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2.9.8 Commands and Functions for RING
AffHilbertFn the affine Hilbert function
AffHilbertSeries the affine Hilbert-Poincare series
ApproxPointsNBM Numerical Border Basis of ideal of points
ArrBoolean boolean arrangement
ArrBraid braid arrangement
ArrCatalanA Catalan arrangement of type A
ArrCatalanB Catalan arrangement of type B
ArrCatalanD Catalan arrangement of type D
ArrGraphical graphical arrangement
ArrShiA Shi arrangement of type A
ArrShiB Shi arrangement of type B
ArrShiCatalanA Shi-Catalan arrangement of type A with multiplicities
ArrShiCatalanB Shi-Catalan arrangement of type B with given multiplicities
ArrShiCatalanD Shi-Catalan arrangement of type D with given multiplicities
ArrShiD Shi arrangement of type D
ArrSignedGraphical signed graphical arrangement
ArrTypeB reflection arrangement of type B
ArrTypeD reflection arrangement of type D
BaseRing the base ring of a ring
BettiDiagram the diagram of the graded Betti numbers
BringIn bring in objects from another ring
CanonicalHom canonical homomorphism
ChainCanonicalHom 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 (quotient) ring
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
IdealOfProjectivePoints ideal of a set of projective points
IdentityMat the identity matrix
implicit implicitization
ImplicitHypersurface implicitization of hypersurface
indet individual indeterminates
indets list of indeterminates in a PolyRing
IndetSymbols the names of the indeterminates in a PolyRing
InducedHom homomorphism induced by a homomorphism
IsCommutative test whether a ring is commutative
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
IsIntegralDomain test whether a ring is integral
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
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
PolyAlgebraHom homomorphism of polynomial algebras
PolyRingHom homomorphism of polynomial rings
PrintBettiDiagram print the diagram of the graded Betti numbers
PrintSectionalMatrix print sectional matrix
QQEmbeddingHom returns the homomorphism QQ --> R
QuotientingHom returns the projection homomorphism into a quotient ring
RandomLinearForm random linear form in polynomial ring
RandomSparseNonSing01Mat random sparse non-singular (0,1) matrix
RandomUnimodularMat random unimodular matrix
reg Castelnuovo-Mumford regularity of a module
RegularityIndex regularity index of a Hilbert function or series
RingElem convert an expression into a RINGELEM
RingElems convert an expression into a RINGELEM
RingID identification for ring
RowMat single row matrix
SectionalMatrix sectional matrix
SymmetricPolys list of symmetric polynomials
zero zero of a ring
ZeroMat matrix filled with 0