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 |