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 |
RingElemList, RingElems | convert expressions into a LIST of 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 |