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4.8.14 Commands and Functions for Rings
The following are commands and functions controlling rings:
AffHilbert the affine Hilbert function
AffHilbertFn the affine Hilbert function
AffHilbertSeries the affine Hilbert-Poincare series
AffPoincare the affine Hilbert-Poincare series
Characteristic the characteristic of a ring
Clear clear the working memory or a ring-bound memory
CurrentRing the current ring
Deg the degree of a polynomial or vector
Delete delete variables from the working memory
Destroy delete rings
Dim the dimension of a ring or quotient object
Hilbert the Hilbert-Poincare' function
HilbertFn the Hilbert function
HilbertPoly the Hilbert polynomial
HilbertSeries the Hilbert-Poincare series
HilbertSeriesMultiDeg the Hilbert-Poincare series wrt a multigrading
HilbertSeriesShifts the Hilbert-Poincare series
HVector the h-vector of a module or quotient object
Image apply ring homomorphism
Indet individual indeterminates
IndetInd the index of an indeterminate
IndetIndex index of an indeterminate
IndetName the name of an indeterminate
Indets list of current indeterminates
MDeg multi-degree of an polynomial
Multiplicity the multiplicity (degree) of a ring or quotient object
NumIndets number of indeterminates
Ord matrix defining a term-ordering
Poincare the Hilbert-Poincare series
PoincareMultiDeg the Hilbert-Poincare series wrt a multigrading
PoincareShifts the Hilbert-Poincare series
QZP change field for polynomials and ideals
Ring returns the ring with a given name
RingEnv name of the current ring
RingEnvs names of all defined rings
RingEnvSet set of names of the ring environments
RMap define ring homomorphism
TypeOfCoeffs type of the coefficients of the current ring
UnivariateIndetIndex the index of the indeterminate of a univariate polynomial
Use command for making a ring active
Using perform commands in non-active ring
WeightsList first row of the weights matrix
WeightsMatrix matrix of generalized weights for indeterminates
ZPQ change field for polynomials and ideals

For details look up each item by name. Online, try ?ItemName or H.Syntax("ItemName").