- Introduction
- Creation of Polynomial Rings and their Ideals
- First Operations on Ideals
- Simple Ideal Constructions
- Basic Commutative Algebra Operations
- QuotientDimension(I) : RngMPol -> RngIntElt
- ColonIdeal(I, J) : RngMPol, RngMPol -> RngMPol
- ColonIdeal(I, f) : RngMPol, RngMPolElt -> RngMPol, RngIntElt
- ColonIdealEquivalent(I, f) : RngMPol, RngMPolElt -> RngMPol, RngMPolElt
- Saturation(I, J) : RngMPol, RngMPol -> RngMPol
- Saturation(I): RngMPol -> RngMPol
- Generic(I) : RngMPol -> RngMPol
- LeadingMonomialIdeal(I) : RngMPol -> RngMPol
- I meet J : RngMPol, RngMPol -> RngMPol
- &meet S : [ RngMPol ] -> RngMPol
- RegularSequence(I): RngMPol -> SeqEnum
- ReesIdeal(P, I): RngMPol, RngMPol -> RngMPol, Map
- Ideal Predicates
- Element Operations with Ideals
- Computation of Varieties
- Multiplicities
- Elimination
- Variable Extension of Ideals
- Homogenization of Ideals
- Extension and Contraction of Ideals
- Dimension of Ideals
- Radical and Decomposition of Ideals
- Normalisation and Noether Normalisation
- Hilbert Series and Hilbert Polynomial
- Syzygies
- Maps between Rings
- Symmetric Polynomials
- Functions for Polynomial Algebra and Module Generators
- MinimalAlgebraGenerators(L) : [ RngMPol ] -> [ RngMPol ]
- HomogeneousModuleTest(P, S, F) : [ RngMPol ], [ RngMPol ], RngMPol -> BoolElt, [ RngMPol ]
- HomogeneousModuleTest(P, S, L) : [ RngMPol ], [ RngMPol ], [ RngMPol ] -> [ BoolElt ], [ [ RngMPol ] ]
- HomogeneousModuleTestBasis(P, S, L) : [ RngMPol ], [ RngMPol ], [ RngMPol ] -> [ BoolElt ], [ [ RngMPol ] ]
- Example Ideal_HomogeneousModuleTest1 (H113E19)
- Bibliography
V2.28, 13 July 2023