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<head><title>Ideal -- the class of all ideals</title>
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<div><h1>Ideal -- the class of all ideals</h1>
<div class="single"><h2>Description</h2>
<div>For basic information about ideals in <em>Macaulay2</em>, see <a href="_ideals.html" title="">ideals</a>.<p/>
Common ways to make an ideal:<ul><li><span><a href="_ideal.html" title="make an ideal">ideal</a> -- make an ideal</span></li>
<li><span><a href="_annihilator.html" title="the annihilator ideal">annihilator</a> -- the annihilator ideal</span></li>
<li><span><a href="_content_lp__Ring__Element_rp.html" title="the content of a polynomial">content</a> -- the content of a polynomial</span></li>
<li><span><a href="_fitting__Ideal.html" title="Fitting ideal of a module">fittingIdeal</a> -- Fitting ideal of a module</span></li>
<li><span><a href="_kernel_lp__Ring__Map_rp.html" title="kernel of a ringmap">kernel(RingMap)</a> -- kernel of a ringmap</span></li>
<li><span><a href="_minors_lp__Z__Z_cm__Matrix_rp.html" title="ideal generated by minors">minors</a> -- ideal generated by minors</span></li>
<li><span><a href="_pfaffians.html" title="ideal generated by Pfaffians">pfaffians</a> -- ideal generated by Pfaffians</span></li>
</ul>
Common ways to get information about an ideal:<ul><li><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></li>
<li><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></li>
<li><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></li>
</ul>
Common operations on ideals:<ul><li><span><a href="___Ideal_sp_pl_sp__Ideal.html" title="sum of ideals">Ideal + Ideal</a> -- sum of ideals</span></li>
<li><span><a href="___Ideal_sp_st_sp__Ideal.html" title="product of ideals">Ideal * Ideal</a> -- product of ideals</span></li>
<li><span><a href="__eq_eq.html" title="equality">Ideal == Ideal</a> -- equality</span></li>
<li><span><a href="__eq_eq.html" title="equality">Ideal == ZZ</a> -- equality</span></li>
<li><span><a href="___Ideal_sp^_sp__Z__Z.html" title="power">Ideal ^ ZZ</a> -- power</span></li>
<li><span><a href="_trim_lp__Ideal_rp.html" title="">trim(Ideal)</a></span></li>
</ul>
Gröbner bases, normal forms, free resolutions<ul><li><span><a href="_gb.html" title="compute a Gröbner basis">gb</a> -- compute a Gröbner basis</span></li>
<li><span><a href="_lead__Term.html" title="get the greatest term">leadTerm</a> -- get the greatest term</span></li>
<li><span><a href="_codim.html" title="compute the codimension">codim</a> -- compute the codimension</span></li>
<li><span><a href="_dim.html" title="compute the Krull dimension">dim</a> -- compute the Krull dimension</span></li>
<li><span><a href="_methods_spfor_spnormal_spforms_spand_spremainder.html" title="calculate the normal form of ring elements and matrices">Matrix % Ideal</a> -- calculate the normal form of ring elements and matrices</span></li>
<li><span><a href="_resolution.html" title="projective resolution">resolution</a> -- projective resolution</span></li>
<li><span><a href="_betti.html" title="display degrees">betti</a> -- display degrees</span></li>
</ul>
Numeric information about homogeneous ideals<ul><li><span><a href="_degree.html" title="">degree</a></span></li>
<li><span><a href="_poincare.html" title="assemble degrees into polynomial">poincare</a> -- assemble degrees into polynomial</span></li>
<li><span><a href="_hilbert__Function.html" title="the Hilbert function">hilbertFunction</a> -- the Hilbert function</span></li>
<li><span><a href="_hilbert__Polynomial.html" title="compute the Hilbert polynomial">hilbertPolynomial</a> -- compute the Hilbert polynomial</span></li>
<li><span><a href="_hilbert__Series.html" title="compute the Hilbert series">hilbertSeries</a> -- compute the Hilbert series</span></li>
<li><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></li>
<li><span><a href="_euler.html" title="Euler characteristic">euler</a> -- Euler characteristic</span></li>
</ul>
Primary decomposition and components of an ideal<ul><li><span><a href="_minimal__Primes.html" title="minimal associated primes of an ideal">minimalPrimes</a> -- minimal associated primes of an ideal</span></li>
<li><span><a href="_radical.html" title="the radical of an ideal">radical</a> -- the radical of an ideal</span></li>
<li><span><a href="_associated__Primes.html" title="find the associated primes of an ideal">associatedPrimes</a> -- find the associated primes of an ideal</span></li>
<li><span><a href="../../PrimaryDecomposition/html/_primary__Decomposition.html" title="irredundant primary decomposition of an ideal">primaryDecomposition</a> -- irredundant primary decomposition of an ideal</span></li>
<li><span><a href="_top__Components.html" title="compute top dimensional component">topComponents</a> -- compute top dimensional component</span></li>
<li><span><a href="_saturate.html" title="saturation of ideal or submodule">saturate</a> -- saturation of ideal or submodule</span></li>
<li><span><a href="_quotient.html" title="quotient or division">quotient</a> -- quotient or division</span></li>
<li><span><a href="_quotient_lp__Ideal_cm__Ideal_rp.html" title="ideal or submodule quotient">Ideal : Ideal</a> -- ideal or submodule quotient</span></li>
<li><span><a href="_intersect.html" title="compute an intersection">intersect</a> -- compute an intersection</span></li>
</ul>
Ideals from geometry<ul><li><span><a href="___Fano.html" title="Fano scheme">Fano</a> -- Fano scheme</span></li>
<li><span><a href="___Grassmannian_lp__Z__Z_cm__Z__Z_rp.html" title="the Grassmannian of linear subspaces of a vector space">Grassmannian</a> -- the Grassmannian of linear subspaces of a vector space</span></li>
<li><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></li>
<li><span><a href="_singular__Locus.html" title="singular locus">singularLocus</a> -- singular locus</span></li>
</ul>
Common ways to use an ideal:<ul><li><span><a href="___Ring_sp_sl_sp__Ideal.html" title="make a quotient ring">Ring / Ideal</a> -- make a quotient ring</span></li>
</ul>
<p/>
An ideal <tt>I</tt> is an immutable object, so if you want to cache information about it, put it in the hash table <tt>I.cache</tt>.</div>
</div>
<div class="single"><h2>See also</h2>
<ul><li><span><a href="_ideals.html" title="">ideals</a></span></li>
</ul>
</div>
<div class="waystouse"><h2>Types of ideal :</h2>
<ul><li><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></li>
</ul>
<h2>Functions and methods returning an ideal :</h2>
<ul><li><span>Ideal * Ring, 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 * Ring, 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>Ring * Ideal, 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>Ring * MonomialIdeal, 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 * Ideal, 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>annihilator(CoherentSheaf), see <span><a href="_annihilator.html" title="the annihilator ideal">annihilator</a> -- the annihilator ideal</span></span></li>
<li><span>annihilator(Ideal), see <span><a href="_annihilator.html" title="the annihilator ideal">annihilator</a> -- the annihilator 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>annihilator(RingElement), see <span><a href="_annihilator.html" title="the annihilator ideal">annihilator</a> -- the annihilator ideal</span></span></li>
<li><span>conductor(RingMap), see <span><a href="../../IntegralClosure/html/_conductor.html" title="the conductor of a finite ring map">conductor</a> -- the conductor of a finite ring map</span></span></li>
<li><span><a href="_content_lp__Ring__Element_rp.html" title="the content of a polynomial">content(RingElement)</a> -- the content of a polynomial</span></li>
<li><span><a href="___Fano_lp__Z__Z_cm__Ideal_rp.html" title="Fano scheme">Fano(ZZ,Ideal)</a> -- Fano scheme</span></li>
<li><span><a href="___Fano_lp__Z__Z_cm__Ideal_cm__Ring_rp.html" title="Fano scheme">Fano(ZZ,Ideal,Ring)</a> -- Fano scheme</span></li>
<li><span><a href="_fitting__Ideal.html" title="Fitting ideal of a module">fittingIdeal</a> -- Fitting ideal of a 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="_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></li>
<li><span>Grassmannian, see <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>homogenize(Ideal,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>icPIdeal(RingElement,RingElement,ZZ), see <span><a href="../../IntegralClosure/html/_ic__P__Ideal.html" title="compute the integral closure in prime characteristic of a principal ideal">icPIdeal</a> -- compute the integral closure in prime characteristic of a principal ideal</span></span></li>
<li><span><a href="_ideal.html" title="make an ideal">ideal</a> -- make an ideal</span></li>
<li><span><a href="___Ideal_sp_st_sp__Ideal.html" title="product of ideals">Ideal * Ideal</a> -- product of ideals</span></li>
<li><span>Ideal * MonomialIdeal, see <span><a href="___Ideal_sp_st_sp__Ideal.html" title="product of ideals">Ideal * Ideal</a> -- product of ideals</span></span></li>
<li><span>MonomialIdeal * Ideal, see <span><a href="___Ideal_sp_st_sp__Ideal.html" title="product of ideals">Ideal * Ideal</a> -- product of ideals</span></span></li>
<li><span><a href="___Ideal_sp_pl_sp__Ideal.html" title="sum of ideals">Ideal + Ideal</a> -- sum of ideals</span></li>
<li><span>Ideal + MonomialIdeal, see <span><a href="___Ideal_sp_pl_sp__Ideal.html" title="sum of ideals">Ideal + Ideal</a> -- sum of ideals</span></span></li>
<li><span>MonomialIdeal + Ideal, see <span><a href="___Ideal_sp_pl_sp__Ideal.html" title="sum of ideals">Ideal + Ideal</a> -- sum of ideals</span></span></li>
<li><span><a href="___Ideal_sp^_sp__Z__Z.html" title="power">Ideal ^ ZZ</a> -- power</span></li>
<li><span><a href="_ideal_lp__List_rp.html" title="make an ideal">ideal(List)</a> -- make an ideal</span></li>
<li><span>ideal(Sequence), see <span><a href="_ideal_lp__List_rp.html" title="make an ideal">ideal(List)</a> -- make an ideal</span></span></li>
<li><span><a href="_ideal_lp__Matrix_rp.html" title="make an ideal">ideal(Matrix)</a> -- make an ideal</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>ideal(Number), see <span><a href="_ideal_lp__Ring__Element_rp.html" title="make an ideal">ideal(RingElement)</a> -- make an ideal</span></span></li>
<li><span><a href="_ideal_lp__Ring__Element_rp.html" title="make an ideal">ideal(RingElement)</a> -- make an ideal</span></li>
<li><span><a href="../../Classic/html/_ideal_lp__String_rp.html" title="make an ideal using classic Macaulay syntax">ideal(String)</a> -- make an ideal using classic Macaulay syntax</span></li>
<li><span><a href="_kernel_lp__Ring__Map_rp.html" title="kernel of a ringmap">kernel(RingMap)</a> -- kernel of a ringmap</span></li>
<li><span>lift(Ideal,type of RingElement), see <span><a href="_lift.html" title="lift to another ring">lift</a> -- lift to another ring</span></span></li>
<li><span><a href="../../PrimaryDecomposition/html/_localize_lp__Ideal_cm__Ideal_rp.html" title="localize an ideal at a prime ideal">localize(Ideal,Ideal)</a> -- localize an ideal at a prime ideal</span></li>
<li><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></li>
<li><span>prune(Ideal), see <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>minimalReduction(Ideal), see <span><a href="../../ReesAlgebra/html/_minimal__Reduction.html" title="minimal reduction of an ideal">minimalReduction</a> -- minimal reduction of an ideal</span></span></li>
<li><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></li>
<li><span>permanents(ZZ,Matrix), see <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><a href="_pfaffians.html" title="ideal generated by Pfaffians">pfaffians</a> -- ideal generated by Pfaffians</span></li>
<li><span>pfaffians(ZZ,Matrix), see <span><a href="_pfaffians.html" title="ideal generated by Pfaffians">pfaffians</a> -- ideal generated by Pfaffians</span></span></li>
<li><span><a href="../../PrimaryDecomposition/html/_primary__Component_lp__Ideal_cm__Ideal_rp.html" title="find a primary component corresponding to an associated prime">primaryComponent(Ideal,Ideal)</a> -- find a primary component corresponding to an associated prime</span></li>
<li><span>Ideal : 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>Ideal : 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>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="_quotient_lp__Ideal_cm__Ideal_rp.html" title="ideal or submodule quotient">quotient(Ideal,Ideal)</a> -- ideal or submodule quotient</span></li>
<li><span>quotient(Ideal,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,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>radical(Ideal), see <span><a href="_radical.html" title="the radical of an ideal">radical</a> -- the radical of an ideal</span></span></li>
<li><span>reesIdeal(Ideal), 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(Ideal,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>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>removeLowestDimension(Ideal), 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>RingMap Ideal, 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(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(Ideal,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(Ideal,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>saturate(MonomialIdeal,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>Schubert, see <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><a href="../../ReesAlgebra/html/_special__Fiber__Ideal.html" title="special fiber of a blowup">specialFiberIdeal</a> -- special fiber of a blowup</span></li>
<li><span>substitute(Ideal,List), see <span><a href="_substitute.html" title="substituting values for variables">substitute</a> -- substituting values for variables</span></span></li>
<li><span>substitute(Ideal,Matrix), see <span><a href="_substitute.html" title="substituting values for variables">substitute</a> -- substituting values for variables</span></span></li>
<li><span>substitute(Ideal,Ring), see <span><a href="_substitute.html" title="substituting values for variables">substitute</a> -- substituting values for variables</span></span></li>
<li><span>substitute(Ideal,RingFamily), see <span><a href="_substitute.html" title="substituting values for variables">substitute</a> -- substituting values for variables</span></span></li>
<li><span>symmetricKernel(Matrix), see <span><a href="../../ReesAlgebra/html/_symmetric__Kernel.html" title="Compute the Rees ring of the image of a matrix">symmetricKernel</a> -- Compute the Rees ring of the image of a matrix</span></span></li>
<li><span>tangentCone, see <span><a href="../../TangentCone/html/_tangent__Cone_lp__Ideal_rp.html" title="">tangentCone(Ideal)</a></span></span></li>
<li><span><a href="_top__Components_lp__Ideal_rp.html" title="compute top dimensional component">topComponents(Ideal)</a> -- compute top dimensional component</span></li>
<li><span><a href="_trim_lp__Ideal_rp.html" title="">trim(Ideal)</a></span></li>
<li><span>truncate(List,Ideal), 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,Ideal), 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 an ideal :</h2>
<ul><li><span>ZZ % Ideal, see <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>Ideal * CoherentSheaf, 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>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>Ideal * Vector, 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>Ideal + RingElement, see <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>Ideal == Ideal, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>Ideal == Module, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>Ideal == MonomialIdeal, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>Ideal == Ring, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>Ideal == ZZ, 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>MonomialIdeal == Ideal, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>Ring == Ideal, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>ZZ == Ideal, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>analyticSpread(Ideal), 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(Ideal,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>associatedGradedRing(Ideal), see <span><a href="../../ReesAlgebra/html/_associated__Graded__Ring.html" title="the associated graded ring of an ideal">associatedGradedRing</a> -- the associated graded ring of an ideal</span></span></li>
<li><span>associatedGradedRing(Ideal,RingElement), see <span><a href="../../ReesAlgebra/html/_associated__Graded__Ring.html" title="the associated graded ring of an ideal">associatedGradedRing</a> -- the associated graded ring of an ideal</span></span></li>
<li><span><a href="../../PrimaryDecomposition/html/_associated__Primes_lp__Ideal_rp.html" title="find the associated primes of an ideal">associatedPrimes(Ideal)</a> -- find the associated primes of an ideal</span></li>
<li><span>basis(Ideal), 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,InfiniteNumber,Ideal), 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,Ideal), 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,Ideal), 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,Ideal), 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,Ideal), 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,Ideal), 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,ZZ,Ideal), 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,Ideal), 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,Ideal), 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,List,Ideal), 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,Ideal), 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__Ideal_rp.html" title="gives the degrees of generators.">betti(Ideal)</a> -- gives the degrees of generators.</span></li>
<li><span><a href="_codim_lp__Ideal_rp.html" title="compute the codimension">codim(Ideal)</a> -- compute the codimension</span></li>
<li><span>CoherentSheaf / Ideal, see <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>comodule(Ideal), 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><a href="_degree_lp__Ideal_rp.html" title="">degree(Ideal)</a></span></li>
<li><span>degreeLength(Ideal), see <span><a href="_degree__Length.html" title="the number of degrees">degreeLength</a> -- the number of degrees</span></span></li>
<li><span>degrees(Ideal), see <span><a href="_degrees_lp__Ring_rp.html" title="degrees of generators">degrees(Ring)</a> -- degrees of generators</span></span></li>
<li><span><a href="_dim_lp__Ideal_rp.html" title="compute the Krull dimension">dim(Ideal)</a> -- compute the Krull dimension</span></li>
<li><span>distinguished(Ideal), see <span><a href="../../ReesAlgebra/html/_distinguished.html" title="compute the distinguished subvarieties of a scheme">distinguished</a> -- compute the distinguished subvarieties of a scheme</span></span></li>
<li><span>distinguished(Ideal,RingElement), see <span><a href="../../ReesAlgebra/html/_distinguished.html" title="compute the distinguished subvarieties of a scheme">distinguished</a> -- compute the distinguished subvarieties of a scheme</span></span></li>
<li><span>distinguishedAndMult(Ideal), see <span><a href="../../ReesAlgebra/html/_distinguished__And__Mult.html" title="compute the distinguished subvarieties of a scheme along with their multiplicities">distinguishedAndMult</a> -- compute the distinguished subvarieties of a scheme along with their multiplicities</span></span></li>
<li><span>distinguishedAndMult(Ideal,RingElement), see <span><a href="../../ReesAlgebra/html/_distinguished__And__Mult.html" title="compute the distinguished subvarieties of a scheme along with their multiplicities">distinguishedAndMult</a> -- compute the distinguished subvarieties of a scheme along with their multiplicities</span></span></li>
<li><span>eliminate(List,Ideal), see <span><a href="../../Elimination/html/_eliminate.html" title="">eliminate</a></span></span></li>
<li><span>eliminate(RingElement,Ideal), see <span><a href="../../Elimination/html/_eliminate.html" title="">eliminate</a></span></span></li>
<li><span><a href="_euler_lp__Ideal_rp.html" title="Euler characteristic">euler(Ideal)</a> -- Euler characteristic</span></li>
<li><span><a href="_eulers_lp__Ideal_rp.html" title="list the sectional Euler characteristics">eulers(Ideal)</a> -- list the sectional Euler characteristics</span></li>
<li><span>Ext(Ideal,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(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(Ideal,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>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^ZZ(Matrix,Ideal), see <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>Ext^ZZ(Ideal,Matrix), see <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>Ext^ZZ(Ideal,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(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(Ideal,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>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>flattenRing(Ideal), see <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>gb(Ideal), see <span><a href="_gb.html" title="compute a Gröbner basis">gb</a> -- compute a Gröbner basis</span></span></li>
<li><span>gbRemove(Ideal), see <span><a href="_gb__Remove.html" title="remove Gröbner basis">gbRemove</a> -- remove Gröbner basis</span></span></li>
<li><span>gbSnapshot(Ideal), 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><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></li>
<li><span>generator(Ideal), see <span><a href="_generator.html" title="provide a single generator">generator</a> -- provide a single generator</span></span></li>
<li><span>Ideal _ 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__Ideal_rp.html" title="the generator matrix of an ideal">generators(Ideal)</a> -- the generator matrix of an ideal</span></li>
<li><span>genus(Ideal), see <span><a href="_genus_lp__Coherent__Sheaf_rp.html" title="arithmetic genus">genus(CoherentSheaf)</a> -- arithmetic genus</span></span></li>
<li><span>hilbertFunction(List,Ideal), see <span><a href="_hilbert__Function.html" title="the Hilbert function">hilbertFunction</a> -- the Hilbert function</span></span></li>
<li><span>hilbertFunction(ZZ,Ideal), 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__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></li>
<li><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></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>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>Function \ Ideal, see <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><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></li>
<li><span><a href="___Ideal_sp_sl_sp__Ideal.html" title="quotient module">Ideal / Ideal</a> -- quotient module</span></li>
<li><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></li>
<li><span>idealizer(Ideal,RingElement), see <span><a href="../../IntegralClosure/html/_idealizer.html" title="compute Hom(I,I) as a quotient ring">idealizer</a> -- compute Hom(I,I) as a quotient ring</span></span></li>
<li><span>independentSets(Ideal), see <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>installHilbertFunction(Ideal,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>integralClosure(Ideal), see <span><a href="../../IntegralClosure/html/_integral__Closure_lp__Ideal_cm__Z__Z_rp.html" title="integral closure of an ideal in an affine domain">integralClosure(Ideal,ZZ)</a> -- integral closure of an ideal in an affine domain</span></span></li>
<li><span><a href="../../IntegralClosure/html/_integral__Closure_lp__Ideal_cm__Z__Z_rp.html" title="integral closure of an ideal in an affine domain">integralClosure(Ideal,ZZ)</a> -- integral closure of an ideal in an affine domain</span></li>
<li><span>irreducibleCharacteristicSeries(Ideal), see <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>isHomogeneous(Ideal), 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(Ideal), 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(Ideal), 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(Ideal,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>isMonomialIdeal(Ideal), see <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>isPrimary(Ideal), see <span><a href="../../PrimaryDecomposition/html/_is__Primary.html" title="determine whether an ideal is primary">isPrimary</a> -- determine whether an ideal is primary</span></span></li>
<li><span>isPrimary(Ideal,Ideal), see <span><a href="../../PrimaryDecomposition/html/_is__Primary.html" title="determine whether an ideal is primary">isPrimary</a> -- determine whether an ideal is primary</span></span></li>
<li><span>isPrime(Ideal), see <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><tt>isReduction(Ideal,Ideal)</tt> (missing documentation<!-- tag: (isReduction,Ideal,Ideal) -->)</span></li>
<li><span><tt>isReduction(Ideal,Ideal,RingElement)</tt> (missing documentation<!-- tag: (isReduction,Ideal,Ideal,RingElement) -->)</span></li>
<li><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></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="_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></li>
<li><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></li>
<li><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></li>
<li><span>lift(Ideal,type of QQ), see <span><a href="_lift.html" title="lift to another ring">lift</a> -- lift to another ring</span></span></li>
<li><span>lift(Ideal,type of ZZ), see <span><a href="_lift.html" title="lift to another ring">lift</a> -- lift to another ring</span></span></li>
<li><span>Matrix % Ideal, 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>RingElement % Ideal, 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>mingens(Ideal), see <span><a href="_mingens_lp__Module_rp.html" title="minimal generator matrix">mingens(Module)</a> -- minimal generator matrix</span></span></li>
<li><span>decompose(Ideal), see <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>minimalPrimes(Ideal), see <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>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>Ideal _ List, see <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><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><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></li>
<li><span>monomialSubideal(Ideal), see <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>multidegree(Ideal), see <span><a href="_multidegree.html" title="multidegree">multidegree</a> -- multidegree</span></span></li>
<li><span>multiplicity(Ideal), see <span><a href="../../ReesAlgebra/html/_multiplicity.html" title="compute the Hilbert-Samuel multiplicity of an ideal">multiplicity</a> -- compute the Hilbert-Samuel multiplicity of an ideal</span></span></li>
<li><span>multiplicity(Ideal,RingElement), see <span><a href="../../ReesAlgebra/html/_multiplicity.html" title="compute the Hilbert-Samuel multiplicity of an ideal">multiplicity</a> -- compute the Hilbert-Samuel multiplicity of an ideal</span></span></li>
<li><span>normalCone(Ideal), see <span><a href="../../ReesAlgebra/html/_normal__Cone.html" title="the normal cone of a subscheme">normalCone</a> -- the normal cone of a subscheme</span></span></li>
<li><span>normalCone(Ideal,RingElement), see <span><a href="../../ReesAlgebra/html/_normal__Cone.html" title="the normal cone of a subscheme">normalCone</a> -- the normal cone of a subscheme</span></span></li>
<li><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></li>
<li><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></li>
<li><span>preimage(RingMap,Ideal), see <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>primaryDecomposition(Ideal), see <span><a href="../../PrimaryDecomposition/html/_primary__Decomposition.html" title="irredundant primary decomposition of an ideal">primaryDecomposition</a> -- irredundant primary decomposition of an ideal</span></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>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>reductionNumber(Ideal,Ideal), see <span><a href="../../ReesAlgebra/html/_reduction__Number.html" title="reduction number of one ideal with respect to another">reductionNumber</a> -- reduction number of one ideal with respect to another</span></span></li>
<li><span>reesAlgebra(Ideal), 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(Ideal,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>regularity(Ideal), see <span><a href="_regularity.html" title="compute the Castelnuovo-Mumford regularity">regularity</a> -- compute the Castelnuovo-Mumford regularity</span></span></li>
<li><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></li>
<li><span>ring(Ideal), 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><a href="___Ring_sp_sl_sp__Ideal.html" title="make a quotient ring">Ring / Ideal</a> -- make a quotient ring</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>singularLocus(Ideal), see <span><a href="_singular__Locus.html" title="singular locus">singularLocus</a> -- singular locus</span></span></li>
<li><span>specialFiber(Ideal), 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(Ideal,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(Ideal), 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(Ideal,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>substitute(Ideal,Option), see <span><a href="_substitute.html" title="substituting values for variables">substitute</a> -- substituting values for variables</span></span></li>
<li><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></li>
<li><span><a href="../../TangentCone/html/_tangent__Cone_lp__Ideal_rp.html" title="">tangentCone(Ideal)</a></span></li>
<li><span>universalEmbedding(Ideal), 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="_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></li>
<li><span>whichGm(Ideal), see <span><a href="../../ReesAlgebra/html/_which__Gm.html" title="largest Gm satisfied by an ideal">whichGm</a> -- largest Gm satisfied by an ideal</span></span></li>
</ul>
</div>
<div class="waystouse"><h2>For the programmer</h2>
<p>The object <a href="___Ideal.html" title="the class of all ideals">Ideal</a> is <span>a <a href="___Type.html">type</a></span>, with ancestor classes <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>
</div>
</body>
</html>
