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Magma
Computer • algebra
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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 (H115E1)
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 (H115E2)
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 (H115E3)
Affine Algebras which are Fields
Example
AlgAff_EllipticCurve (H115E4)
Example
AlgAff_Factorization (H115E5)
Example
AlgAff_MultiExtension (H115E6)
Rings and Fields of Fractions of Affine Algebras
RingOfFractions(Q) : RngMPolRes -> RngFunFrac
Numerator(a) : RngFunFracElt -> RngMPolResElt
Example
AlgAff_FieldOfFractions (H115E7)
Example
AlgAff_Extension (H115E8)
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V2.28, 28 February 2025