Introduction
Creation of Affine Algebras quo< P | J > : RngMPol, RngMPol -> RngMPolRes P / J : RngMPol, RngMPol -> RngMPolRes AffineAlgebra< R, X | L > : Fld, List, List -> RngMPolRes Example AlgAff_Creation (H99E1)
Operations on Affine Algebras Q . i : RngMPolRes, RngIntElt -> RngMPolResElt CoefficientRing(Q) : RngMPolRes -> Rng Rank(Q) : RngMPolRes -> RngIntElt DivisorIdeal(I) : RngMPolRes -> RngMPol PreimageIdeal(I) : RngMPolRes -> RngMPol PreimageRing(Q) : RngMPolRes -> RngMPol OriginalRing(Q) : RngMPolRes -> Rng I eq J : RngMPolRes, RngMPolRes -> BoolElt I subset J : RngMPolRes, RngMPolRes -> BoolElt I + J : RngMPolRes, RngMPolRes -> RngMPolRes I * J : RngMPolRes, RngMPolRes -> RngMPolRes I ^ n : RngMPolRes, RngIntElt -> BoolElt I meet J : RngMPolRes, RngMPolRes -> RngMPolRes IsProper(I) : RngMPolRes -> BoolElt IsZero(I) : RngMPolRes -> BoolElt IsPrime(I) : RngMPolRes -> BoolElt IsPrimary(I) : RngMPolRes -> BoolElt IsRadical(I) : RngMPolRes -> BoolElt PrimaryDecomposition(I) : RngMPolRes -> [ RngMPolRes ], [ RngMPolRes ] RadicalDecomposition(I) : RngMPolRes -> [ RngMPolRes ] Example AlgAff_Operations (H99E2)
Maps between Affine Algebras AffineAlgebraMapKernel(phi) : Map -> MPol
Finite Dimensional Affine Algebras HasFiniteDimension(Q) : RngMPolRes -> BoolElt Dimension(Q) : RngMPolRes -> RngIntElt VectorSpace(Q) : RngMPolRes -> ModTupFld, Map MonomialBasis(Q) : RngMPolRes -> [ RngMPolResElt ] MatrixAlgebra(Q) : RngMPolRes -> AlgMat, Map RepresentationMatrix(f) : RngMPolResElt -> AlgMatElt IsUnit(f) : RngMPolResElt -> BoolElt IsNilpotent(f) : RngMPolResElt -> BoolElt, RngIntElt MinimalPolynomial(f) : RngMPolResElt -> RngUPol Example AlgAff_MinimalPolynomial (H99E3)
Affine Algebras which are Fields Example AlgAff_EllipticCurve (H99E4) Example AlgAff_Factorization (H99E5) Example AlgAff_MultiExtension (H99E6)
Rings and Fields of Fractions of Affine Algebras RingOfFractions(Q) : RngMPolRes -> RngFunFrac Numerator(a) : RngFunFrac -> RngMPolResElt Example AlgAff_FieldOfFractions (H99E7) Example AlgAff_Extension (H99E8) [Next][Prev] [Right] [____] [Up] [Index] [Root]
