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 (H118E1)

 
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 (H118E2)

 
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 (H118E3)

 
Affine Algebras which are Fields
      Example AlgAff_EllipticCurve (H118E4)
      Example AlgAff_Factorization (H118E5)
      Example AlgAff_MultiExtension (H118E6)

 
Rings and Fields of Fractions of Affine Algebras
      RingOfFractions(Q) : RngMPolRes -> RngFunFrac
      Numerator(a) : RngFunFracElt -> RngMPolResElt
      Example AlgAff_FieldOfFractions (H118E7)
      Example AlgAff_Extension (H118E8)

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