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2.9.8 Commands and Functions for RING
AffHilbertFn the affine Hilbert function
BaseRing the base ring of a ring
BettiDiagram the diagram of the graded Betti numbers
CanonicalHom canonical homomorphism
characteristic the characteristic of a ring
CoeffEmbeddingHom returns the coefficient embedding homomorphism of a polynomial ring
CoeffRing the ring of coefficients of a polynomial ring
ColMat single column matrix
DefiningIdeal defining ideal of a quotient ring
DensePoly the sum of all power-products of a given degree
depth Depth of a module
DiagMat matrix with given diagonal
dim the dimension of a ring or quotient object
EmbeddingHom returns the embedding homomorphism of a fraction field
GenericPoints random projective points
GradingMat matrix of generalized weights for indeterminates
HilbertFn the Hilbert function
HilbertPoly the Hilbert polynomial
HilbertSeries the Hilbert-Poincare series
HilbertSeriesMultiDeg the Hilbert-Poincare series wrt a multigrading
HVector the h-vector of a module or quotient object
ideal ideal generated by list
IdealOfPoints ideal of a set of affine points
IdentityMat the identity matrix
implicit implicitization
ImplicitHypersurface implicitization of hypersurface
indet individual indeterminates
indets list of indetermiantes in a PolyRing
IndetSymbols the names of the indeterminates in a PolyRing
InducedHom homomorphism induced by a homomorphism
IsField test whether a ring is a field
IsFiniteField test whether a ring is a finite field
IsFractionField test whether a ring is a fraction field
IsPolyRing test whether a ring is a polynomial ring
IsQQ test whether a ring is the ring of rationals
IsQuotientRing test whether a ring is a quotient ring
IsStdGraded checks if the grading is standard
IsTrueGCDDomain test whether a ring is a true GCD domain
IsZZ test whether a ring is the ring of integers
LogCardinality extension degree of a finite field
MakeTerm returns a monomial (power-product) with given exponents
matrix convert a list into a matrix
multiplicity the multiplicity (degree) of a ring or quotient object
NewFractionField create a new fraction field
NewFreeModule create a new FreeModule
NewMat Zero matrix
NewPolyRing create a new PolyRing
NewQuotientRing create a new quotient ring
NewWeylAlgebra create a new Weyl Algebra
NumIndets number of indeterminates
one one of a ring
operators, shortcuts Special characters equivalent to commands
OrdMat matrix defining a term-ordering
poincare [OBSOLESCENT] [OBSOLESCENT] the Hilbert-Poincare series
PolyAlgebraHom homomorphism of polynomial algebras
PolyRingHom homomorphism of polynomial rings
PrintBettiDiagram the diagram of the graded Betti numbers
QQEmbeddingHom returns the homomorphism QQ --> R
QuotientingHom returns the projection homomorphism into a quotient ring
RandomUnimodularMat random unimodular matrix
ReadExpr Read RINGELEM expression from string
reg Castelnuovo-Mumford regularity of a module
RegularityIndex regularity index of a Hilbert function or series
RingElem convert an expression into a RINGELEM
RingID identification for ring
RowMat single row matrix
SubalgebraRepr representation of a polynomial as a subalgebra element
SymmetricPolys list of symmetric polynomials
TmpChainCanonicalHom canonical homomorphism
TmpNBM Numerical Border Basis of ideal of points
WeightsMatrix [OBSOLESCENT] [OBSOLESCENT] matrix of generalized weights for indeterminates
zero zero of a ring
ZeroMat matrix filled with 0