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2.9.9 Commands and Functions for RING
AffHilbert the affine Hilbert function
AffHilbertFn the affine Hilbert function
BaseRing the base ring of an object
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
DiagMat matrix with given diagonal
dim the dimension of a ring or quotient object
GenericPoints random projective points
hilbert the Hilbert-Poincare' function
HilbertFn the Hilbert function
HilbertPoly the Hilbert polynomial
HilbertSeries the Hilbert-Poincare series
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
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
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
LogCardinality extension degree of a finite field
LogToTerm 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
NumIndets number of indeterminates
one one of a ring
OrdMat matrix defining a term-ordering
poincare the Hilbert-Poincare series
PolyAlgebraHom homomorphism of polynomial algebras
PolyRingHom homomorphism of polynomial rings
RegularityIndex regularity index of a Hilbert function or series
RingElem convert an expression into a RINGELEM
RowMat single row matrix
TmpNBM Numerical Border Basis of ideal of points
WeightsMatrix matrix of generalized weights for indeterminates
zero zero of a ring
ZeroMat matrix filled with 0