# PolynomialRing -- the class of all ordered monoid rings

## Description

Every element of a polynomial ring is also a RingElement.

## Methods that use a polynomial ring :

• ambient(PolynomialRing), see ambient(Ring) -- ambient polynomial ring
• codim(PolynomialRing), see codim(QuotientRing) -- compute the codimension
• degreesMonoid(PolynomialRing), see degreesMonoid -- get the monoid of degrees
• depth(Ideal,PolynomialRing) (missing documentation) -- computes the depth of a ring
• describe(PolynomialRing), see describe -- real description
• dim(PolynomialRing), see dim(Ring) -- compute the Krull dimension
• Grassmannian(ZZ,ZZ,PolynomialRing), see Grassmannian(ZZ,ZZ) -- the Grassmannian of linear subspaces of a vector space
• heft(PolynomialRing) (missing documentation)
• hilbertSeries(PolynomialRing) -- compute the Hilbert series of a ring
• isAffineRing(PolynomialRing), see isAffineRing -- whether something is an affine ring
• isPolynomialRing(PolynomialRing), see isPolynomialRing -- whether someting is a polynomial ring
• isSkewCommutative(PolynomialRing), see isSkewCommutative -- whether a ring has skew commuting variables
• monoid(PolynomialRing), see monoid -- make or retrieve a monoid
• newCoordinateSystem(PolynomialRing,Matrix), see newCoordinateSystem -- change variables
• newRing(PolynomialRing), see newRing -- make a copy of a ring, with some features changed
• numgens(PolynomialRing), see numgens(Ring) -- number of generators of a polynomial ring
• options(PolynomialRing), see options(Ring) -- get values used for optional arguments
• precision(PolynomialRing), see precision
• presentation(PolynomialRing,QuotientRing) -- presentation of a quotient ring
• selectVariables(List,PolynomialRing) -- make a subring of a polynomial ring generated by selected variables

## For the programmer

The object PolynomialRing is a type, with ancestor classes EngineRing < Ring < Type < MutableHashTable < HashTable < Thing.