| 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 |