[next][previous][up][top][index]
search for:

Ideal -- the class of all ideals

The type Ideal is a member of the class Type. Each object of class Ideal is called an ideal. Each ideal is also a member of class HashTable.

More general types (whose methods may also apply) :

  • HashTable -- the class of all hash tables
  • See also:

  • ideals
  • Common ways to make an ideal:

  • ideal -- make an ideal
  • annihilator -- the annihilator ideal
  • content -- the content of a polynomial
  • fittingIdeal -- Fitting ideal of a module
  • kernel RingMap -- kernel of a map
  • Common ways to get information about an ideal:

  • codim Ideal -- calculate the codimension
  • dim Ideal -- calculate the dimension
  • generators Ideal -- matrix of generators
  • isSubset(Ideal,Ideal) -- whether something is a subset of another
  • Common operations on ideals:

  • Ideal + Ideal -- sum of ideals
  • Ideal * Ideal -- product of ideals
  • Ideal == Ideal -- equality
  • Ideal == ZZ -- equality
  • Ideal : Ideal -- ideal quotient
  • Ideal ^ ZZ -- power of an ideal
  • decompose Ideal -- irreducible components of an ideal
  • gb Ideal -- compute a Groebner basis
  • radical Ideal -- compute the radical of an ideal
  • saturate -- saturation of ideal or submodule
  • top -- compute the top dimensional components
  • trim Ideal -- simplify the presentation
  • Common ways to use an ideal:

  • Ring / Ideal -- quotient ring
  • An ideal I is an immutable object, so if you want to cache information about it, put it in the hash table I.cache.

    Functions and methods returning a an ideal :

  • ann' Module
  • annihilator CoherentSheaf
  • annihilator Ideal
  • annihilator Module -- the annihilator ideal
  • annihilator RingElement
  • conductor RingMap -- compute the conductor of a finite ring map
  • content Matrix
  • content RingElement
  • Fano(ZZ,Ideal)
  • Fano(ZZ,Ideal,Ring)
  • fittingIdeal(ZZ,Module)
  • graphIdeal RingMap
  • Grassmannian(ZZ,ZZ)
  • Grassmannian(ZZ,ZZ,Ring)
  • homogenize(Ideal,RingElement)
  • ideal Sequence
  • Ideal * Ideal -- product of ideals
  • Ideal * MonomialIdeal
  • Ideal * Ring
  • Ideal + Ideal -- sum of ideals
  • Ideal + MonomialIdeal
  • Ideal : Ideal -- ideal quotient
  • Ideal : RingElement
  • Ideal ^ ZZ -- power of an ideal
  • ideal -- make an ideal
  • ideal List
  • ideal Matrix
  • ideal Module
  • ideal RingElement
  • kernel RingMap
  • lift(Ideal,Ring)
  • localize(Ideal,Ideal) -- localize an ideal at a prime ideal
  • minors(ZZ,Matrix) -- ideal generated by minors
  • Module : Module
  • MonomialIdeal * Ideal
  • MonomialIdeal * Ring
  • MonomialIdeal + Ideal
  • pfaffians(ZZ,Matrix)
  • primaryComponent(Ideal,Ideal) -- find a primary component corresponding to an associated prime
  • quotient(Ideal,Ideal)
  • quotient(Ideal,RingElement)
  • quotient(Module,Module)
  • radical Ideal
  • removeLowestDimension Ideal
  • Ring * Ideal
  • Ring * MonomialIdeal
  • RingElement * Ideal
  • RingMap Ideal
  • saturate Ideal
  • saturate(Ideal,Ideal)
  • saturate(Ideal,RingElement)
  • substitute(Ideal,List)
  • substitute(Ideal,Matrix)
  • substitute(Ideal,Ring)
  • top Ideal
  • trim Ideal
  • truncate(List,Ideal)
  • truncate(ZZ,Ideal)
  • Methods for using an ideal :

  • ass Ideal -- find the associated primes of an ideal
  • basis Ideal
  • basis(List,Ideal)
  • basis(ZZ,Ideal)
  • betti Ideal
  • codim Ideal
  • CoherentSheaf / Ideal
  • decompose Ideal
  • degree Ideal
  • degrees Ideal -- degrees of generators
  • dim Ideal
  • EngineRing / Ideal
  • euler Ideal
  • expression Ideal
  • Ext(Ideal,Ideal)
  • Ext(Ideal,Module)
  • Ext(Ideal,Ring)
  • Ext(Module,Ideal)
  • Ext^ZZ(Ideal,Ideal)
  • Ext^ZZ(Ideal,Module)
  • Ext^ZZ(Ideal,Ring)
  • Ext^ZZ(Matrix,Ideal)
  • Ext^ZZ(Module,Ideal)
  • gb Ideal
  • genera Ideal
  • generators Ideal
  • hilbertFunction(List,Ideal)
  • hilbertFunction(ZZ,Ideal)
  • hilbertPolynomial Ideal
  • hilbertSeries Ideal
  • Hom(Ideal,Ideal)
  • Hom(Ideal,Module)
  • Hom(Ideal,Ring)
  • Hom(Module,Ideal)
  • Hom(Ring,Ideal)
  • Ideal * CoherentSheaf
  • Ideal * Module
  • Ideal / Ideal -- quotient module
  • Ideal == Ideal
  • Ideal == Module
  • Ideal == MonomialIdeal
  • Ideal == Ring
  • Ideal == ZZ -- equality
  • Ideal _ {...} -- map from free module to some generators
  • Ideal _ ZZ
  • irreducibleCharacteristicSeries Ideal
  • isHomogeneous Ideal
  • isMonomialIdeal Ideal
  • isSubset(Ideal,Ideal)
  • isSubset(Ideal,Module)
  • isSubset(Module,Ideal)
  • jacobian Ideal
  • leadTerm Ideal
  • leadTerm(ZZ,Ideal)
  • lift(Ideal,ZZ)
  • map Ideal
  • map(Ideal,Ideal)
  • Matrix % Ideal
  • mingens Ideal
  • minPresIdeal Ideal
  • minPresMapIdeal Ideal
  • Module / Ideal -- quotient module by an ideal
  • Module : Ideal
  • Module == Ideal
  • module Ideal -- turn an ideal into a module
  • MonomialIdeal == Ideal
  • monomialIdeal Ideal -- make a monomial ideal
  • monomialSubideal Ideal -- find the largest monomial ideal in an ideal
  • net Ideal
  • newdecompose Ideal
  • numgens Ideal
  • poincare Ideal
  • primaryDecomposition Ideal -- find a primary decomposition of an ideal
  • quotient(Module,Ideal)
  • resolution Ideal -- make a projective resolution
  • Ring / Ideal -- quotient ring
  • Ring == Ideal
  • ring Ideal
  • RingElement % Ideal
  • saturate(Module,Ideal)
  • singularLocus Ideal
  • substitute(Ideal,Option)
  • toString Ideal
  • variety Ideal
  • ZZ % Ideal
  • ZZ * Ideal
  • ZZ == Ideal

  • [next][previous][up][top][index]
    search for: