Creation of Affine Algebras
quo< P | J > : RngMPol, RngMPol -> RngMPolRes
P / J : RngMPol, RngMPol -> RngMPolRes
AffineAlgebra< R, X | R > : Fld, List, List -> RngMPolRes
Example AlgAff_Creation (H51E1)
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(I) : 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
ColonIdeal(I, 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 ]
Finite Dimensional Affine Algebras
Dimension(Q) : RngMPolRes -> RngIntElt
VectorSpace(Q) : RngMPolRes -> ModTupFld, Map
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 (H51E2)
Affine Algebras which are Fields
Example AlgAff_EllipticCurve (H51E3)
Example AlgAff_Factorization (H51E4)