>
<li><span><span><a href="___Module_sp^_st_st_sp__Z__Z.html" title="tensor power">Module ^** ZZ</a> -- tensor power</span></span></li>
<li><span><span><a href="___Module_sp_us_sp__Array.html" title="inclusion from summand">Module _ Array</a> -- inclusion from summand</span></span></li>
<li><span><span><a href="___Module_sp_us_sp__List.html" title="map from free module to some generators">Module _ List</a> -- map from free module to some generators</span></span></li>
<li><span><span><a href="___Module_sp__Array.html" title="make a chain complex from a module">Module Array</a> -- make a chain complex from a module</span></span></li>
<li><span><span><a href="_module_lp__Coherent__Sheaf_rp.html" title="get the module defining a coherent sheaf">module(CoherentSheaf)</a> -- get the module defining a coherent sheaf</span></span></li>
<li><span><span><a href="_module_lp__Ideal_rp.html" title="turn an ideal into a module">module(Ideal)</a> -- turn an ideal into a module</span></span></li>
<li><span><span><a href="_module_lp__Ring_rp.html" title="">module(Ring)</a></span></span></li>
<li><span><span><a href="_module_lp__Sheaf__Of__Rings_rp.html" title="make or get a module">module(SheafOfRings)</a> -- make or get a module</span></span></li>
<li><span><span><a href="_module_lp__Vector_rp.html" title="the module of a vector">module(Vector)</a> -- the module of a vector</span></span></li>
<li><span><span><a href="___Module__Map.html" title="the class of all maps between modules">ModuleMap</a> -- the class of all maps between modules</span></span></li>
<li><span><span><a href="_modulo_lp__Matrix_cm__Matrix_rp.html" title="find the pre-image (pullback) of image of a map (low level version)">modulo(Matrix,Matrix)</a> -- find the pre-image (pullback) of image of a map (low level version)</span></span></li>
<li><span><span><a href="___Monoid.html" title="the class of all monoids">Monoid</a> -- the class of all monoids</span></span></li>
<li><span><span><a href="___Monoid_sp_st_st_sp__Monoid.html" title="tensor product of monoids">Monoid ** Monoid</a> -- tensor product of monoids</span></span></li>
<li><span><span><a href="___Monoid__Element.html" title="the class of all monoid elements">MonoidElement</a> -- the class of all monoid elements</span></span></li>
<li><span><span><a href="___Monomial.html" title="name for an optional argument">Monomial</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_monomial__Curve__Ideal.html" title="make the ideal of a monomial curve">monomialCurveIdeal</a> -- make the ideal of a monomial curve</span></span></li>
<li><span><span><a href="___Monomial__Ideal.html" title="the class of all monomial ideals handled by the engine">MonomialIdeal</a> -- the class of all monomial ideals handled by the engine</span></span></li>
<li><span><span><a href="_monomial__Ideal.html" title="make a monomial ideal">monomialIdeal</a> -- make a monomial ideal</span></span></li>
<li><span><span><a href="___Monomial__Ideal_sp-_sp__Monomial__Ideal.html" title="monomial ideal difference">MonomialIdeal - MonomialIdeal</a> -- monomial ideal difference</span></span></li>
<li><span><span><a href="_monomial__Ideal_lp__Ideal_rp.html" title="monomial ideal of lead monomials of a Gröbner basis">monomialIdeal(Ideal)</a> -- monomial ideal of lead monomials of a Gröbner basis</span></span></li>
<li><span><span><a href="_monomial__Ideal_lp__Matrix_rp.html" title="monomial ideal of lead monomials">monomialIdeal(Matrix)</a> -- monomial ideal of lead monomials</span></span></li>
<li><span><span><a href="___Monomials.html" title="whether to display the number of monomial">Monomials</a> -- whether to display the number of monomial</span></span></li>
<li><span><span><a href="_monomials.html" title="matrix of monomials in a ring element or matrix">monomials</a> -- matrix of monomials in a ring element or matrix</span></span></li>
<li><span><span><a href="_monomials_lp..._cm_sp__Variables_sp_eq_gt_sp..._rp.html" title="specify variables">monomials(..., Variables => ...)</a> -- specify variables</span></span></li>
<li><span><span><a href="___Monomial__Size.html" title="name for an optional argument">MonomialSize</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_monomial__Subideal.html" title="find the largest monomial ideal in an ideal">monomialSubideal</a> -- find the largest monomial ideal in an ideal</span></span></li>
<li><span><span><a href="_multidegree.html" title="multidegree">multidegree</a> -- multidegree</span></span></li>
<li><span><span><a href="_mutable_spmatrices.html" title="">mutable matrices</a></span></span></li>
<li><span><span><a href="_mutable__Identity_lp__Ring_cm__Z__Z_rp.html" title="make a mutable identity matrix">mutableIdentity(Ring,ZZ)</a> -- make a mutable identity matrix</span></span></li>
<li><span><span><a href="___Mutable__List.html" title="the class of all mutable lists">MutableList</a> -- the class of all mutable lists</span></span></li>
<li><span><span><a href="___Mutable__Matrix.html" title="the class of all mutable matrices">MutableMatrix</a> -- the class of all mutable matrices</span></span></li>
<li><span><span><a href="_mutable__Matrix.html" title="make a mutable matrix">mutableMatrix</a> -- make a mutable matrix</span></span></li>
<li><span><span><a href="___Mutable__Matrix_sp_us_sp__Sequence_sp_eq_sp__Thing.html" title="assignment to an element of a mutable matrix">MutableMatrix _ Sequence = Thing</a> -- assignment to an element of a mutable matrix</span></span></li>
<li><span><span><a href="_mutable__Matrix_lp__Ring_cm__Z__Z_cm__Z__Z_rp.html" title="make a mutable matrix filled with zeroes">mutableMatrix(Ring,ZZ,ZZ)</a> -- make a mutable matrix filled with zeroes</span></span></li>
<li><span><span><a href="_net.html" title="format for printing, as a net">net</a> -- format for printing, as a net</span></span></li>
<li><span><span><a href="___Net_sp^_sp__Z__Z.html" title="raise a net or string">Net ^ ZZ</a> -- raise a net or string</span></span></li>
<li><span><span><a href="___Net_sp_vb_sp__Net.html" title="join strings or nets">Net | Net</a> -- join strings or nets</span></span></li>
<li><span><span><a href="___Net_sp_vb_vb_sp__Net.html" title="join nets or strings vertically">Net || Net</a> -- join nets or strings vertically</span></span></li>
<li><span><span><a href="_net_lp__String_rp.html" title="convert a string to a net">net(String)</a> -- convert a string to a net</span></span></li>
<li><span><span><a href="___Net__File.html" title="the class of all net files">NetFile</a> -- the class of all net files</span></span></li>
<li><span><span><a href="_net__List_lp__Visible__List_rp.html" title="a table of boxes">netList(VisibleList)</a> -- a table of boxes</span></span></li>
<li><span><span><a href="_new_sp__Chain__Complex.html" title="make a new chain complex from scratch">new ChainComplex</a> -- make a new chain complex from scratch</span></span></li>
<li><span><span><a href="_new_sp__Hash__Table_spfrom_sp__List.html" title="make a hash table from a list">new HashTable from List</a> -- make a hash table from a list</span></span></li>
<li><span><span><a href="_new__Coordinate__System.html" title="change variables">newCoordinateSystem</a> -- change variables</span></span></li>
<li><span><span><a href="___New__From__Method.html" title="">NewFromMethod</a></span></span></li>
<li><span><span><a href="_newline.html" title="the new line character sequence">newline</a> -- the new line character sequence</span></span></li>
<li><span><span><a href="___New__Method.html" title="">NewMethod</a></span></span></li>
<li><span><span><a href="_new__Net__File.html" title="create a new net file">newNetFile</a> -- create a new net file</span></span></li>
<li><span><span><a href="___New__Of__From__Method.html" title="">NewOfFromMethod</a></span></span></li>
<li><span><span><a href="___New__Of__Method.html" title="">NewOfMethod</a></span></span></li>
<li><span><span><a href="_new__Ring.html" title="make a copy of a ring, with some features changed">newRing</a> -- make a copy of a ring, with some features changed</span></span></li>
<li><span><span><a href="_nextkey.html" title="the next key in a database">nextkey</a> -- the next key in a database</span></span></li>
<li><span><span><a href="___Non__Associative__Product.html" title="the class of all nonassociative product expressions">NonAssociativeProduct</a> -- the class of all nonassociative product expressions</span></span></li>
<li><span><span><a href="___No__Print.html" title="top level method for non-printing results">NoPrint</a> -- top level method for non-printing results</span></span></li>
<li><span><span><a href="_norm.html" title="">norm</a></span></span></li>
<li><span><span><a href="_not_spdocumented_spyet.html" title="">not documented yet</a></span></span></li>
<li><span><span><a href="___Nothing.html" title="the empty class">Nothing</a> -- the empty class</span></span></li>
<li><span><span><a href="_notify.html" title="whether to notify the user when a file is loaded">notify</a> -- whether to notify the user when a file is loaded</span></span></li>
<li><span><span><a href="_not__Implemented.html" title="print an 'not implemented' error message">notImplemented</a> -- print an 'not implemented' error message</span></span></li>
<li><span><span><a href="_null.html" title="the unique member of the empty class">null</a> -- the unique member of the empty class</span></span></li>
<li><span><span><a href="_nullary__Methods.html" title="">nullaryMethods</a></span></span></li>
<li><span><span><a href="_nullhomotopy.html" title="make a null homotopy">nullhomotopy</a> -- make a null homotopy</span></span></li>
<li><span><span><a href="___Number.html" title="the class of all numbers">Number</a> -- the class of all numbers</span></span></li>
<li><span><span><a href="_number.html" title="count how many elements of a list satisfy a condition">number</a> -- count how many elements of a list satisfy a condition</span></span></li>
<li><span><span><a href="_num__Columns_lp__Matrix_rp.html" title="number of columns in a matrix or mutable matrix">numColumns(Matrix)</a> -- number of columns in a matrix or mutable matrix</span></span></li>
<li><span><span><a href="_numerator.html" title="numerator of a fraction">numerator</a> -- numerator of a fraction</span></span></li>
<li><span><span><a href="_numeric.html" title="convert to floating point">numeric</a> -- convert to floating point</span></span></li>
<li><span><span><a href="_numgens.html" title="the number of generators">numgens</a> -- the number of generators</span></span></li>
<li><span><span><a href="_numgens_lp__Coherent__Sheaf_rp.html" title="the number of generators of the underlying module">numgens(CoherentSheaf)</a> -- the number of generators of the underlying module</span></span></li>
<li><span><span><a href="_numgens_lp__General__Ordered__Monoid_rp.html" title="number of generators of a monoid">numgens(GeneralOrderedMonoid)</a> -- number of generators of a monoid</span></span></li>
<li><span><span><a href="_numgens_lp__Ideal_rp.html" title="number of generators of an ideal">numgens(Ideal)</a> -- number of generators of an ideal</span></span></li>
<li><span><span><a href="_numgens_lp__Module_rp.html" title="number of generators of a module">numgens(Module)</a> -- number of generators of a module</span></span></li>
<li><span><span><a href="_numgens_lp__Ring_rp.html" title="number of generators of a polynomial ring">numgens(Ring)</a> -- number of generators of a polynomial ring</span></span></li>
<li><span><span><a href="_num__Rows_lp__Matrix_rp.html" title="number of rows in a matrix or mutable matrix">numRows(Matrix)</a> -- number of rows in a matrix or mutable matrix</span></span></li>
<li><span><span><a href="_odd.html" title="tell whether an integer is odd">odd</a> -- tell whether an integer is odd</span></span></li>
<li><span><span><a href="_of.html" title="a keyword">of</a> -- a keyword</span></span></li>
<li><span><span><a href="_of__Class.html" title="English phrases for types">ofClass</a> -- English phrases for types</span></span></li>
<li><span><span><a href="_on.html" title="trace a function each time it's run">on</a> -- trace a function each time it's run</span></span></li>
<li><span><span><a href="___One__Expression.html" title="the class all one expressions">OneExpression</a> -- the class all one expressions</span></span></li>
<li><span><span><a href="_oo.html" title="the last output value">oo</a> -- the last output value</span></span></li>
<li><span><span><a href="___O__O_sp_us_sp__Variety.html" title="the structure sheaf">OO _ Variety</a> -- the structure sheaf</span></span></li>
<li><span><span><a href="_ooo.html" title="the next to the last output value">ooo</a> -- the next to the last output value</span></span></li>
<li><span><span><a href="_oooo.html" title="the third to the last output value">oooo</a> -- the third to the last output value</span></span></li>
<li><span><span><a href="_open__Database.html" title="open a database file">openDatabase</a> -- open a database file</span></span></li>
<li><span><span><a href="_open__Database__Out.html" title="open a database file for writing">openDatabaseOut</a> -- open a database file for writing</span></span></li>
<li><span><span><a href="_open__Files.html" title="list the open files">openFiles</a> -- list the open files</span></span></li>
<li><span><span><a href="_open__In_lp__String_rp.html" title="open an output file">openIn(String)</a> -- open an output file</span></span></li>
<li><span><span><a href="_open__In__Out.html" title="open an input output file">openInOut</a> -- open an input output file</span></span></li>
<li><span><span><a href="_open__Listener_lp__String_rp.html" title="open a port for listening">openListener(String)</a> -- open a port for listening</span></span></li>
<li><span><span><a href="_open__Out_lp__String_rp.html" title="open an output file">openOut(String)</a> -- open an output file</span></span></li>
<li><span><span><a href="_open__Out__Append_lp__String_rp.html" title="open an output file for appending">openOutAppend(String)</a> -- open an output file for appending</span></span></li>
<li><span><span><a href="___Option.html" title="the class of all pairs x => y">Option</a> -- the class of all pairs x => y</span></span></li>
<li><span><span><a href="_optional_spargument_spdocumentation_sptemplate.html" title="">optional argument documentation template</a></span></span></li>
<li><span><span><a href="_optional_spargument_spname_spdocumentation_sptemplate.html" title="">optional argument name documentation template</a></span></span></li>
<li><span><span><a href="___Options.html" title="name for an optional argument">Options</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_options.html" title="get options">options</a> -- get options</span></span></li>
<li><span><span><a href="_options_lp__Function_rp.html" title="get optional arguments and default values for a function that accepts them">options(Function)</a> -- get optional arguments and default values for a function that accepts them</span></span></li>
<li><span><span><a href="_options_lp__Monoid_rp.html" title="get values used for optional arguments">options(Monoid)</a> -- get values used for optional arguments</span></span></li>
<li><span><span><a href="_options_lp__Package_rp.html" title="">options(Package)</a></span></span></li>
<li><span><span><a href="_options_lp__Ring_rp.html" title="get values used for optional arguments">options(Ring)</a> -- get values used for optional arguments</span></span></li>
<li><span><span><a href="___Option__Table.html" title="the class of hash tables for optional arguments">OptionTable</a> -- the class of hash tables for optional arguments</span></span></li>
<li><span><span><a href="___Option__Table_sp_pl_pl_sp__Option__Table.html" title="">OptionTable ++ OptionTable</a></span></span></li>
<li><span><span><a href="___Option__Table_sp_gt_gt_sp__Function.html" title="attaching options to a function">OptionTable >> Function</a> -- attaching options to a function</span></span></li>
<li><span><span><a href="___Order.html" title="specify the order of a Hilbert series required">Order</a> -- specify the order of a Hilbert series required</span></span></li>
<li><span><span><a href="_order.html" title="a key used internally ">order</a> -- a key used internally </span></span></li>
<li><span><span><a href="___Ordered__Monoid.html" title="the class of all ordered monoids">OrderedMonoid</a> -- the class of all ordered monoids</span></span></li>
<li><span><span><a href="___Output__Dictionary.html" title="the dictionary for output values">OutputDictionary</a> -- the dictionary for output values</span></span></li>
<li><span><span><a href="_override.html" title="override default values for optional arguments">override</a> -- override default values for optional arguments</span></span></li>
<li><span><span><a href="_overview_spdocumentation_sptemplate.html" title="">overview documentation template</a></span></span></li>
<li><span><span><a href="___Package.html" title="the class of all packages">Package</a> -- the class of all packages</span></span></li>
<li><span><span><a href="_package.html" title="get containing package">package</a> -- get containing package</span></span></li>
<li><span><span><a href="_package_spdocumentation_sptemplate.html" title="">package documentation template</a></span></span></li>
<li><span><span><a href="___Package__Dictionary.html" title="the dictionary for names of packages">PackageDictionary</a> -- the dictionary for names of packages</span></span></li>
<li><span><span><a href="___Package__Prefix.html" title="name for an optional argument">PackagePrefix</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_pad.html" title="pad a string with spaces">pad</a> -- pad a string with spaces</span></span></li>
<li><span><span><a href="_pager.html" title="display with paging">pager</a> -- display with paging</span></span></li>
<li><span><span><a href="___Pair__Limit.html" title="name for an optional argument">PairLimit</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="___Pairs__Remaining.html" title="whether to display the number of S-pairs remaining">PairsRemaining</a> -- whether to display the number of S-pairs remaining</span></span></li>
<li><span><span><a href="___Parenthesize.html" title="">Parenthesize</a></span></span></li>
<li><span><span><a href="_parsing_spprecedence_cm_spin_spdetail.html" title="">parsing precedence, in detail</a></span></span></li>
<li><span><span><a href="_part.html" title="select terms of a polynomial by degree or weight">part</a> -- select terms of a polynomial by degree or weight</span></span></li>
<li><span><span><a href="_part_lp__List_cm__Ring__Element_rp.html" title="sum of terms of a polynomial of a given degree(s)">part(List,RingElement)</a> -- sum of terms of a polynomial of a given degree(s)</span></span></li>
<li><span><span><a href="_part_lp__Z__Z_cm__Z__Z_cm__Visible__List_cm__Ring__Element_rp.html" title="select terms of a polynomial by degree or weight">part(ZZ,ZZ,VisibleList,RingElement)</a> -- select terms of a polynomial by degree or weight</span></span></li>
<li><span><span><a href="___Partition.html" title="a type of list representing a partition of a natural number">Partition</a> -- a type of list representing a partition of a natural number</span></span></li>
<li><span><span><a href="_partition.html" title="partition a set or list by values of a function">partition</a> -- partition a set or list by values of a function</span></span></li>
<li><span><span><a href="___Partition_sp_us_sp__Z__Z.html" title="get element">Partition _ ZZ</a> -- get element</span></span></li>
<li><span><span><a href="_partitions.html" title="list the partitions of an integer">partitions</a> -- list the partitions of an integer</span></span></li>
<li><span><span><a href="_partitions_lp__Z__Z_rp.html" title="list the partitions of an integer">partitions(ZZ)</a> -- list the partitions of an integer</span></span></li>
<li><span><span><a href="_partitions_lp__Z__Z_cm__Z__Z_rp.html" title="list the partitions of an integer">partitions(ZZ,ZZ)</a> -- list the partitions of an integer</span></span></li>
<li><span><span><a href="_parts_lp__Ring__Element_rp.html" title="display a polynomial degree by degree">parts(RingElement)</a> -- display a polynomial degree by degree</span></span></li>
<li><span><span><a href="_pdim.html" title="calculate the projective dimension">pdim</a> -- calculate the projective dimension</span></span></li>
<li><span><span><a href="_pdim_lp__Coherent__Sheaf_rp.html" title="calculate the projective dimension">pdim(CoherentSheaf)</a> -- calculate the projective dimension</span></span></li>
<li><span><span><a href="_pdim_lp__Module_rp.html" title="calculate the projective dimension of a module">pdim(Module)</a> -- calculate the projective dimension of a module</span></span></li>
<li><span><span><a href="_peek.html" title="examine contents of an object">peek</a> -- examine contents of an object</span></span></li>
<li><span><span><a href="_peek_sq_lp__Z__Z_cm__Thing_rp.html" title="examine contents of an object">peek'(ZZ,Thing)</a> -- examine contents of an object</span></span></li>
<li><span><span><a href="_permanents.html" title="ideal generated by square permanents of a matrix">permanents</a> -- ideal generated by square permanents of a matrix</span></span></li>
<li><span><span><a href="_permutations.html" title="produce all permutations of a list">permutations</a> -- produce all permutations of a list</span></span></li>
<li><span><span><a href="_pfaffians.html" title="ideal generated by Pfaffians">pfaffians</a> -- ideal generated by Pfaffians</span></span></li>
<li><span><span><a href="_pi.html" title="">pi</a></span></span></li>
<li><span><span><a href="_pivots_lp__Matrix_rp.html" title="list of pivot locations of a matrix">pivots(Matrix)</a> -- list of pivot locations of a matrix</span></span></li>
<li><span><span><a href="_plus.html" title="addition">plus</a> -- addition</span></span></li>
<li><span><span><a href="_poincare.html" title="assemble degrees into polynomial">poincare</a> -- assemble degrees into polynomial</span></span></li>
<li><span><span><a href="_poincare_lp__Chain__Complex_rp.html" title="assemble degrees of a chain complex into a polynomial">poincare(ChainComplex)</a> -- assemble degrees of a chain complex into a polynomial</span></span></li>
<li><span><span><a href="_poincare_lp__Ideal_rp.html" title="assemble degrees of the quotient of the ambient ring by an ideal into a polynomial">poincare(Ideal)</a> -- assemble degrees of the quotient of the ambient ring by an ideal into a polynomial</span></span></li>
<li><span><span><a href="_poincare_lp__Module_rp.html" title="assemble degrees of an module into a polynomial">poincare(Module)</a> -- assemble degrees of an module into a polynomial</span></span></li>
<li><span><span><a href="_poincare_lp__Ring_rp.html" title="assemble degrees of an ring into a polynomial">poincare(Ring)</a> -- assemble degrees of an ring into a polynomial</span></span></li>
<li><span><span><a href="_poincare__N.html" title="assemble degrees into polynomial">poincareN</a> -- assemble degrees into polynomial</span></span></li>
<li><span><span><a href="___Polynomial__Ring.html" title="the class of all ordered monoid rings">PolynomialRing</a> -- the class of all ordered monoid rings</span></span></li>
<li><span><span><a href="_position_lp..._cm_sp__Reverse_sp_eq_gt_sp..._rp.html" title="search the list in reverse order">position(..., Reverse => ...)</a> -- search the list in reverse order</span></span></li>
<li><span><span><a href="_position_lp__Visible__List_cm__Visible__List_cm__Function_rp.html" title="find first element of a list satisfying a condition">position(VisibleList,VisibleList,Function)</a> -- find first element of a list satisfying a condition</span></span></li>
<li><span><span><a href="___Power.html" title="the class of all power expressions">Power</a> -- the class of all power expressions</span></span></li>
<li><span><span><a href="_power.html" title="power">power</a> -- power</span></span></li>
<li><span><span><a href="_powermod.html" title="powers of integers mod N">powermod</a> -- powers of integers mod N</span></span></li>
<li><span><span><a href="_powers.html" title="">powers</a></span></span></li>
<li><span><span><a href="_precision.html" title="">precision</a></span></span></li>
<li><span><span><a href="_prefix__Path.html" title="absolute locations of Macaulay2 files">prefixPath</a> -- absolute locations of Macaulay2 files</span></span></li>
<li><span><span><a href="_preimage.html" title="preimage of an ideal under a ring map">preimage</a> -- preimage of an ideal under a ring map</span></span></li>
<li><span><span><a href="_prepend_lp__Thing_cm__Basic__List_rp.html" title="add an element to the beginning of a list">prepend(Thing,BasicList)</a> -- add an element to the beginning of a list</span></span></li>
<li><span><span><a href="_presentation.html" title="presentation of a module or ring">presentation</a> -- presentation of a module or ring</span></span></li>
<li><span><span><a href="_presentation_lp__Module_rp.html" title="presentation of a module">presentation(Module)</a> -- presentation of a module</span></span></li>
<li><span><span><a href="_presentation_lp__Polynomial__Ring_cm__Quotient__Ring_rp.html" title="presentation of a quotient ring">presentation(PolynomialRing,QuotientRing)</a> -- presentation of a quotient ring</span></span></li>
<li><span><span><a href="_pretty.html" title="a pretty printer">pretty</a> -- a pretty printer</span></span></li>
<li><span><span><a href="___Primary__Tag.html" title="for internal use only: a symbol used in storing documentation">PrimaryTag</a> -- for internal use only: a symbol used in storing documentation</span></span></li>
<li><span><span><a href="___Primitive__Element.html" title="specify a primitive element">PrimitiveElement</a> -- specify a primitive element</span></span></li>
<li><span><span><a href="___Print.html" title="top level method for printing results">Print</a> -- top level method for printing results</span></span></li>
<li><span><span><a href="_print.html" title="print something">print</a> -- print something</span></span></li>
<li><span><span><a href="_printing__Accuracy.html" title="current accuracy for printing numbers">printingAccuracy</a> -- current accuracy for printing numbers</span></span></li>
<li><span><span><a href="_printing__Lead__Limit.html" title="maximum number of leading zeroes to use when printing real numbers">printingLeadLimit</a> -- maximum number of leading zeroes to use when printing real numbers</span></span></li>
<li><span><span><a href="_printing__Precision.html" title="current precision for printing numbers">printingPrecision</a> -- current precision for printing numbers</span></span></li>
<li><span><span><a href="_printing__Separator.html" title="string used to separate mantissa from exponent when printing real numbers">printingSeparator</a> -- string used to separate mantissa from exponent when printing real numbers</span></span></li>
<li><span><span><a href="_printing__Time__Limit.html" title="">printingTimeLimit</a></span></span></li>
<li><span><span><a href="_printing__Trail__Limit.html" title="maximum number of additional trailing digits to use when printing real numbers">printingTrailLimit</a> -- maximum number of additional trailing digits to use when printing real numbers</span></span></li>
<li><span><span><a href="_print__String.html" title="lowlevel function to print a string, net, or symbol">printString</a> -- lowlevel function to print a string, net, or symbol</span></span></li>
<li><span><span><a href="_print__Width.html" title="">printWidth</a></span></span></li>
<li><span><span><a href="___Product.html" title="the class of all product expressions">Product</a> -- the class of all product expressions</span></span></li>
<li><span><span><a href="_product.html" title="">product</a></span></span></li>
<li><span><span><a href="_product_lp__List_rp.html" title="product of elements">product(List)</a> -- product of elements</span></span></li>
<li><span><span><a href="_product_lp__Set_rp.html" title="product of elements">product(Set)</a> -- product of elements</span></span></li>
<li><span><span><a href="_product_lp__Tally_rp.html" title="product of elements">product(Tally)</a> -- product of elements</span></span></li>
<li><span><span><a href="_product_lp__Visible__List_cm__Function_rp.html" title="product of values of a function">product(VisibleList,Function)</a> -- product of values of a function</span></span></li>
<li><span><span><a href="_product_lp__Visible__List_cm__Visible__List_cm__Function_rp.html" title="product of results of applying a function pairwise">product(VisibleList,VisibleList,Function)</a> -- product of results of applying a function pairwise</span></span></li>
<li><span><span><a href="_product_lp__Z__Z_cm__Function_rp.html" title="product of consecutive values of a function">product(ZZ,Function)</a> -- product of consecutive values of a function</span></span></li>
<li><span><span><a href="___Product__Order.html" title="product ordering">ProductOrder</a> -- product ordering</span></span></li>
<li><span><span><a href="_profile.html" title="profile a function">profile</a> -- profile a function</span></span></li>
<li><span><span><a href="_profile__Summary.html" title="display profiling data">profileSummary</a> -- display profiling data</span></span></li>
<li><span><span><a href="___Proj_lp__Ring_rp.html" title="make a projective variety">Proj(Ring)</a> -- make a projective variety</span></span></li>
<li><span><span><a href="___Projective.html" title="whether to produce a projective Hilbert polynomial">Projective</a> -- whether to produce a projective Hilbert polynomial</span></span></li>
<li><span><span><a href="___Projective__Hilbert__Polynomial.html" title="the class of all Hilbert polynomials">ProjectiveHilbertPolynomial</a> -- the class of all Hilbert polynomials</span></span></li>
<li><span><span><a href="_projective__Hilbert__Polynomial.html" title="Hilbert polynomial of projective space">projectiveHilbertPolynomial</a> -- Hilbert polynomial of projective space</span></span></li>
<li><span><span><a href="___Projective__Hilbert__Polynomial_sp__Z__Z.html" title="value of polynomial">ProjectiveHilbertPolynomial ZZ</a> -- value of polynomial</span></span></li>
<li><span><span><a href="___Projective__Variety.html" title="the class of all projective varieties">ProjectiveVariety</a> -- the class of all projective varieties</span></span></li>
<li><span><span><a href="_promote.html" title="promote to another ring">promote</a> -- promote to another ring</span></span></li>
<li><span><span><a href="_protect.html" title="protect a symbol">protect</a> -- protect a symbol</span></span></li>
<li><span><span><a href="_prune.html" title="prune, e.g., compute a minimal presentation">prune</a> -- prune, e.g., compute a minimal presentation</span></span></li>
<li><span><span><a href="_pruning__Map.html" title="">pruningMap</a></span></span></li>
<li><span><span><a href="___Pseudocode.html" title="the class of pseudocodes">Pseudocode</a> -- the class of pseudocodes</span></span></li>
<li><span><span><a href="_pseudocode.html" title="produce the pseudocode for a function">pseudocode</a> -- produce the pseudocode for a function</span></span></li>
<li><span><span><a href="_pseudo__Remainder.html" title="compute the pseudo-remainder">pseudoRemainder</a> -- compute the pseudo-remainder</span></span></li>
<li><span><span><a href="_push__Forward_lp__Ring__Map_cm__Module_rp.html" title="">pushForward(RingMap,Module)</a></span></span></li>
<li><span><span><a href="___Pushforward__Computation.html" title="a type of list used internally">PushforwardComputation</a> -- a type of list used internally</span></span></li>
<li><span><span><a href="___Q__Q.html" title="the class of all rational numbers">QQ</a> -- the class of all rational numbers</span></span></li>
<li><span><span><a href="___Quotient.html" title="value for an optional argument">Quotient</a> -- value for an optional argument</span></span></li>
<li><span><span><a href="_quotient.html" title="quotient or division">quotient</a> -- quotient or division</span></span></li>
<li><span><span><a href="_quotient_sq.html" title="matrix quotient (opposite)">quotient'</a> -- matrix quotient (opposite)</span></span></li>
<li><span><span><a href="_quotient_lp..._cm_sp__Basis__Element__Limit_sp_eq_gt_sp..._rp.html" title="">quotient(..., BasisElementLimit => ...)</a></span></span></li>
<li><span><span><a href="_quotient_lp..._cm_sp__Degree__Limit_sp_eq_gt_sp..._rp.html" title="">quotient(..., DegreeLimit => ...)</a></span></span></li>
<li><span><span><a href="_quotient_lp..._cm_sp__Minimal__Generators_sp_eq_gt_sp..._rp.html" title="Decides whether quotient computes and outputs a trimmed set of generators; default is true">quotient(..., MinimalGenerators => ...)</a> -- Decides whether quotient computes and outputs a trimmed set of generators; default is true</span></span></li>
<li><span><span><a href="_quotient_lp..._cm_sp__Pair__Limit_sp_eq_gt_sp..._rp.html" title="">quotient(..., PairLimit => ...)</a></span></span></li>
<li><span><span><a href="_quotient_lp..._cm_sp__Strategy_sp_eq_gt_sp..._rp.html" title="Possible strategies are: Iterate, Linear, and Quotient">quotient(..., Strategy => ...)</a> -- Possible strategies are: Iterate, Linear, and Quotient</span></span></li>
<li><span><span><a href="_quotient_lp__Ideal_cm__Ideal_rp.html" title="ideal or submodule quotient">quotient(Ideal,Ideal)</a> -- ideal or submodule quotient</span></span></li>
<li><span><span><a href="_quotient_lp__Matrix_cm__Groebner__Basis_rp.html" title="matrix quotient">quotient(Matrix,GroebnerBasis)</a> -- matrix quotient</span></span></li>
<li><span><span><a href="_quotient__Remainder.html" title="matrix quotient and remainder">quotientRemainder</a> -- matrix quotient and remainder</span></span></li>
<li><span><span><a href="_quotient__Remainder_sq.html" title="matrix quotient and remainder (opposite)">quotientRemainder'</a> -- matrix quotient and remainder (opposite)</span></span></li>
<li><span><span><a href="_quotient__Remainder_lp__Ring__Element_cm__Ring__Element_rp.html" title="quotient and remainder">quotientRemainder(RingElement,RingElement)</a> -- quotient and remainder</span></span></li>
<li><span><span><a href="___Quotient__Ring.html" title="the class of all quotient rings">QuotientRing</a> -- the class of all quotient rings</span></span></li>
<li><span><span><a href="_radical.html" title="the radical of an ideal">radical</a> -- the radical of an ideal</span></span></li>
<li><span><span><a href="_random.html" title="get a random element">random</a> -- get a random element</span></span></li>
<li><span><span><a href="_random_lp__List_rp.html" title="shuffle a list randomly">random(List)</a> -- shuffle a list randomly</span></span></li>
<li><span><span><a href="_random_lp__Module_cm__Module_rp.html" title="make a random module map">random(Module,Module)</a> -- make a random module map</span></span></li>
<li><span><span><a href="_random_lp__R__R_rp.html" title="random real number">random(RR)</a> -- random real number</span></span></li>
<li><span><span><a href="_random_lp__R__R_cm__R__R_rp.html" title="random real number">random(RR,RR)</a> -- random real number</span></span></li>
<li><span><span><a href="_random_lp__Type_rp.html" title="random element of a type">random(Type)</a> -- random element of a type</span></span></li>
<li><span><span><a href="_random_lp__Z__Z_rp.html" title="random integer">random(ZZ)</a> -- random integer</span></span></li>
<li><span><span><a href="_random_lp__Z__Z_cm__Z__Z_rp.html" title="random integer in a range">random(ZZ,ZZ)</a> -- random integer in a range</span></span></li>
<li><span><span><a href="_random__Mutable__Matrix_lp__Z__Z_cm__Z__Z_cm__R__R_cm__Z__Z_rp.html" title="a random mutable matrix of integers">randomMutableMatrix(ZZ,ZZ,RR,ZZ)</a> -- a random mutable matrix of integers</span></span></li>
<li><span><span><a href="_rank.html" title="compute the rank">rank</a> -- compute the rank</span></span></li>
<li><span><span><a href="_read.html" title="read from a file">read</a> -- read from a file</span></span></li>
<li><span><span><a href="_read_lp__File_rp.html" title="read from a file">read(File)</a> -- read from a file</span></span></li>
<li><span><span><a href="_read_lp__File_cm__Z__Z_rp.html" title="read from a file">read(File,ZZ)</a> -- read from a file</span></span></li>
<li><span><span><a href="_read_lp__Sequence_rp.html" title="read from a file">read(Sequence)</a> -- read from a file</span></span></li>
<li><span><span><a href="_read_lp__String_rp.html" title="read from a file">read(String)</a> -- read from a file</span></span></li>
<li><span><span><a href="___Real__Field.html" title="the class of all real fields">RealField</a> -- the class of all real fields</span></span></li>
<li><span><span><a href="_real__Part.html" title="real part">realPart</a> -- real part</span></span></li>
<li><span><span><a href="_recursion__Depth.html" title="the current recursion depth">recursionDepth</a> -- the current recursion depth</span></span></li>
<li><span><span><a href="_recursion__Limit.html" title="set the limit on recursion">recursionLimit</a> -- set the limit on recursion</span></span></li>
<li><span><span><a href="___Reduce.html" title="name for an optional argument">Reduce</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_reduce__Hilbert.html" title="reduce a Hilbert series expression">reduceHilbert</a> -- reduce a Hilbert series expression</span></span></li>
<li><span><span><a href="_register__Finalizer.html" title="register a string that will be displayed when an object is garbage collected">registerFinalizer</a> -- register a string that will be displayed when an object is garbage collected</span></span></li>
<li><span><span><a href="_regularity.html" title="compute the Castelnuovo-Mumford regularity">regularity</a> -- compute the Castelnuovo-Mumford regularity</span></span></li>
<li><span><span><a href="_regularity_lp..._cm_sp__Weights_sp_eq_gt_sp..._rp.html" title="">regularity(..., Weights => ...)</a></span></span></li>
<li><span><span><a href="_relations.html" title="the defining relations">relations</a> -- the defining relations</span></span></li>
<li><span><span><a href="_relativize__Filename.html" title="relativize a file name">relativizeFilename</a> -- relativize a file name</span></span></li>
<li><span><span><a href="_remainder.html" title="matrix remainder">remainder</a> -- matrix remainder</span></span></li>
<li><span><span><a href="_remainder_sq.html" title="matrix quotient and remainder (opposite)">remainder'</a> -- matrix quotient and remainder (opposite)</span></span></li>
<li><span><span><a href="___Remake__All__Documentation.html" title="name for an optional argument">RemakeAllDocumentation</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_remove__Hook.html" title="remove a hook function from an object">removeHook</a> -- remove a hook function from an object</span></span></li>
<li><span><span><a href="_remove__Hook_lp__Hash__Table_cm__Thing_cm__Function_rp.html" title="remove a hook function from an object">removeHook(HashTable,Thing,Function)</a> -- remove a hook function from an object</span></span></li>
<li><span><span><a href="_remove__Hook_lp__Symbol_cm__Function_rp.html" title="remove a hook function from an object">removeHook(Symbol,Function)</a> -- remove a hook function from an object</span></span></li>
<li><span><span><a href="_remove__Lowest__Dimension.html" title="remove components of lowest dimension">removeLowestDimension</a> -- remove components of lowest dimension</span></span></li>
<li><span><span><a href="_reorganize.html" title="reorganize a database file">reorganize</a> -- reorganize a database file</span></span></li>
<li><span><span><a href="_replace_lp__String_cm__String_cm__String_rp.html" title="regular expression replacement of substrings">replace(String,String,String)</a> -- regular expression replacement of substrings</span></span></li>
<li><span><span><a href="_replace_lp__Z__Z_cm__Thing_cm__Visible__List_rp.html" title="copy a list, replacing an element">replace(ZZ,Thing,VisibleList)</a> -- copy a list, replacing an element</span></span></li>
<li><span><span><a href="___Rerun__Examples.html" title="name for an optional argument">RerunExamples</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_reshape_lp__Module_cm__Module_cm__Matrix_rp.html" title="reshape a matrix">reshape(Module,Module,Matrix)</a> -- reshape a matrix</span></span></li>
<li><span><span><a href="___Resolution.html" title="the class of all resolution computations">Resolution</a> -- the class of all resolution computations</span></span></li>
<li><span><span><a href="_resolution.html" title="projective resolution">resolution</a> -- projective resolution</span></span></li>
<li><span><span><a href="_resolution_lp..._cm_sp__Degree__Limit_sp_eq_gt_sp..._rp.html" title="compute only up to this degree">resolution(..., DegreeLimit => ...)</a> -- compute only up to this degree</span></span></li>
<li><span><span><a href="_resolution_lp..._cm_sp__Hard__Degree__Limit_sp_eq_gt_sp..._rp.html" title="">resolution(..., HardDegreeLimit => ...)</a></span></span></li>
<li><span><span><a href="_resolution_lp..._cm_sp__Length__Limit_sp_eq_gt_sp..._rp.html" title="stop when the resolution reaches this length">resolution(..., LengthLimit => ...)</a> -- stop when the resolution reaches this length</span></span></li>
<li><span><span><a href="_resolution_lp..._cm_sp__Pair__Limit_sp_eq_gt_sp..._rp.html" title="stop when this number of pairs has been handled">resolution(..., PairLimit => ...)</a> -- stop when this number of pairs has been handled</span></span></li>
<li><span><span><a href="_resolution_lp..._cm_sp__Sort__Strategy_sp_eq_gt_sp..._rp.html" title="">resolution(..., SortStrategy => ...)</a></span></span></li>
<li><span><span><a href="_resolution_lp..._cm_sp__Stop__Before__Computation_sp_eq_gt_sp..._rp.html" title="whether to stop the computation immediately">resolution(..., StopBeforeComputation => ...)</a> -- whether to stop the computation immediately</span></span></li>
<li><span><span><a href="_resolution_lp..._cm_sp__Strategy_sp_eq_gt_sp..._rp.html" title="">resolution(..., Strategy => ...)</a></span></span></li>
<li><span><span><a href="_resolution_lp..._cm_sp__Syzygy__Limit_sp_eq_gt_sp..._rp.html" title="stop when this number of syzygies are obtained">resolution(..., SyzygyLimit => ...)</a> -- stop when this number of syzygies are obtained</span></span></li>
<li><span><span><a href="_resolution_lp__Ideal_rp.html" title="compute a projective resolution of (the quotient ring corresponding to) an ideal">resolution(Ideal)</a> -- compute a projective resolution of (the quotient ring corresponding to) an ideal</span></span></li>
<li><span><span><a href="_resolution_lp__Matrix_rp.html" title="given a module map represented by a matrix, produce a comparison map between resolutions of its source and target">resolution(Matrix)</a> -- given a module map represented by a matrix, produce a comparison map between resolutions of its source and target</span></span></li>
<li><span><span><a href="_resolution_lp__Module_rp.html" title="compute a projective resolution of a module">resolution(Module)</a> -- compute a projective resolution of a module</span></span></li>
<li><span><span><a href="___Result.html" title="name for an optional argument">Result</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_return.html" title="return from a function">return</a> -- return from a function</span></span></li>
<li><span><span><a href="_return__Code.html" title="">returnCode</a></span></span></li>
<li><span><span><a href="___Reverse.html" title="name for an optional argument">Reverse</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="___Right.html" title="value for an optional argument">Right</a> -- value for an optional argument</span></span></li>
<li><span><span><a href="_right_spshift.html" title="">right shift</a></span></span></li>
<li><span><span><a href="___Ring.html" title="the class of all rings">Ring</a> -- the class of all rings</span></span></li>
<li><span><span><a href="_ring.html" title="get the associated ring of an object">ring</a> -- get the associated ring of an object</span></span></li>
<li><span><span><a href="___Ring_sp_st_st_sp__Ring.html" title="tensor product">Ring ** Ring</a> -- tensor product</span></span></li>
<li><span><span><a href="___Ring_sp_sl_sp__Ideal.html" title="make a quotient ring">Ring / Ideal</a> -- make a quotient ring</span></span></li>
<li><span><span><a href="___Ring_sp^_sp__List.html" title="make a free module">Ring ^ List</a> -- make a free module</span></span></li>
<li><span><span><a href="___Ring_sp^_sp__Z__Z.html" title="make a free module">Ring ^ ZZ</a> -- make a free module</span></span></li>
<li><span><span><a href="___Ring_sp_us_sp__List.html" title="make a monomial from a list of exponents">Ring _ List</a> -- make a monomial from a list of exponents</span></span></li>
<li><span><span><a href="___Ring_sp_us_sp__String.html" title="get a ring variable by name">Ring _ String</a> -- get a ring variable by name</span></span></li>
<li><span><span><a href="___Ring_sp_us_sp__Z__Z.html" title="get a ring variable by index">Ring _ ZZ</a> -- get a ring variable by index</span></span></li>
<li><span><span><a href="___Ring_sp__Array.html" title="the standard way to make a polynomial ring">Ring Array</a> -- the standard way to make a polynomial ring</span></span></li>
<li><span><span><a href="___Ring_sp__List.html" title="make a local polynomial ring">Ring List</a> -- make a local polynomial ring</span></span></li>
<li><span><span><a href="___Ring_sp__Ordered__Monoid.html" title="make a polynomial ring">Ring OrderedMonoid</a> -- make a polynomial ring</span></span></li>
<li><span><span><a href="___Ring__Element.html" title="the class of all ring elements handled by the engine">RingElement</a> -- the class of all ring elements handled by the engine</span></span></li>
<li><span><span><a href="___Ring__Element_sp.._sp__Ring__Element.html" title="a sequence of consecutive generators of a polynomial ring">RingElement .. RingElement</a> -- a sequence of consecutive generators of a polynomial ring</span></span></li>
<li><span><span><a href="___Ring__Element_sp.._lt_sp__Ring__Element.html" title="a sequence of consecutive generators of a polynomial ring">RingElement ..< RingElement</a> -- a sequence of consecutive generators of a polynomial ring</span></span></li>
<li><span><span><a href="___Ring__Element_sp_sl_sp__Ring__Element.html" title="fraction">RingElement / RingElement</a> -- fraction</span></span></li>
<li><span><span><a href="___Ring__Element_sp^_sp__Z__Z.html" title="power">RingElement ^ ZZ</a> -- power</span></span></li>
<li><span><span><a href="___Ring__Element_sp__Array.html" title="substitution of variables">RingElement Array</a> -- substitution of variables</span></span></li>
<li><span><span><a href="___Ring__Family.html" title="">RingFamily</a></span></span></li>
<li><span><span><a href="___Ring__Family_sp_us_st.html" title="a unary postfix operator, used for indicating pushforward maps">RingFamily _*</a> -- a unary postfix operator, used for indicating pushforward maps</span></span></li>
<li><span><span><a href="___Ring__Map.html" title="the class of all ring maps">RingMap</a> -- the class of all ring maps</span></span></li>
<li><span><span><a href="___Ring__Map_sp_st_st_sp__Matrix.html" title="tensor product of a module map via a ring map">RingMap ** Matrix</a> -- tensor product of a module map via a ring map</span></span></li>
<li><span><span><a href="___Ring__Map_sp_st_st_sp__Module.html" title="tensor product of a module via a ring map">RingMap ** Module</a> -- tensor product of a module via a ring map</span></span></li>
<li><span><span><a href="___Ring__Map_sp__Ring__Element.html" title="apply a ring map">RingMap RingElement</a> -- apply a ring map</span></span></li>
<li><span><span><a href="_root__Path.html" title="">rootPath</a></span></span></li>
<li><span><span><a href="_root__U__R__I.html" title="">rootURI</a></span></span></li>
<li><span><span><a href="_rotate_lp__Z__Z_cm__Visible__List_rp.html" title="rotate a list">rotate(ZZ,VisibleList)</a> -- rotate a list</span></span></li>
<li><span><span><a href="_round.html" title="round a number">round</a> -- round a number</span></span></li>
<li><span><span><a href="_row_spand_spcolumn_spoperations.html" title="">row and column operations</a></span></span></li>
<li><span><span><a href="_row__Add.html" title="add a multiple of one row to another">rowAdd</a> -- add a multiple of one row to another</span></span></li>
<li><span><span><a href="___Row__Expression.html" title="the class of all matrix expressions">RowExpression</a> -- the class of all matrix expressions</span></span></li>
<li><span><span><a href="_row__Mult.html" title="multiply a row by a ring element">rowMult</a> -- multiply a row by a ring element</span></span></li>
<li><span><span><a href="_row__Permute.html" title="permute some rows">rowPermute</a> -- permute some rows</span></span></li>
<li><span><span><a href="_row__Swap.html" title="interchange rows">rowSwap</a> -- interchange rows</span></span></li>
<li><span><span><a href="___R__R.html" title="the class of all real numbers">RR</a> -- the class of all real numbers</span></span></li>
<li><span><span><a href="_rsort_lp..._cm_sp__Degree__Order_sp_eq_gt_sp..._rp.html" title="specify Ascending, Descending, or null">rsort(..., DegreeOrder => ...)</a> -- specify Ascending, Descending, or null</span></span></li>
<li><span><span><a href="_rsort_lp..._cm_sp__Monomial__Order_sp_eq_gt_sp..._rp.html" title="specify Ascending or Descending monomial order">rsort(..., MonomialOrder => ...)</a> -- specify Ascending or Descending monomial order</span></span></li>
<li><span><span><a href="___Run__Examples.html" title="name for an optional argument">RunExamples</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_run__Hooks.html" title="run the hook functions stored in an object">runHooks</a> -- run the hook functions stored in an object</span></span></li>
<li><span><span><a href="_run__Hooks_lp__Hash__Table_cm__Thing_cm__Thing_rp.html" title="run the hook functions stored in an object">runHooks(HashTable,Thing,Thing)</a> -- run the hook functions stored in an object</span></span></li>
<li><span><span><a href="_run__Hooks_lp__Symbol_cm__Thing_rp.html" title="run the hook functions stored in an object">runHooks(Symbol,Thing)</a> -- run the hook functions stored in an object</span></span></li>
<li><span><span><a href="_run__Length__Encode_lp__Visible__List_rp.html" title="run length encoding">runLengthEncode(VisibleList)</a> -- run length encoding</span></span></li>
<li><span><span><a href="_same.html" title="whether everything in a list is the same">same</a> -- whether everything in a list is the same</span></span></li>
<li><span><span><a href="_saturate.html" title="saturation of ideal or submodule">saturate</a> -- saturation of ideal or submodule</span></span></li>
<li><span><span><a href="_saturate_lp..._cm_sp__Basis__Element__Limit_sp_eq_gt_sp..._rp.html" title="">saturate(..., BasisElementLimit => ...)</a></span></span></li>
<li><span><span><a href="_saturate_lp..._cm_sp__Degree__Limit_sp_eq_gt_sp..._rp.html" title="">saturate(..., DegreeLimit => ...)</a></span></span></li>
<li><span><span><a href="_saturate_lp..._cm_sp__Minimal__Generators_sp_eq_gt_sp..._rp.html" title="whether to compute minimal generators">saturate(..., MinimalGenerators => ...)</a> -- whether to compute minimal generators</span></span></li>
<li><span><span><a href="_saturate_lp..._cm_sp__Pair__Limit_sp_eq_gt_sp..._rp.html" title="">saturate(..., PairLimit => ...)</a></span></span></li>
<li><span><span><a href="_saturate_lp..._cm_sp__Strategy_sp_eq_gt_sp..._rp.html" title="">saturate(..., Strategy => ...)</a></span></span></li>
<li><span><span><a href="_scan.html" title="apply a function to each element">scan</a> -- apply a function to each element</span></span></li>
<li><span><span><a href="_scan_lp__Z__Z_cm__Function_rp.html" title="apply a function to 0 .. n-1">scan(ZZ,Function)</a> -- apply a function to 0 .. n-1</span></span></li>
<li><span><span><a href="_scan__Keys.html" title="apply a function to each key in a hash table or database">scanKeys</a> -- apply a function to each key in a hash table or database</span></span></li>
<li><span><span><a href="_scan__Lines.html" title="apply a function to each line of a file">scanLines</a> -- apply a function to each line of a file</span></span></li>
<li><span><span><a href="_scan__Pairs.html" title="apply a function to pairs in a hash table">scanPairs</a> -- apply a function to pairs in a hash table</span></span></li>
<li><span><span><a href="_scan__Pairs_lp__Hash__Table_cm__Function_rp.html" title="apply a function to pairs in a hash table">scanPairs(HashTable,Function)</a> -- apply a function to pairs in a hash table</span></span></li>
<li><span><span><a href="_scan__Values.html" title="apply a function to each value in a hash table">scanValues</a> -- apply a function to each value in a hash table</span></span></li>
<li><span><span><a href="_schreyer__Order.html" title="create or obtain free modules with Schryer monomial orders">schreyerOrder</a> -- create or obtain free modules with Schryer monomial orders</span></span></li>
<li><span><span><a href="_schreyer__Order_lp__Matrix_rp.html" title="create a matrix with the same entries whose source free module has a Schreyer monomial order">schreyerOrder(Matrix)</a> -- create a matrix with the same entries whose source free module has a Schreyer monomial order</span></span></li>
<li><span><span><a href="_schreyer__Order_lp__Module_rp.html" title="obtain Schreyer order information">schreyerOrder(Module)</a> -- obtain Schreyer order information</span></span></li>
<li><span><span><a href="___Schubert_lp__Z__Z_cm__Z__Z_cm__Visible__List_rp.html" title="find the Pluecker ideal of a Schubert variety">Schubert(ZZ,ZZ,VisibleList)</a> -- find the Pluecker ideal of a Schubert variety</span></span></li>
<li><span><span><a href="_script__Command__Line.html" title="the command line arguments to be used when running a script">scriptCommandLine</a> -- the command line arguments to be used when running a script</span></span></li>
<li><span><span><a href="___Scripted__Functor.html" title="the class of all scripted functors">ScriptedFunctor</a> -- the class of all scripted functors</span></span></li>
<li><span><span><a href="_search__Path_lp__List_cm__String_rp.html" title="search a path for a file">searchPath(List,String)</a> -- search a path for a file</span></span></li>
<li><span><span><a href="_sec.html" title="secant">sec</a> -- secant</span></span></li>
<li><span><span><a href="_sech.html" title="hyperbolic secant">sech</a> -- hyperbolic secant</span></span></li>
<li><span><span><a href="_see__Parsing.html" title="display parsing precedence table for Macaulay2 operators">seeParsing</a> -- display parsing precedence table for Macaulay2 operators</span></span></li>
<li><span><span><a href="_select.html" title="select from a list, hash table, or string">select</a> -- select from a list, hash table, or string</span></span></li>
<li><span><span><a href="_select_lp__Hash__Table_cm__Function_rp.html" title="select part of a hash table">select(HashTable,Function)</a> -- select part of a hash table</span></span></li>
<li><span><span><a href="_select_lp__Z__Z_cm__Hash__Table_cm__Function_rp.html" title="select a limited number of pairs from a hash table">select(ZZ,HashTable,Function)</a> -- select a limited number of pairs from a hash table</span></span></li>
<li><span><span><a href="_select__In__Subring.html" title="select columns in a subring">selectInSubring</a> -- select columns in a subring</span></span></li>
<li><span><span><a href="_select__Variables_lp__List_cm__Polynomial__Ring_rp.html" title="make a subring of a polynomial ring generated by selected variables">selectVariables(List,PolynomialRing)</a> -- make a subring of a polynomial ring generated by selected variables</span></span></li>
<li><span><span><a href="___Self__Initializing__Type.html" title="the class of all self initializing types">SelfInitializingType</a> -- the class of all self initializing types</span></span></li>
<li><span><span><a href="___Separate__Exec.html" title="name for an optional argument">SeparateExec</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_separate__Regexp.html" title="separate a string into pieces, with separators determined by a regular expression">separateRegexp</a> -- separate a string into pieces, with separators determined by a regular expression</span></span></li>
<li><span><span><a href="_separate__Regexp_lp__String_cm__String_rp.html" title="separate a string into pieces, with separators determined by a regular expression">separateRegexp(String,String)</a> -- separate a string into pieces, with separators determined by a regular expression</span></span></li>
<li><span><span><a href="_separate__Regexp_lp__String_cm__Z__Z_cm__String_rp.html" title="separate a string into pieces, with separators determined by a regular expression">separateRegexp(String,ZZ,String)</a> -- separate a string into pieces, with separators determined by a regular expression</span></span></li>
<li><span><span><a href="___Set.html" title="the class of all sets">Set</a> -- the class of all sets</span></span></li>
<li><span><span><a href="_set.html" title="make a set">set</a> -- make a set</span></span></li>
<li><span><span><a href="___Set_sp_sh_qu_sp__Thing.html" title="test set membership">Set #? Thing</a> -- test set membership</span></span></li>
<li><span><span><a href="___Set_sp_st_sp__Set.html" title="intersection of sets">Set * Set</a> -- intersection of sets</span></span></li>
<li><span><span><a href="___Set_sp_st_st_sp__Set.html" title="Cartesian product">Set ** Set</a> -- Cartesian product</span></span></li>
<li><span><span><a href="___Set_sp_pl_sp__Set.html" title="set union">Set + Set</a> -- set union</span></span></li>
<li><span><span><a href="___Set_sp-_sp__Set.html" title="set difference">Set - Set</a> -- set difference</span></span></li>
<li><span><span><a href="_set__Group__I__D.html" title="set the process group identifier">setGroupID</a> -- set the process group identifier</span></span></li>
<li><span><span><a href="_set__Random__Seed.html" title="set starting point for random number generator">setRandomSeed</a> -- set starting point for random number generator</span></span></li>
<li><span><span><a href="_set__Random__Seed_lp_rp.html" title="set starting point for random number generator">setRandomSeed()</a> -- set starting point for random number generator</span></span></li>
<li><span><span><a href="_set__Random__Seed_lp__String_rp.html" title="set starting point for random number generator">setRandomSeed(String)</a> -- set starting point for random number generator</span></span></li>
<li><span><span><a href="_set__Random__Seed_lp__Z__Z_rp.html" title="set starting point for random number generator">setRandomSeed(ZZ)</a> -- set starting point for random number generator</span></span></li>
<li><span><span><a href="_setup.html" title="">setup</a></span></span></li>
<li><span><span><a href="_setup__Emacs.html" title="">setupEmacs</a></span></span></li>
<li><span><span><a href="_sheaf.html" title="make a coherent sheaf">sheaf</a> -- make a coherent sheaf</span></span></li>
<li><span><span><a href="_sheaf_lp__Module_rp.html" title="make a coherent sheaf">sheaf(Module)</a> -- make a coherent sheaf</span></span></li>
<li><span><span><a href="_sheaf_lp__Ring_rp.html" title="make a coherent sheaf of rings">sheaf(Ring)</a> -- make a coherent sheaf of rings</span></span></li>
<li><span><span><a href="_sheaf_lp__Variety_rp.html" title="make a coherent sheaf">sheaf(Variety)</a> -- make a coherent sheaf</span></span></li>
<li><span><span><a href="_sheaf_lp__Variety_cm__Module_rp.html" title="make a coherent sheaf">sheaf(Variety,Module)</a> -- make a coherent sheaf</span></span></li>
<li><span><span><a href="_sheaf_lp__Variety_cm__Ring_rp.html" title="make a coherent sheaf of rings">sheaf(Variety,Ring)</a> -- make a coherent sheaf of rings</span></span></li>
<li><span><span><a href="_sheaf__Ext^__Z__Z_lp__Coherent__Sheaf_cm__Coherent__Sheaf_rp.html" title="sheaf Ext of coherent sheaves">sheafExt^ZZ(CoherentSheaf,CoherentSheaf)</a> -- sheaf Ext of coherent sheaves</span></span></li>
<li><span><span><a href="_sheaf__Hom_lp__Coherent__Sheaf_cm__Coherent__Sheaf_rp.html" title="sheaf Hom">sheafHom(CoherentSheaf,CoherentSheaf)</a> -- sheaf Hom</span></span></li>
<li><span><span><a href="___Sheaf__Of__Rings.html" title="the class of sheaves of rings">SheafOfRings</a> -- the class of sheaves of rings</span></span></li>
<li><span><span><a href="___Sheaf__Of__Rings_sp^_sp__List.html" title="make a graded free coherent sheaf">SheafOfRings ^ List</a> -- make a graded free coherent sheaf</span></span></li>
<li><span><span><a href="_shield.html" title="shield evaluation from interrupts">shield</a> -- shield evaluation from interrupts</span></span></li>
<li><span><span><a href="_show.html" title="display various TeX, hypertext, or a URL, in an external application">show</a> -- display various TeX, hypertext, or a URL, in an external application</span></span></li>
<li><span><span><a href="_show__Class__Structure.html" title="display class structure">showClassStructure</a> -- display class structure</span></span></li>
<li><span><span><a href="_show__Html.html" title="convert hypertext to html and display with a browser">showHtml</a> -- convert hypertext to html and display with a browser</span></span></li>
<li><span><span><a href="_show__Structure.html" title="display parent structure">showStructure</a> -- display parent structure</span></span></li>
<li><span><span><a href="_show__Tex.html" title="convert to TeX and display on screen">showTex</a> -- convert to TeX and display on screen</span></span></li>
<li><span><span><a href="_show__User__Structure.html" title="show parent structure for those types defined by user">showUserStructure</a> -- show parent structure for those types defined by user</span></span></li>
<li><span><span><a href="_sin.html" title="compute the sine">sin</a> -- compute the sine</span></span></li>
<li><span><span><a href="_singular__Locus.html" title="singular locus">singularLocus</a> -- singular locus</span></span></li>
<li><span><span><a href="_sinh.html" title="compute the hyperbolic sine">sinh</a> -- compute the hyperbolic sine</span></span></li>
<li><span><span><a href="_size.html" title="the size of an object">size</a> -- the size of an object</span></span></li>
<li><span><span><a href="_size2.html" title="number of binary digits to the left of the point">size2</a> -- number of binary digits to the left of the point</span></span></li>
<li><span><span><a href="___Size__Limit.html" title="name for an optional argument">SizeLimit</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_smith__Normal__Form_lp__Matrix_rp.html" title="smith normal form for a matrix over ZZ or a PID">smithNormalForm(Matrix)</a> -- smith normal form for a matrix over ZZ or a PID</span></span></li>
<li><span><span><a href="_solve.html" title="solve a linear equation">solve</a> -- solve a linear equation</span></span></li>
<li><span><span><a href="_some__Terms.html" title="select some terms of a polynomial">someTerms</a> -- select some terms of a polynomial</span></span></li>
<li><span><span><a href="___Sort.html" title="">Sort</a></span></span></li>
<li><span><span><a href="_sort_lp..._cm_sp__Degree__Order_sp_eq_gt_sp..._rp.html" title="specify Ascending, Descending, or null">sort(..., DegreeOrder => ...)</a> -- specify Ascending, Descending, or null</span></span></li>
<li><span><span><a href="_sort_lp..._cm_sp__Monomial__Order_sp_eq_gt_sp..._rp.html" title="specify Ascending or Descending monomial order">sort(..., MonomialOrder => ...)</a> -- specify Ascending or Descending monomial order</span></span></li>
<li><span><span><a href="_sort_lp__List_rp.html" title="sort a list">sort(List)</a> -- sort a list</span></span></li>
<li><span><span><a href="_sort_lp__Matrix_rp.html" title="sort the columns of a matrix">sort(Matrix)</a> -- sort the columns of a matrix</span></span></li>
<li><span><span><a href="_sort__Columns.html" title="permutation giving sort order">sortColumns</a> -- permutation giving sort order</span></span></li>
<li><span><span><a href="_sort__Columns_lp..._cm_sp__Degree__Order_sp_eq_gt_sp..._rp.html" title="specify Ascending, Descending, or null">sortColumns(..., DegreeOrder => ...)</a> -- specify Ascending, Descending, or null</span></span></li>
<li><span><span><a href="_sort__Columns_lp..._cm_sp__Monomial__Order_sp_eq_gt_sp..._rp.html" title="specify Ascending or Descending monomial order">sortColumns(..., MonomialOrder => ...)</a> -- specify Ascending or Descending monomial order</span></span></li>
<li><span><span><a href="___Sort__Strategy.html" title="specify a strategy for sorting S-pairs">SortStrategy</a> -- specify a strategy for sorting S-pairs</span></span></li>
<li><span><span><a href="_source.html" title="source of a map">source</a> -- source of a map</span></span></li>
<li><span><span><a href="_source_lp__Chain__Complex__Map_rp.html" title=" find the source of a map of chain complexes">source(ChainComplexMap)</a> -- find the source of a map of chain complexes</span></span></li>
<li><span><span><a href="_source_lp__Graded__Module__Map_rp.html" title="find the source of a map of graded modules">source(GradedModuleMap)</a> -- find the source of a map of graded modules</span></span></li>
<li><span><span><a href="_source_lp__Matrix_rp.html" title="find the source module of matrix">source(Matrix)</a> -- find the source module of matrix</span></span></li>
<li><span><span><a href="_source_lp__Ring__Map_rp.html" title="find the source ring for a map of rings">source(RingMap)</a> -- find the source ring for a map of rings</span></span></li>
<li><span><span><a href="___Source__Code.html" title="name for an optional argument">SourceCode</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="___Source__Ring.html" title="name for an optional argument">SourceRing</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="___Sparse__Monomial__Vector__Expression.html" title="the class of all sparse monomial vector expressions">SparseMonomialVectorExpression</a> -- the class of all sparse monomial vector expressions</span></span></li>
<li><span><span><a href="___Sparse__Vector__Expression.html" title="the class of all sparse vector expressions">SparseVectorExpression</a> -- the class of all sparse vector expressions</span></span></li>
<li><span><span><a href="___Spec_lp__Ring_rp.html" title="make an affine variety">Spec(Ring)</a> -- make an affine variety</span></span></li>
<li><span><span><a href="_specifying_sptypical_spvalues.html" title="">specifying typical values</a></span></span></li>
<li><span><span><a href="_splice.html" title="remove subsequences">splice</a> -- remove subsequences</span></span></li>
<li><span><span><a href="_sqrt.html" title="square root function">sqrt</a> -- square root function</span></span></li>
<li><span><span><a href="___Standard.html" title="the standard top level printing method">Standard</a> -- the standard top level printing method</span></span></li>
<li><span><span><a href="_standard__Form.html" title="convert to standard form">standardForm</a> -- convert to standard form</span></span></li>
<li><span><span><a href="_standard__Pairs.html" title="find the standard pairs of a monomial ideal">standardPairs</a> -- find the standard pairs of a monomial ideal</span></span></li>
<li><span><span><a href="_stash__Value.html" title="stash values of functions in their arguments">stashValue</a> -- stash values of functions in their arguments</span></span></li>
<li><span><span><a href="_status.html" title="status of a resolution computation">status</a> -- status of a resolution computation</span></span></li>
<li><span><span><a href="_stderr.html" title="the standard error output file">stderr</a> -- the standard error output file</span></span></li>
<li><span><span><a href="_stdio.html" title="the standard input output file">stdio</a> -- the standard input output file</span></span></li>
<li><span><span><a href="_step.html" title="step by single lines in the debugger">step</a> -- step by single lines in the debugger</span></span></li>
<li><span><span><a href="___Stop__Before__Computation.html" title="name for an optional argument">StopBeforeComputation</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_stop__If__Error.html" title="whether to stop the program when an error occurs">stopIfError</a> -- whether to stop the program when an error occurs</span></span></li>
<li><span><span><a href="___Stop__With__Minimal__Generators.html" title="name for an optional argument">StopWithMinimalGenerators</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="___Strategy.html" title="name for an optional argument">Strategy</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="___String_sp_sh_sp__Z__Z.html" title="get character from string">String # ZZ</a> -- get character from string</span></span></li>
<li><span><span><a href="___String_sp_sh_qu_sp__Z__Z.html" title="check for character in string">String #? ZZ</a> -- check for character in string</span></span></li>
<li><span><span><a href="___String_sp.._sp__String.html" title="a sequence of consecutive strings">String .. String</a> -- a sequence of consecutive strings</span></span></li>
<li><span><span><a href="___String_sp.._lt_sp__String.html" title="a sequence of consecutive strings, not including the endpoint">String ..< String</a> -- a sequence of consecutive strings, not including the endpoint</span></span></li>
<li><span><span><a href="___String_sp^_sp__Sequence.html" title="vertically stacked copies of a string">String ^ Sequence</a> -- vertically stacked copies of a string</span></span></li>
<li><span><span><a href="___String_sp_us_sp__Sequence.html" title="substring">String _ Sequence</a> -- substring</span></span></li>
<li><span><span><a href="___String_sp_us_sp__Z__Z.html" title="get element from string">String _ ZZ</a> -- get element from string</span></span></li>
<li><span><span><a href="_sublists.html" title="process interspersed sublists of a list">sublists</a> -- process interspersed sublists of a list</span></span></li>
<li><span><span><a href="_submatrix.html" title="">submatrix</a></span></span></li>
<li><span><span><a href="_submatrix_sq.html" title="exclude rows and/or columns of a matrix">submatrix'</a> -- exclude rows and/or columns of a matrix</span></span></li>
<li><span><span><a href="_submatrix_lp__Matrix_cm__Visible__List_rp.html" title="select columns">submatrix(Matrix,VisibleList)</a> -- select columns</span></span></li>
<li><span><span><a href="_submatrix_lp__Matrix_cm__Visible__List_cm__Visible__List_rp.html" title="select part of a matrix">submatrix(Matrix,VisibleList,VisibleList)</a> -- select part of a matrix</span></span></li>
<li><span><span><a href="_subquotient.html" title="make a subquotient module">subquotient</a> -- make a subquotient module</span></span></li>
<li><span><span><a href="___Subring__Limit.html" title="stop after finding enough elements of a subring">SubringLimit</a> -- stop after finding enough elements of a subring</span></span></li>
<li><span><span><a href="___Subscript.html" title="the class of all subscript expressions">Subscript</a> -- the class of all subscript expressions</span></span></li>
<li><span><span><a href="_subscript.html" title="specify the function in a scripted functor for a subscript">subscript</a> -- specify the function in a scripted functor for a subscript</span></span></li>
<li><span><span><a href="_subsets.html" title="produce all the subsets">subsets</a> -- produce all the subsets</span></span></li>
<li><span><span><a href="_subsets_lp__List_rp.html" title="produce all the subsets">subsets(List)</a> -- produce all the subsets</span></span></li>
<li><span><span><a href="_subsets_lp__List_cm__Z__Z_rp.html" title="produce all the subsets">subsets(List,ZZ)</a> -- produce all the subsets</span></span></li>
<li><span><span><a href="_subsets_lp__Set_rp.html" title="produce all the subsets">subsets(Set)</a> -- produce all the subsets</span></span></li>
<li><span><span><a href="_subsets_lp__Set_cm__Z__Z_rp.html" title="produce all the subsets">subsets(Set,ZZ)</a> -- produce all the subsets</span></span></li>
<li><span><span><a href="_subsets_lp__Z__Z_rp.html" title="produce all the subsets">subsets(ZZ)</a> -- produce all the subsets</span></span></li>
<li><span><span><a href="_subsets_lp__Z__Z_cm__Z__Z_rp.html" title="produce all the subsets">subsets(ZZ,ZZ)</a> -- produce all the subsets</span></span></li>
<li><span><span><a href="_substituting_spvalues_spfor_spvariables.html" title="">substituting values for variables</a></span></span></li>
<li><span><span><a href="_substring.html" title="extract part of a string">substring</a> -- extract part of a string</span></span></li>
<li><span><span><a href="___Sum.html" title="the class of all sum expressions">Sum</a> -- the class of all sum expressions</span></span></li>
<li><span><span><a href="_sum.html" title="compute the sum">sum</a> -- compute the sum</span></span></li>
<li><span><span><a href="_sum_lp__Chain__Complex_rp.html" title="direct sum of the components of a chain complex">sum(ChainComplex)</a> -- direct sum of the components of a chain complex</span></span></li>
<li><span><span><a href="_sum_lp__Chain__Complex__Map_rp.html" title="direct sum of the components of a chain map">sum(ChainComplexMap)</a> -- direct sum of the components of a chain map</span></span></li>
<li><span><span><a href="_sum_lp__List_rp.html" title="sum the elements of a list">sum(List)</a> -- sum the elements of a list</span></span></li>
<li><span><span><a href="_sum_lp__Set_rp.html" title="sum of elements">sum(Set)</a> -- sum of elements</span></span></li>
<li><span><span><a href="_sum_lp__Tally_rp.html" title="sum of elements">sum(Tally)</a> -- sum of elements</span></span></li>
<li><span><span><a href="_sum_lp__Visible__List_cm__Function_rp.html" title="sum results of applying a function">sum(VisibleList,Function)</a> -- sum results of applying a function</span></span></li>
<li><span><span><a href="_sum_lp__Visible__List_cm__Visible__List_cm__Function_rp.html" title="sum results of applying a function pairwise">sum(VisibleList,VisibleList,Function)</a> -- sum results of applying a function pairwise</span></span></li>
<li><span><span><a href="_sum_lp__Z__Z_cm__Function_rp.html" title="sum consecutive values of a function">sum(ZZ,Function)</a> -- sum consecutive values of a function</span></span></li>
<li><span><span><a href="___Sum__Of__Twists.html" title="the class of all sums of twists">SumOfTwists</a> -- the class of all sums of twists</span></span></li>
<li><span><span><a href="_super.html" title="get the ambient module">super</a> -- get the ambient module</span></span></li>
<li><span><span><a href="___Superscript.html" title="the class of all superscript expressions">Superscript</a> -- the class of all superscript expressions</span></span></li>
<li><span><span><a href="_superscript.html" title="specify the function in a scripted functor for a superscript">superscript</a> -- specify the function in a scripted functor for a superscript</span></span></li>
<li><span><span><a href="_support.html" title="list of variables occurring in a polynomial or matrix">support</a> -- list of variables occurring in a polynomial or matrix</span></span></li>
<li><span><span><a href="_support_lp__Ideal_rp.html" title="list of variables occurring in the generators of an ideal">support(Ideal)</a> -- list of variables occurring in the generators of an ideal</span></span></li>
<li><span><span><a href="___S__V__D.html" title="singular value decomposition of a matrix">SVD</a> -- singular value decomposition of a matrix</span></span></li>
<li><span><span><a href="___S__V__D_lp..._cm_sp__Divide__Conquer_sp_eq_gt_sp..._rp.html" title="Use the lapack divide and conquer SVD algorithm">SVD(..., DivideConquer => ...)</a> -- Use the lapack divide and conquer SVD algorithm</span></span></li>
<li><span><span><a href="_switch_lp__Z__Z_cm__Z__Z_cm__Visible__List_rp.html" title="copy a list, switching two elements">switch(ZZ,ZZ,VisibleList)</a> -- copy a list, switching two elements</span></span></li>
<li><span><span><a href="___Symbol.html" title="the class of all symbols">Symbol</a> -- the class of all symbols</span></span></li>
<li><span><span><a href="_symbol.html" title="get a symbol">symbol</a> -- get a symbol</span></span></li>
<li><span><span><a href="___Symbol_sp.._sp__Symbol.html" title="sequences of consecutive symbols">Symbol .. Symbol</a> -- sequences of consecutive symbols</span></span></li>
<li><span><span><a href="___Symbol_sp.._lt_sp__Symbol.html" title="sequences of consecutive symbols">Symbol ..< Symbol</a> -- sequences of consecutive symbols</span></span></li>
<li><span><span><a href="___Symbol_sp_us_sp__Ring.html" title="get a ring variable by name">Symbol _ Ring</a> -- get a ring variable by name</span></span></li>
<li><span><span><a href="___Symbol_sp_us_sp__Thing.html" title="index variable">Symbol _ Thing</a> -- index variable</span></span></li>
<li><span><span><a href="___Symbol_sp_us_sp__Thing_sp_eq_sp__Thing.html" title="assignment to an indexed variable">Symbol _ Thing = Thing</a> -- assignment to an indexed variable</span></span></li>
<li><span><span><a href="_symmetric__Algebra.html" title="the symmetric algebra of a module">symmetricAlgebra</a> -- the symmetric algebra of a module</span></span></li>
<li><span><span><a href="_symmetric__Power.html" title="symmetric power">symmetricPower</a> -- symmetric power</span></span></li>
<li><span><span><a href="_symmetric__Power_lp__Z__Z_cm__Matrix_rp.html" title="symmetric power">symmetricPower(ZZ,Matrix)</a> -- symmetric power</span></span></li>
<li><span><span><a href="_synonym.html" title="synonym for members of a class">synonym</a> -- synonym for members of a class</span></span></li>
<li><span><span><a href="___S__Y__N__O__P__S__I__S.html" title="">SYNOPSIS</a></span></span></li>
<li><span><span><a href="___S__Y__N__O__P__S__I__S_lp..._cm_sp__Heading_sp_eq_gt_sp..._rp.html" title="">SYNOPSIS(..., Heading => ...)</a></span></span></li>
<li><span><span><a href="_syz.html" title="the syzygy matrix">syz</a> -- the syzygy matrix</span></span></li>
<li><span><span><a href="_syz_lp__Groebner__Basis_rp.html" title="retrieve the syzygy matrix">syz(GroebnerBasis)</a> -- retrieve the syzygy matrix</span></span></li>
<li><span><span><a href="_syz_lp__Matrix_rp.html" title="compute the syzygy matrix">syz(Matrix)</a> -- compute the syzygy matrix</span></span></li>
<li><span><span><a href="___Syzygies.html" title="name for an optional argument">Syzygies</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="___Syzygy__Limit.html" title="name for an optional argument">SyzygyLimit</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="___Syzygy__Matrix.html" title="name for an optional argument">SyzygyMatrix</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="___Syzygy__Rows.html" title="name for an optional argument">SyzygyRows</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_syzygy__Scheme.html" title="construct a syzygy scheme">syzygyScheme</a> -- construct a syzygy scheme</span></span></li>
<li><span><span><a href="___Table.html" title="the class of all table expressions">Table</a> -- the class of all table expressions</span></span></li>
<li><span><span><a href="_take_lp__Basic__List_cm__List_rp.html" title="">take(BasicList,List)</a></span></span></li>
<li><span><span><a href="_take_lp__Basic__List_cm__Z__Z_rp.html" title="">take(BasicList,ZZ)</a></span></span></li>
<li><span><span><a href="___Tally.html" title="the class of all tally results">Tally</a> -- the class of all tally results</span></span></li>
<li><span><span><a href="_tally.html" title="tally the elements of a list or sequence">tally</a> -- tally the elements of a list or sequence</span></span></li>
<li><span><span><a href="___Tally_sp_st_st_sp__Tally.html" title="Cartesian product of tallies">Tally ** Tally</a> -- Cartesian product of tallies</span></span></li>
<li><span><span><a href="___Tally_sp_pl_sp__Tally.html" title="union of tallies">Tally + Tally</a> -- union of tallies</span></span></li>
<li><span><span><a href="___Tally_sp-_sp__Tally.html" title="difference of tallies">Tally - Tally</a> -- difference of tallies</span></span></li>
<li><span><span><a href="___Tally_sp^_st_st_sp__Z__Z.html" title="Cartesian power of sets and tallies">Tally ^** ZZ</a> -- Cartesian power of sets and tallies</span></span></li>
<li><span><span><a href="___Tally_sp_us_sp__Thing.html" title="get a count from a tally">Tally _ Thing</a> -- get a count from a tally</span></span></li>
<li><span><span><a href="_tally_lp__Visible__List_rp.html" title="tally the elements of a list, sequence, or array">tally(VisibleList)</a> -- tally the elements of a list, sequence, or array</span></span></li>
<li><span><span><a href="_tan.html" title="compute the tangent">tan</a> -- compute the tangent</span></span></li>
<li><span><span><a href="_tangent__Sheaf.html" title="tangent sheaf of a projective variety">tangentSheaf</a> -- tangent sheaf of a projective variety</span></span></li>
<li><span><span><a href="_tangent__Sheaf_lp__Projective__Variety_rp.html" title="tangent sheaf of a projective variety">tangentSheaf(ProjectiveVariety)</a> -- tangent sheaf of a projective variety</span></span></li>
<li><span><span><a href="_tanh.html" title="compute the hyperbolic tangent">tanh</a> -- compute the hyperbolic tangent</span></span></li>
<li><span><span><a href="_target.html" title="target of a map">target</a> -- target of a map</span></span></li>
<li><span><span><a href="_target_lp__Chain__Complex__Map_rp.html" title=" find the target of a map of chain complexes">target(ChainComplexMap)</a> -- find the target of a map of chain complexes</span></span></li>
<li><span><span><a href="_target_lp__Graded__Module__Map_rp.html" title="find the target of a map of graded modules">target(GradedModuleMap)</a> -- find the target of a map of graded modules</span></span></li>
<li><span><span><a href="_target_lp__Groebner__Basis_rp.html" title="find target of a Gröbner basis">target(GroebnerBasis)</a> -- find target of a Gröbner basis</span></span></li>
<li><span><span><a href="_target_lp__Matrix_rp.html" title="find the target module of matrix">target(Matrix)</a> -- find the target module of matrix</span></span></li>
<li><span><span><a href="_target_lp__Ring__Map_rp.html" title="find the target ring for a map of rings">target(RingMap)</a> -- find the target ring for a map of rings</span></span></li>
<li><span><span><a href="_tensor.html" title="tensor product">tensor</a> -- tensor product</span></span></li>
<li><span><span><a href="_tensor_lp__Module_cm__Module_rp.html" title="tensor product">tensor(Module,Module)</a> -- tensor product</span></span></li>
<li><span><span><a href="_tensor_lp__Ring_cm__Ring_rp.html" title="tensor product">tensor(Ring,Ring)</a> -- tensor product</span></span></li>
<li><span><span><a href="_tensor_lp__Ring_cm__Ring__Map_cm__Matrix_rp.html" title="tensor product via a ring map">tensor(Ring,RingMap,Matrix)</a> -- tensor product via a ring map</span></span></li>
<li><span><span><a href="_tensor__Associativity.html" title="associativity isomorphisms for tensor products">tensorAssociativity</a> -- associativity isomorphisms for tensor products</span></span></li>
<li><span><span><a href="_terms.html" title="provide a list of terms of a polynomial">terms</a> -- provide a list of terms of a polynomial</span></span></li>
<li><span><span><a href="_tex.html" title="convert to TeX format">tex</a> -- convert to TeX format</span></span></li>
<li><span><span><a href="___Te__Xmacs.html" title="the TeXmacs top level printing method">TeXmacs</a> -- the TeXmacs top level printing method</span></span></li>
<li><span><span><a href="_tex__Math.html" title="convert to TeX math format">texMath</a> -- convert to TeX math format</span></span></li>
<li><span><span><a href="_the_spdebugger.html" title="">the debugger</a></span></span></li>
<li><span><span><a href="_then.html" title="condition testing">then</a> -- condition testing</span></span></li>
<li><span><span><a href="___Thing.html" title="the class of all things">Thing</a> -- the class of all things</span></span></li>
<li><span><span><a href="___Thing_sp_sl_sl_sp__Function.html" title="apply a function">Thing // Function</a> -- apply a function</span></span></li>
<li><span><span><a href="_throw.html" title="throw an exception">throw</a> -- throw an exception</span></span></li>
<li><span><span><a href="___Time.html" title="the class of all timing results">Time</a> -- the class of all timing results</span></span></li>
<li><span><span><a href="_times.html" title="multiplication">times</a> -- multiplication</span></span></li>
<li><span><span><a href="_to.html" title="loop control">to</a> -- loop control</span></span></li>
<li><span><span><a href="_to__Absolute__Path.html" title="the absolute path version of a file name">toAbsolutePath</a> -- the absolute path version of a file name</span></span></li>
<li><span><span><a href="_to__C__C.html" title="convert to high-precision complex number">toCC</a> -- convert to high-precision complex number</span></span></li>
<li><span><span><a href="_to__Dual.html" title="inverse system">toDual</a> -- inverse system</span></span></li>
<li><span><span><a href="_to__External__String.html" title="convert to a readable string">toExternalString</a> -- convert to a readable string</span></span></li>
<li><span><span><a href="_to__Field_lp__Ring_rp.html" title="declare that a ring is a field">toField(Ring)</a> -- declare that a ring is a field</span></span></li>
<li><span><span><a href="_to__List_lp__Basic__List_rp.html" title="list of elements">toList(BasicList)</a> -- list of elements</span></span></li>
<li><span><span><a href="_to__List_lp__Set_rp.html" title="list of elements">toList(Set)</a> -- list of elements</span></span></li>
<li><span><span><a href="_to__Lower.html" title="convert to lower case">toLower</a> -- convert to lower case</span></span></li>
<li><span><span><a href="_top__Coefficients.html" title="first variable and its coefficient of a polynomial or matrix">topCoefficients</a> -- first variable and its coefficient of a polynomial or matrix</span></span></li>
<li><span><span><a href="_top__Components.html" title="compute top dimensional component">topComponents</a> -- compute top dimensional component</span></span></li>
<li><span><span><a href="_top__Components_lp__Ideal_rp.html" title="compute top dimensional component">topComponents(Ideal)</a> -- compute top dimensional component</span></span></li>
<li><span><span><a href="_top__Components_lp__Module_rp.html" title="compute top dimensional component">topComponents(Module)</a> -- compute top dimensional component</span></span></li>
<li><span><span><a href="_top__Level__Mode.html" title="the current top level mode">topLevelMode</a> -- the current top level mode</span></span></li>
<li><span><span><a href="___Tor.html" title="Tor module">Tor</a> -- Tor module</span></span></li>
<li><span><span><a href="___Tor_us__Z__Z_lp__Module_cm__Module_rp.html" title="compute a Tor module">Tor_ZZ(Module,Module)</a> -- compute a Tor module</span></span></li>
<li><span><span><a href="_to__R__R.html" title="convert to high-precision real number">toRR</a> -- convert to high-precision real number</span></span></li>
<li><span><span><a href="_to__String.html" title="convert to a string">toString</a> -- convert to a string</span></span></li>
<li><span><span><a href="___Total__Pairs.html" title="whether to display the total number of S-pairs">TotalPairs</a> -- whether to display the total number of S-pairs</span></span></li>
<li><span><span><a href="_to__Upper.html" title="convert to upper case">toUpper</a> -- convert to upper case</span></span></li>
<li><span><span><a href="_trace_lp__Matrix_rp.html" title="trace of a matrix">trace(Matrix)</a> -- trace of a matrix</span></span></li>
<li><span><span><a href="_transpose.html" title="transpose a table or a matrix">transpose</a> -- transpose a table or a matrix</span></span></li>
<li><span><span><a href="_transpose_lp__Chain__Complex__Map_rp.html" title="transpose a map of chain complexes">transpose(ChainComplexMap)</a> -- transpose a map of chain complexes</span></span></li>
<li><span><span><a href="_transpose_lp__List_rp.html" title=" transposes a table">transpose(List)</a> -- transposes a table</span></span></li>
<li><span><span><a href="_transpose_lp__Matrix_rp.html" title="transpose a matrix">transpose(Matrix)</a> -- transpose a matrix</span></span></li>
<li><span><span><a href="___Tree__Node.html" title="a type of basic list used to represent a rooted tree">TreeNode</a> -- a type of basic list used to represent a rooted tree</span></span></li>
<li><span><span><a href="_trim.html" title="minimize generators and relations">trim</a> -- minimize generators and relations</span></span></li>
<li><span><span><a href="_trim_lp__Ideal_rp.html" title="">trim(Ideal)</a></span></span></li>
<li><span><span><a href="_trim_lp__Module_rp.html" title="">trim(Module)</a></span></span></li>
<li><span><span><a href="_trim_lp__Quotient__Ring_rp.html" title="">trim(QuotientRing)</a></span></span></li>
<li><span><span><a href="_trim_lp__Ring_rp.html" title="">trim(Ring)</a></span></span></li>
<li><span><span><a href="_true.html" title="">true</a></span></span></li>
<li><span><span><a href="_truncate.html" title="truncate the module at a specified degree">truncate</a> -- truncate the module at a specified degree</span></span></li>
<li><span><span><a href="_truncate__Output.html" title="">truncateOutput</a></span></span></li>
<li><span><span><a href="_tutorial.html" title="convert documentation from tutorial format">tutorial</a> -- convert documentation from tutorial format</span></span></li>
<li><span><span><a href="_typical__Values.html" title="types of values returned by functions">typicalValues</a> -- types of values returned by functions</span></span></li>
<li><span><span><a href="_ultimate.html" title="ultimate value for an iteration">ultimate</a> -- ultimate value for an iteration</span></span></li>
<li><span><span><a href="_unbag_lp__Bag_rp.html" title="">unbag(Bag)</a></span></span></li>
<li><span><span><a href="_uncurry.html" title="uncurry a function">uncurry</a> -- uncurry a function</span></span></li>
<li><span><span><a href="___Undo.html" title="name for an optional argument">Undo</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_undocumented.html" title="">undocumented</a></span></span></li>
<li><span><span><a href="_uniform.html" title="test whether elements of a list are of the same class">uniform</a> -- test whether elements of a list are of the same class</span></span></li>
<li><span><span><a href="_uninstall__Package_lp__String_rp.html" title="uninstall a package">uninstallPackage(String)</a> -- uninstall a package</span></span></li>
<li><span><span><a href="___Unmixed.html" title="name for an optional argument">Unmixed</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="___Update__Only.html" title="only copies of newer files should replace files">UpdateOnly</a> -- only copies of newer files should replace files</span></span></li>
<li><span><span><a href="___Upper__Triangular.html" title="name for an optional argument">UpperTriangular</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="___U__R__L.html" title="a type representing a URL">URL</a> -- a type representing a URL</span></span></li>
<li><span><span><a href="___Usage.html" title="shows the usage of a function">Usage</a> -- shows the usage of a function</span></span></li>
<li><span><span><a href="_use.html" title="install or activate object">use</a> -- install or activate object</span></span></li>
<li><span><span><a href="_use_lp__Package_rp.html" title="activate a previously dismissed package">use(Package)</a> -- activate a previously dismissed package</span></span></li>
<li><span><span><a href="_use_lp__Ring_rp.html" title="install ring variables and ring operations">use(Ring)</a> -- install ring variables and ring operations</span></span></li>
<li><span><span><a href="___Use__Hilbert__Function.html" title="">UseHilbertFunction</a></span></span></li>
<li><span><span><a href="___User__Mode.html" title="name for an optional argument">UserMode</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_user__Symbols.html" title="a list of the user's symbols">userSymbols</a> -- a list of the user's symbols</span></span></li>
<li><span><span><a href="_using_sppackages.html" title="">using packages</a></span></span></li>
<li><span><span><a href="_utf8.html" title="encode and decode unicode utf-8-encoded strings">utf8</a> -- encode and decode unicode utf-8-encoded strings</span></span></li>
<li><span><span><a href="_value.html" title="evaluate">value</a> -- evaluate</span></span></li>
<li><span><span><a href="_value_lp__Indexed__Variable_rp.html" title="retrieve the value of an indexed variable">value(IndexedVariable)</a> -- retrieve the value of an indexed variable</span></span></li>
<li><span><span><a href="_value_lp__Pseudocode_rp.html" title="execute pseudocode">value(Pseudocode)</a> -- execute pseudocode</span></span></li>
<li><span><span><a href="_value_lp__String_rp.html" title="evaluate a string">value(String)</a> -- evaluate a string</span></span></li>
<li><span><span><a href="_value_lp__Symbol_rp.html" title="retrieve the value of a symbol">value(Symbol)</a> -- retrieve the value of a symbol</span></span></li>
<li><span><span><a href="_values_lp__Hash__Table_rp.html" title="values in a hash table">values(HashTable)</a> -- values in a hash table</span></span></li>
<li><span><span><a href="___Variable.html" title="specify a name for a variable">Variable</a> -- specify a name for a variable</span></span></li>
<li><span><span><a href="___Variables.html" title="name for an optional argument">Variables</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_variety.html" title="get the variety">variety</a> -- get the variety</span></span></li>
<li><span><span><a href="_variety_lp__Coherent__Sheaf_rp.html" title="">variety(CoherentSheaf)</a></span></span></li>
<li><span><span><a href="_variety_lp__Ideal_rp.html" title="the closed projective subvariety defined by an ideal">variety(Ideal)</a> -- the closed projective subvariety defined by an ideal</span></span></li>
<li><span><span><a href="_variety_lp__Sheaf__Of__Rings_rp.html" title="get the variety">variety(SheafOfRings)</a> -- get the variety</span></span></li>
<li><span><span><a href="_vars.html" title="variables">vars</a> -- variables</span></span></li>
<li><span><span><a href="_vars_lp__General__Ordered__Monoid_rp.html" title="row matrix of the variables">vars(GeneralOrderedMonoid)</a> -- row matrix of the variables</span></span></li>
<li><span><span><a href="_vars_lp__List_rp.html" title="a sequence of variables">vars(List)</a> -- a sequence of variables</span></span></li>
<li><span><span><a href="_vars_lp__Ring_rp.html" title="row matrix of the variables">vars(Ring)</a> -- row matrix of the variables</span></span></li>
<li><span><span><a href="___Vector.html" title="the class of all elements of free modules that are handled by the engine">Vector</a> -- the class of all elements of free modules that are handled by the engine</span></span></li>
<li><span><span><a href="_vector.html" title="make a vector">vector</a> -- make a vector</span></span></li>
<li><span><span><a href="___Vector_sp_st_st_sp__Vector.html" title="tensor product">Vector ** Vector</a> -- tensor product</span></span></li>
<li><span><span><a href="___Verbose.html" title="request verbose feedback">Verbose</a> -- request verbose feedback</span></span></li>
<li><span><span><a href="___Verify.html" title="verify that a map is well-defined">Verify</a> -- verify that a map is well-defined</span></span></li>
<li><span><span><a href="___Vertical__List.html" title="a type of visible self-initializing list that prints vertically">VerticalList</a> -- a type of visible self-initializing list that prints vertically</span></span></li>
<li><span><span><a href="___Vertical__Space.html" title="name for an optional argument">VerticalSpace</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_view__Help.html" title="view online doc with a web browser">viewHelp</a> -- view online doc with a web browser</span></span></li>
<li><span><span><a href="___Virtual__Tally.html" title="">VirtualTally</a></span></span></li>
<li><span><span><a href="___Visible__List_sp_sl_sp__Function.html" title="apply a function to elements of a list">VisibleList / Function</a> -- apply a function to elements of a list</span></span></li>
<li><span><span><a href="_w3.html" title="">w3</a></span></span></li>
<li><span><span><a href="_wedge__Product_lp__Z__Z_cm__Z__Z_cm__Module_rp.html" title="the exterior multiplication map">wedgeProduct(ZZ,ZZ,Module)</a> -- the exterior multiplication map</span></span></li>
<li><span><span><a href="_weight__Range.html" title="the pair of lowest and highest weights of the monomials">weightRange</a> -- the pair of lowest and highest weights of the monomials</span></span></li>
<li><span><span><a href="___Weyl__Algebra.html" title="name for an optional argument">WeylAlgebra</a> -- name for an optional argument</span></span></li>
<li><span><span><a href="_what_spis_spa_spsubquotient_spmodule_qu.html" title="">what is a subquotient module?</a></span></span></li>
<li><span><span><a href="_when.html" title="a keyword">when</a> -- a keyword</span></span></li>
<li><span><span><a href="_width.html" title="width of a file or net">width</a> -- width of a file or net</span></span></li>
<li><span><span><a href="_width_lp__File_rp.html" title="get window width">width(File)</a> -- get window width</span></span></li>
<li><span><span><a href="_width_lp__Net_rp.html" title="width of a net">width(Net)</a> -- width of a net</span></span></li>
<li><span><span><a href="___Wikipedia_lp__String_rp.html" title="link to a Wikipedia entry">Wikipedia(String)</a> -- link to a Wikipedia entry</span></span></li>
<li><span><span><a href="___Wrap.html" title="a key for methods for wrapping printed output">Wrap</a> -- a key for methods for wrapping printed output</span></span></li>
<li><span><span><a href="_wrap.html" title="">wrap</a></span></span></li>
<li><span><span><a href="___Wrapper__Type.html" title="a class of lists with abbreviated constructors">WrapperType</a> -- a class of lists with abbreviated constructors</span></span></li>
<li><span><span><a href="_xor.html" title="logical exclusive-or">xor</a> -- logical exclusive-or</span></span></li>
<li><span><span><a href="_youngest.html" title="the youngest member of a sequence">youngest</a> -- the youngest member of a sequence</span></span></li>
<li><span><span><a href="_zero.html" title="whether something is zero">zero</a> -- whether something is zero</span></span></li>
<li><span><span><a href="___Zero__Expression.html" title="the class of all zero expressions">ZeroExpression</a> -- the class of all zero expressions</span></span></li>
<li><span><span><a href="_zeta.html" title="Riemann zeta function">zeta</a> -- Riemann zeta function</span></span></li>
<li><span><span><a href="___Z__Z.html" title="the class of all integers">ZZ</a> -- the class of all integers</span></span></li>
<li><span><span><a href="___Z__Z_sp_am_sp__Z__Z.html" title="logical and">ZZ & ZZ</a> -- logical and</span></span></li>
<li><span><span><a href="___Z__Z_sp.._sp__Z__Z.html" title="sequences of consecutive integers">ZZ .. ZZ</a> -- sequences of consecutive integers</span></span></li>
<li><span><span><a href="___Z__Z_sp.._lt_sp__Z__Z.html" title="sequences of consecutive integers">ZZ ..< ZZ</a> -- sequences of consecutive integers</span></span></li>
<li><span><span><a href="___Z__Z_sp_co_sp__Thing.html" title="repeat an item">ZZ : Thing</a> -- repeat an item</span></span></li>
<li><span><span><a href="___Z__Z_sp_us_sp__Module.html" title="integers or zero element">ZZ _ Module</a> -- integers or zero element</span></span></li>
<li><span><span><a href="___Z__Z_sp_vb_sp__Z__Z.html" title="logical or">ZZ | ZZ</a> -- logical or</span></span></li>
</ul>
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