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 powerproducts 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 HilbertPoincare series

HilbertSeriesMultiDeg

the HilbertPoincare series wrt a multigrading

HVector

the hvector 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 (powerproduct) 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 termordering

poincare [OBSOLESCENT]

[OBSOLESCENT] the HilbertPoincare 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

CastelnuovoMumford 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
