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<div><h1>Module -- the class of all modules</h1>
<div class="single"><h2>Description</h2>
<div><p/>
See <a href="_modules.html" title="">modules</a> for an overview of modules in Macaulay2. See <a href="_modules_spin_sp__Macaulay2.html" title="">modules in Macaulay2</a> for a tutorial overview of modules.<p/>
Modules in Macaulay2 are implemented as <a href="_subquotient_spmodules.html" title="the way Macaulay2 represents modules">subquotient modules</a>. Submodules and quotients of free modules are perhaps the most common and important modules, and subquotients form the smallest class of modules that naturally includes these cases.<p/>
Common ways to make a module:<ul><li><span><a href="___Ring_sp^_sp__Z__Z.html" title="make a free module">Ring ^ ZZ</a> -- make a free module</span></li>
<li><span><a href="___Ring_sp^_sp__List.html" title="make a free module">Ring ^ List</a> -- make a free module</span></li>
<li><span><a href="_cokernel.html" title="cokernel of a map of modules, graded modules, or chaincomplexes">cokernel(Matrix)</a> -- cokernel of a map of modules, graded modules, or chaincomplexes</span></li>
<li><span><a href="_image.html" title="image of a map">image(Matrix)</a> -- image of a map</span></li>
<li><span><a href="_kernel_lp__Matrix_rp.html" title="kernel of a matrix">kernel(Matrix)</a> -- kernel of a matrix</span></li>
</ul>
Common ways to get information about modules:<ul><li><tt>ring Module</tt></li>
<li><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></li>
<li><span><a href="_degrees_lp__Ring_rp.html" title="degrees of generators">degrees(Module)</a> -- degrees of generators</span></li>
<li><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></li>
<li><span><a href="_relations.html" title="the defining relations">relations(Module)</a> -- the defining relations</span></li>
<li><span><a href="_is__Free__Module.html" title="whether something is a free module">isFreeModule</a> -- whether something is a free module</span></li>
<li><span><a href="_is__Homogeneous.html" title="whether something is homogeneous (graded)">isHomogeneous(Module)</a> -- whether something is homogeneous (graded)</span></li>
</ul>
Numerical information about a module:<ul><li><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></li>
<li><span><a href="_dim_lp__Module_rp.html" title="compute the Krull dimension">dim(Module)</a> -- compute the Krull dimension</span></li>
<li><span><a href="_rank.html" title="compute the rank">rank(Module)</a> -- compute the rank</span></li>
</ul>
Submodules, quotients, and subquotient modules:<ul><li><span><a href="_ambient_lp__Module_rp.html" title="ambient free module">ambient(Module)</a> -- ambient free module</span></li>
<li><span><a href="_cover_lp__Module_rp.html" title="get the covering free module">cover(Module)</a> -- get the covering free module</span></li>
<li><span><a href="_super.html" title="get the ambient module">super(Module)</a> -- get the ambient module</span></li>
<li><span><a href="___Module_sp_sl_sp__Module.html" title="quotient module">Module / Module</a> -- quotient module</span></li>
<li><span><a href="_subquotient.html" title="make a subquotient module">subquotient(Matrix,Matrix)</a> -- make a subquotient module</span></li>
<li><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></li>
</ul>
Common operations on modules:<ul><li><span><a href="___Module_sp_pl_sp__Module.html" title="sum of submodules">Module + Module</a> -- sum of submodules</span></li>
<li><span><a href="__eq_eq.html" title="equality">Module == Module</a> -- equality</span></li>
<li><span><a href="___Module_sp_pl_pl_sp__Module.html" title="direct sum of modules">Module ++ Module</a> -- direct sum of modules</span></li>
<li><span><a href="___Module_sp^_sp__List.html" title="projection onto summand">Module ^ List</a> -- projection onto summand</span></li>
<li><span><a href="___Module_sp_st_st_sp__Module.html" title="tensor product">Module ** Module</a> -- tensor product</span></li>
<li><span><a href="___Module_sp^_st_st_sp__Z__Z.html" title="tensor power">Module ^** ZZ</a> -- tensor power</span></li>
<li><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></li>
</ul>
Minimalization:<ul><li><span><a href="_mingens_lp__Module_rp.html" title="minimal generator matrix">mingens(Module)</a> -- minimal generator matrix</span></li>
<li><span><a href="_trim_lp__Module_rp.html" title="">trim(Module)</a></span></li>
<li><span><a href="_minimal__Presentation_lp__Module_rp.html" title="minimal presentation of a module">minimalPresentation(Module)</a> -- minimal presentation of a module</span></li>
</ul>
Graded modules:<ul><li><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></li>
<li><span><a href="_truncate.html" title="truncate the module at a specified degree">truncate</a> -- truncate the module at a specified degree</span></li>
<li><span><a href="_degree_lp__Module_rp.html" title="">degree(Module)</a></span></li>
<li><span><a href="_genera_lp__Coherent__Sheaf_rp.html" title="list of the successive linear sectional arithmetic genera">genera(Module)</a> -- list of the successive linear sectional arithmetic genera</span></li>
<li><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></li>
<li><span><a href="_hilbert__Function.html" title="the Hilbert function">hilbertFunction(ZZ,Module)</a> -- the Hilbert function</span></li>
<li><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></li>
<li><span><a href="_regularity.html" title="compute the Castelnuovo-Mumford regularity">regularity(Module)</a> -- compute the Castelnuovo-Mumford regularity</span></li>
</ul>
Annihilators, quotients and Gröbner bases:<ul><li><span><a href="_gb.html" title="compute a Gröbner basis">gb(Module)</a> -- compute a Gröbner basis</span></li>
<li><span><a href="_quotient_lp__Ideal_cm__Ideal_rp.html" title="ideal or submodule quotient">Module : Ideal</a> -- ideal or submodule quotient</span></li>
<li><span><a href="_annihilator.html" title="the annihilator ideal">annihilator(Module)</a> -- the annihilator ideal</span></li>
<li><span><a href="_saturate.html" title="saturation of ideal or submodule">saturate(Module,Ideal)</a> -- saturation of ideal or submodule</span></li>
</ul>
Common homological computations:<ul><li><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></li>
<li><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></li>
<li><span><a href="___Hom.html" title="module of homomorphisms">Hom</a> -- module of homomorphisms</span></li>
<li><span><a href="_homomorphism.html" title="get the homomorphism from element of Hom">homomorphism(Matrix)</a> -- get the homomorphism from element of Hom</span></li>
<li><span><a href="___Ext^__Z__Z_lp__Module_cm__Module_rp.html" title="Ext module">Ext^ZZ(Module,Module)</a> -- Ext module</span></li>
<li><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></li>
<li><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></li>
<li><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></li>
<li><span><a href="_fitting__Ideal.html" title="Fitting ideal of a module">fittingIdeal(ZZ,Module)</a> -- Fitting ideal of a module</span></li>
</ul>
Multilinear algebra:<ul><li><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></li>
</ul>
</div>
</div>
<div class="waystouse"><h2>Functions and methods returning a module :</h2>
<ul><li><span>Ideal * Module, see <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>MonomialIdeal * Module, see <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>RingElement * Module, see <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>InexactFieldFamily ^ ZZ, see <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><a href="_ambient_lp__Module_rp.html" title="ambient free module">ambient(Module)</a> -- ambient free module</span></li>
<li><span><a href="___Chain__Complex_sp^_sp__Z__Z.html" title="access member, cohomological degree">ChainComplex ^ ZZ</a> -- access member, cohomological degree</span></li>
<li><span><a href="___Chain__Complex_sp_us_sp__Z__Z.html" title="component">ChainComplex _ ZZ</a> -- component</span></li>
<li><span>GradedModule _ ZZ, see <span><a href="___Chain__Complex_sp_us_sp__Z__Z.html" title="component">ChainComplex _ ZZ</a> -- component</span></span></li>
<li><span>coimage(Matrix), see <span><a href="_coimage.html" title="coimage of a map">coimage</a> -- coimage of a map</span></span></li>
<li><span>cokernel(Matrix), see <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>cokernel(RingElement), see <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>comodule(Ideal), see <span><a href="_comodule.html" title="submodule to quotient module">comodule</a> -- submodule to quotient module</span></span></li>
<li><span>comodule(Module), see <span><a href="_comodule.html" title="submodule to quotient module">comodule</a> -- submodule to quotient module</span></span></li>
<li><span>quotient(Ideal), see <span><a href="_comodule.html" title="submodule to quotient module">comodule</a> -- submodule to quotient module</span></span></li>
<li><span>quotient(Module), see <span><a href="_comodule.html" title="submodule to quotient module">comodule</a> -- submodule to quotient module</span></span></li>
<li><span><a href="_cover_lp__Module_rp.html" title="get the covering free module">cover(Module)</a> -- get the covering free module</span></li>
<li><span><a href="_dual_lp__Module_rp.html" title="dual module">dual(Module)</a> -- dual module</span></li>
<li><span><a href="___Ext_lp__Module_cm__Module_rp.html" title="total Ext module">Ext(Module,Module)</a> -- total Ext module</span></li>
<li><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></li>
<li><span>Ext^ZZ(CoherentSheaf,SheafOfRings), see <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>Ext^ZZ(SheafOfRings,CoherentSheaf), see <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>Ext^ZZ(SheafOfRings,SheafOfRings), see <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><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></li>
<li><span>Ext^ZZ(SheafOfRings,SumOfTwists), see <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><a href="___Ext^__Z__Z_lp__Module_cm__Module_rp.html" title="Ext module">Ext^ZZ(Module,Module)</a> -- Ext module</span></li>
<li><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></li>
<li><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></li>
<li><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></li>
<li><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></li>
<li><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></li>
<li><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></li>
<li><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></li>
<li><span><a href="___Hom_lp__Coherent__Sheaf_cm__Coherent__Sheaf_rp.html" title="global Hom">Hom(CoherentSheaf,CoherentSheaf)</a> -- global Hom</span></li>
<li><span>Hom(CoherentSheaf,SheafOfRings), see <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>Hom(SheafOfRings,CoherentSheaf), see <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>Hom(SheafOfRings,SheafOfRings), see <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>Hom(Ideal,Ideal), see <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>Hom(Ideal,Module), see <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>Hom(Ideal,Ring), see <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>Hom(Module,Ideal), see <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><a href="___Hom_lp__Module_cm__Module_rp.html" title="module of homomorphisms">Hom(Module,Module)</a> -- module of homomorphisms</span></li>
<li><span>Hom(Module,Ring), see <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>Hom(Ring,Ideal), see <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>Hom(Ring,Module), see <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>homogenize(Module,RingElement), see <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>homogenize(Module,RingElement,List), see <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><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></li>
<li><span><a href="___Ideal_sp_sl_sp__Ideal.html" title="quotient module">Ideal / Ideal</a> -- quotient module</span></li>
<li><span>image(Matrix), see <span><a href="_image.html" title="image of a map">image</a> -- image of a map</span></span></li>
<li><span>image(RingElement), see <span><a href="_image.html" title="image of a map">image</a> -- image of a map</span></span></li>
<li><span><a href="_kernel_lp__Matrix_rp.html" title="kernel of a matrix">kernel(Matrix)</a> -- kernel of a matrix</span></li>
<li><span>kernel(RingElement), see <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><a href="_minimal__Presentation_lp__Module_rp.html" title="minimal presentation of a module">minimalPresentation(Module)</a> -- minimal presentation of a module</span></li>
<li><span>prune(Module), see <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><a href="___Module_sp_st_st_sp__Module.html" title="tensor product">Module ** Module</a> -- tensor product</span></li>
<li><span><a href="___Module_sp_st_st_sp__Ring.html" title="tensor product">Module ** Ring</a> -- tensor product</span></li>
<li><span>Ring ** Module, see <span><a href="___Module_sp_st_st_sp__Ring.html" title="tensor product">Module ** Ring</a> -- tensor product</span></span></li>
<li><span><a href="___Module_sp_pl_sp__Module.html" title="sum of submodules">Module + Module</a> -- sum of submodules</span></li>
<li><span><a href="___Module_sp_pl_pl_sp__Module.html" title="direct sum of modules">Module ++ Module</a> -- direct sum of modules</span></li>
<li><span>Module / Ideal, see <span><a href="___Module_sp_sl_sp__Module.html" title="quotient module">Module / Module</a> -- quotient module</span></span></li>
<li><span>Module / List, see <span><a href="___Module_sp_sl_sp__Module.html" title="quotient module">Module / Module</a> -- quotient module</span></span></li>
<li><span><a href="___Module_sp_sl_sp__Module.html" title="quotient module">Module / Module</a> -- quotient module</span></li>
<li><span>Module / RingElement, see <span><a href="___Module_sp_sl_sp__Module.html" title="quotient module">Module / Module</a> -- quotient module</span></span></li>
<li><span>Module / Sequence, see <span><a href="___Module_sp_sl_sp__Module.html" title="quotient module">Module / Module</a> -- quotient module</span></span></li>
<li><span>Module / Vector, see <span><a href="___Module_sp_sl_sp__Module.html" title="quotient module">Module / Module</a> -- quotient module</span></span></li>
<li><span><a href="___Module_sp^_sp__Z__Z.html" title="direct sum">Module ^ ZZ</a> -- direct sum</span></li>
<li><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></li>
<li><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></li>
<li><span>module(MonomialIdeal), see <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><a href="_module_lp__Ring_rp.html" title="">module(Ring)</a></span></li>
<li><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></li>
<li><span><a href="_push__Forward_lp__Ring__Map_cm__Module_rp.html" title="">pushForward(RingMap,Module)</a></span></li>
<li><span>Module : Ideal, see <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>Module : RingElement, see <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>quotient(Module,Ideal), see <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>quotient(Module,RingElement), see <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>removeLowestDimension(Module), see <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><a href="___Ring_sp^_sp__List.html" title="make a free module">Ring ^ List</a> -- make a free module</span></li>
<li><span><a href="___Ring_sp^_sp__Z__Z.html" title="make a free module">Ring ^ ZZ</a> -- make a free module</span></li>
<li><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></li>
<li><span>RingMap Module, see <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>saturate(Module), see <span><a href="_saturate.html" title="saturation of ideal or submodule">saturate</a> -- saturation of ideal or submodule</span></span></li>
<li><span>saturate(Module,Ideal), see <span><a href="_saturate.html" title="saturation of ideal or submodule">saturate</a> -- saturation of ideal or submodule</span></span></li>
<li><span>saturate(Module,RingElement), see <span><a href="_saturate.html" title="saturation of ideal or submodule">saturate</a> -- saturation of ideal or submodule</span></span></li>
<li><span>sheafExt^ZZ(CoherentSheaf,SheafOfRings), see <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>sheafExt^ZZ(SheafOfRings,CoherentSheaf), see <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>sheafExt^ZZ(SheafOfRings,SheafOfRings), see <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>sheafHom(CoherentSheaf,SheafOfRings), see <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>sheafHom(SheafOfRings,CoherentSheaf), see <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>sheafHom(SheafOfRings,SheafOfRings), see <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><a href="_subquotient.html" title="make a subquotient module">subquotient</a> -- make a subquotient module</span></li>
<li><span>substitute(Module,List), see <span><a href="_substitute.html" title="substituting values for variables">substitute</a> -- substituting values for variables</span></span></li>
<li><span>substitute(Module,Matrix), see <span><a href="_substitute.html" title="substituting values for variables">substitute</a> -- substituting values for variables</span></span></li>
<li><span>substitute(Module,Ring), see <span><a href="_substitute.html" title="substituting values for variables">substitute</a> -- substituting values for variables</span></span></li>
<li><span>substitute(Module,RingFamily), see <span><a href="_substitute.html" title="substituting values for variables">substitute</a> -- substituting values for variables</span></span></li>
<li><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></li>
<li><span>super(Module), see <span><a href="_super.html" title="get the ambient module">super</a> -- get the ambient module</span></span></li>
<li><span><a href="_tensor_lp__Module_cm__Module_rp.html" title="tensor product">tensor(Module,Module)</a> -- tensor product</span></li>
<li><span>tensor(RingMap,Module), see <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><a href="_top__Components_lp__Module_rp.html" title="compute top dimensional component">topComponents(Module)</a> -- compute top dimensional component</span></li>
<li><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></li>
<li><span><a href="_trim_lp__Module_rp.html" title="">trim(Module)</a></span></li>
<li><span>truncate(List,Module), see <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>truncate(ZZ,Module), see <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>
</ul>
<h2>Methods that use a module :</h2>
<ul><li><span>Ideal == Module, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>Module == Ideal, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>Module == Module, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>Module == ZZ, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>ZZ == Module, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><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></li>
<li><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></li>
<li><span>analyticSpread(Module), see <span><a href="../../ReesAlgebra/html/_analytic__Spread.html" title="compute the analytic spread of a module or ideal">analyticSpread</a> -- compute the analytic spread of a module or ideal</span></span></li>
<li><span>analyticSpread(Module,RingElement), see <span><a href="../../ReesAlgebra/html/_analytic__Spread.html" title="compute the analytic spread of a module or ideal">analyticSpread</a> -- compute the analytic spread of a module or ideal</span></span></li>
<li><span>annihilator(Module), see <span><a href="_annihilator.html" title="the annihilator ideal">annihilator</a> -- the annihilator ideal</span></span></li>
<li><span>basis(InfiniteNumber,InfiniteNumber,Module), see <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>basis(InfiniteNumber,List,Module), see <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>basis(InfiniteNumber,ZZ,Module), see <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>basis(List,InfiniteNumber,Module), see <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>basis(List,List,Module), see <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>basis(List,Module), see <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>basis(Module), see <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>basis(ZZ,InfiniteNumber,Module), see <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>basis(ZZ,Module), see <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>basis(ZZ,ZZ,Module), see <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><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></li>
<li><span>ChainComplex ** Module, see <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>Module ** ChainComplex, see <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>Module ** ChainComplexMap, see <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>ChainComplexMap ** Module, see <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><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></li>
<li><span>components(Module), see <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><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></li>
<li><span><a href="_degree_lp__Module_rp.html" title="">degree(Module)</a></span></li>
<li><span>degreeLength(Module), see <span><a href="_degree__Length.html" title="the number of degrees">degreeLength</a> -- the number of degrees</span></span></li>
<li><span>degrees(Module), see <span><a href="_degrees_lp__Ring_rp.html" title="degrees of generators">degrees(Ring)</a> -- degrees of generators</span></span></li>
<li><span>degreesMonoid(Module), see <span><a href="_degrees__Monoid.html" title="get the monoid of degrees">degreesMonoid</a> -- get the monoid of degrees</span></span></li>
<li><span>degreesRing(Module), see <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><a href="_dim_lp__Module_rp.html" title="compute the Krull dimension">dim(Module)</a> -- compute the Krull dimension</span></li>
<li><span>directSum(Module), see <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><a href="_euler_lp__Module_rp.html" title="Euler characteristic">euler(Module)</a> -- Euler characteristic</span></li>
<li><span>eulers(Module), see <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>Ext(Ideal,Module), see <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>Ext(Module,Ideal), see <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>Ext(Module,Ring), see <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><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></li>
<li><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></li>
<li><span>Ext^ZZ(Ideal,Module), see <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>Ext^ZZ(Module,Ideal), see <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>Ext^ZZ(Module,Ring), see <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><a href="_factor_lp__Module_rp.html" title="factor a ZZ-module">factor(Module)</a> -- factor a ZZ-module</span></li>
<li><span>fittingIdeal(ZZ,Module), see <span><a href="_fitting__Ideal.html" title="Fitting ideal of a module">fittingIdeal</a> -- Fitting ideal of a module</span></span></li>
<li><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></li>
<li><span>gb(Module), see <span><a href="_gb.html" title="compute a Gröbner basis">gb</a> -- compute a Gröbner basis</span></span></li>
<li><span>gbRemove(Module), see <span><a href="_gb__Remove.html" title="remove Gröbner basis">gbRemove</a> -- remove Gröbner basis</span></span></li>
<li><span>gbSnapshot(Module), see <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>genera(Module), see <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>generator(Module), see <span><a href="_generator.html" title="provide a single generator">generator</a> -- provide a single generator</span></span></li>
<li><span>Module _ ZZ, see <span><a href="_generators_spof_spideals_spand_spmodules.html" title="">generators of ideals and modules</a></span></span></li>
<li><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></li>
<li><span>genus(Module), see <span><a href="_genus_lp__Coherent__Sheaf_rp.html" title="arithmetic genus">genus(CoherentSheaf)</a> -- arithmetic genus</span></span></li>
<li><span>gradedModule(Module), see <span><a href="_graded__Module.html" title="make a graded module">gradedModule</a> -- make a graded module</span></span></li>
<li><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></li>
<li><span>Module ** GradedModule, see <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>heft(Module), see <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>hilbertFunction(List,Module), see <span><a href="_hilbert__Function.html" title="the Hilbert function">hilbertFunction</a> -- the Hilbert function</span></span></li>
<li><span>hilbertFunction(ZZ,Module), see <span><a href="_hilbert__Function.html" title="the Hilbert function">hilbertFunction</a> -- the Hilbert function</span></span></li>
<li><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></li>
<li><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></li>
<li><span>Hom(ChainComplexMap,Module), see <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><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></li>
<li><span>Hom(Module,ChainComplexMap), see <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>Hom(Module,Matrix), see <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>Hom(ChainComplex,Module), see <span><a href="___Hom_lp__Module_cm__Chain__Complex_rp.html" title="">Hom(Module,ChainComplex)</a></span></span></li>
<li><span><a href="___Hom_lp__Module_cm__Chain__Complex_rp.html" title="">Hom(Module,ChainComplex)</a></span></li>
<li><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></li>
<li><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></li>
<li><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></li>
<li><span>inducedMap(Module,Nothing,Matrix), see <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>inducedMap(Nothing,Module,Matrix), see <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>inducesWellDefinedMap(Module,Module,Matrix), see <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>inducesWellDefinedMap(Module,Nothing,Matrix), see <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>inducesWellDefinedMap(Nothing,Module,Matrix), see <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>installHilbertFunction(Module,RingElement), see <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>isDirectSum(Module), see <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>isFreeModule(Module), see <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>isHomogeneous(Module), see <span><a href="_is__Homogeneous.html" title="whether something is homogeneous (graded)">isHomogeneous</a> -- whether something is homogeneous (graded)</span></span></li>
<li><span>isIdeal(Module), see <span><a href="_is__Ideal.html" title="whether something is an ideal">isIdeal</a> -- whether something is an ideal</span></span></li>
<li><span>isLinearType(Module), see <span><a href="../../ReesAlgebra/html/_is__Linear__Type.html" title="is a module of linear type">isLinearType</a> -- is a module of linear type</span></span></li>
<li><span>isLinearType(Module,RingElement), see <span><a href="../../ReesAlgebra/html/_is__Linear__Type.html" title="is a module of linear type">isLinearType</a> -- is a module of linear type</span></span></li>
<li><span>isModule(Module), see <span><a href="_is__Module.html" title="whether something is a module">isModule</a> -- whether something is a module</span></span></li>
<li><span>isQuotientModule(Module), see <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><tt>isReduction(Module,Module)</tt> (missing documentation<!-- tag: (isReduction,Module,Module) -->)</span></li>
<li><span><tt>isReduction(Module,Module,RingElement)</tt> (missing documentation<!-- tag: (isReduction,Module,Module,RingElement) -->)</span></li>
<li><span>isSubmodule(Module), see <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><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></li>
<li><span>isSubset(Ideal,Module), see <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>isSubset(Module,Ideal), see <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><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></li>
<li><span><a href="_length_lp__Module_rp.html" title="length">length(Module)</a> -- length</span></li>
<li><span><a href="_map_lp__Module_rp.html" title="identity map">map(Module)</a> -- identity map</span></li>
<li><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></li>
<li><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></li>
<li><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></li>
<li><span>map(Module,Module,Number), see <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><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></li>
<li><span>map(Module,Module,ZZ), see <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>map(Module,ZZ,ZZ), see <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>map(Module,Module,RingMap,List), see <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><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></li>
<li><span>map(Module,Nothing,RingMap,List), see <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>map(Module,Nothing,RingMap,Matrix), see <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>map(Module,RingMap), see <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><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></li>
<li><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></li>
<li><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></li>
<li><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></li>
<li><span><a href="___Matrix_sp_st_st_sp__Module.html" title="tensor product">Matrix ** Module</a> -- tensor product</span></li>
<li><span>Module ** Matrix, see <span><a href="___Matrix_sp_st_st_sp__Module.html" title="tensor product">Matrix ** Module</a> -- tensor product</span></span></li>
<li><span>Matrix % Module, see <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><a href="_mingens_lp__Module_rp.html" title="minimal generator matrix">mingens(Module)</a> -- minimal generator matrix</span></li>
<li><span>GradedModule ++ Module, see <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>Module ++ GradedModule, see <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><a href="___Module_sp^_sp__Array.html" title="projection onto summand">Module ^ Array</a> -- projection onto summand</span></li>
<li><span><a href="___Module_sp^_sp__List.html" title="projection onto summand">Module ^ List</a> -- projection onto summand</span></li>
<li><span><a href="___Module_sp^_st_st_sp__Z__Z.html" title="tensor power">Module ^** ZZ</a> -- tensor power</span></li>
<li><span><a href="___Module_sp_us_sp__Array.html" title="inclusion from summand">Module _ Array</a> -- inclusion from summand</span></li>
<li><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></li>
<li><span><tt>Module _*</tt> (missing documentation<!-- tag: (_*,Module) -->)</span></li>
<li><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></li>
<li><span>monomialIdeal(Module), see <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>multidegree(Module), see <span><a href="_multidegree.html" title="multidegree">multidegree</a> -- multidegree</span></span></li>
<li><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></li>
<li><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></li>
<li><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></li>
<li><span><a href="_presentation_lp__Module_rp.html" title="presentation of a module">presentation(Module)</a> -- presentation of a module</span></li>
<li><span>Module : Module, see <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>quotient(Module,Module), see <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><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></li>
<li><span>rank(Module), see <span><a href="_rank.html" title="compute the rank">rank</a> -- compute the rank</span></span></li>
<li><span>reesAlgebra(Module), see <span><a href="../../ReesAlgebra/html/_rees__Algebra.html" title="compute the defining ideal of the Rees Algebra">reesAlgebra</a> -- compute the defining ideal of the Rees Algebra</span></span></li>
<li><span>reesAlgebra(Module,RingElement), see <span><a href="../../ReesAlgebra/html/_rees__Algebra.html" title="compute the defining ideal of the Rees Algebra">reesAlgebra</a> -- compute the defining ideal of the Rees Algebra</span></span></li>
<li><span>reesIdeal(Module), see <span><a href="../../ReesAlgebra/html/_rees__Ideal.html" title="compute the defining ideal of the Rees Algebra">reesIdeal</a> -- compute the defining ideal of the Rees Algebra</span></span></li>
<li><span>reesIdeal(Module,RingElement), see <span><a href="../../ReesAlgebra/html/_rees__Ideal.html" title="compute the defining ideal of the Rees Algebra">reesIdeal</a> -- compute the defining ideal of the Rees Algebra</span></span></li>
<li><span>regularity(Module), see <span><a href="_regularity.html" title="compute the Castelnuovo-Mumford regularity">regularity</a> -- compute the Castelnuovo-Mumford regularity</span></span></li>
<li><span>relations(Module), see <span><a href="_relations.html" title="the defining relations">relations</a> -- the defining relations</span></span></li>
<li><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></li>
<li><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></li>
<li><span>ring(Module), see <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>Ring / Module, see <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><a href="_schreyer__Order_lp__Module_rp.html" title="obtain Schreyer order information">schreyerOrder(Module)</a> -- obtain Schreyer order information</span></li>
<li><span>Module ~, see <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><a href="_sheaf_lp__Module_rp.html" title="make a coherent sheaf">sheaf(Module)</a> -- make a coherent sheaf</span></li>
<li><span><a href="_sheaf_lp__Variety_cm__Module_rp.html" title="make a coherent sheaf">sheaf(Variety,Module)</a> -- make a coherent sheaf</span></li>
<li><span>specialFiber(Module), see <span><a href="../../ReesAlgebra/html/_special__Fiber.html" title="special fiber of a blowup">specialFiber</a> -- special fiber of a blowup</span></span></li>
<li><span>specialFiber(Module,RingElement), see <span><a href="../../ReesAlgebra/html/_special__Fiber.html" title="special fiber of a blowup">specialFiber</a> -- special fiber of a blowup</span></span></li>
<li><span>specialFiberIdeal(Module), see <span><a href="../../ReesAlgebra/html/_special__Fiber__Ideal.html" title="special fiber of a blowup">specialFiberIdeal</a> -- special fiber of a blowup</span></span></li>
<li><span>specialFiberIdeal(Module,RingElement), see <span><a href="../../ReesAlgebra/html/_special__Fiber__Ideal.html" title="special fiber of a blowup">specialFiberIdeal</a> -- special fiber of a blowup</span></span></li>
<li><span>subquotient(Module,Matrix,Matrix), see <span><a href="_subquotient.html" title="make a subquotient module">subquotient</a> -- make a subquotient module</span></span></li>
<li><span>subquotient(Module,Matrix,Nothing), see <span><a href="_subquotient.html" title="make a subquotient module">subquotient</a> -- make a subquotient module</span></span></li>
<li><span>subquotient(Module,Nothing,Matrix), see <span><a href="_subquotient.html" title="make a subquotient module">subquotient</a> -- make a subquotient module</span></span></li>
<li><span>subquotient(Module,Nothing,Nothing), see <span><a href="_subquotient.html" title="make a subquotient module">subquotient</a> -- make a subquotient module</span></span></li>
<li><span>substitute(Module,Option), see <span><a href="_substitute.html" title="substituting values for variables">substitute</a> -- substituting values for variables</span></span></li>
<li><span>symmetricAlgebra(Module), see <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>tensor(Ring,RingMap,Module), see <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>tensorAssociativity(Module,Module,Module), see <span><a href="_tensor__Associativity.html" title="associativity isomorphisms for tensor products">tensorAssociativity</a> -- associativity isomorphisms for tensor products</span></span></li>
<li><span>universalEmbedding(Module), see <span><a href="../../ReesAlgebra/html/_universal__Embedding.html" title="Compute the universal embedding">universalEmbedding</a> -- Compute the universal embedding</span></span></li>
<li><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></li>
<li><span><a href="___Z__Z_sp_us_sp__Module.html" title="integers or zero element">ZZ _ Module</a> -- integers or zero element</span></li>
</ul>
</div>
<div class="waystouse"><h2>For the programmer</h2>
<p>The object <a href="___Module.html" title="the class of all modules">Module</a> is <span>a <a href="___Type.html">type</a></span>, with ancestor classes <a href="___Immutable__Type.html" title="the class of immutable types">ImmutableType</a> < <a href="___Hash__Table.html" title="the class of all hash tables">HashTable</a> < <a href="___Thing.html" title="the class of all things">Thing</a>.</p>
</div>
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