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# PolynomialRing -- the class of all ordered monoid rings

## Description

Every element of a polynomial ring is also a RingElement.

## See also

- polynomial rings

### Menu

- hilbertSeries(PolynomialRing) -- compute the Hilbert series of a ring

## Functions and methods returning a polynomial ring:

- degreesRing -- the ring or monoid of degrees
- `InexactFieldFamily Array` -- see Ring Array -- the standard way to make a polynomial ring
- Ring Array -- the standard way to make a polynomial ring
- `InexactFieldFamily List` -- see Ring List -- make a local polynomial ring
- Ring List -- make a local polynomial ring
- `InexactFieldFamily Monoid` -- see Ring Monoid -- make a polynomial ring
- Ring Monoid -- make a polynomial ring

## Methods that use a polynomial ring:

- `ambient(PolynomialRing)` -- see ambient(Ring) -- ambient polynomial ring
- `codim(PolynomialRing)` -- see codim(QuotientRing) -- compute the codimension
- `degreeGroup(PolynomialRing)` -- see degreeGroup -- the degree group of a ring or monoid
- `describe(PolynomialRing)` -- see describe -- real description
- `dim(PolynomialRing)` -- see dim(Ring) -- compute the Krull dimension
- `flattenRing(PolynomialRing)` -- see flattenRing -- write a ring as a (quotient of a) polynomial ring
- `Grassmannian(ZZ,ZZ,PolynomialRing)` -- see Grassmannian -- compute the ideal of the Grassmannian of linear subspaces of a vector space
- `heft(PolynomialRing)` -- see heft -- heft vector of ring or monoid
- hilbertSeries(PolynomialRing) -- compute the Hilbert series of a ring
- `isAffineRing(PolynomialRing)` -- see isAffineRing -- whether something is an affine ring
- `isHomogeneous(PolynomialRing)` -- see isHomogeneous -- whether something is homogeneous (graded)
- `isPolynomialRing(PolynomialRing)` -- see isPolynomialRing -- whether something is a polynomial ring
- `isSkewCommutative(PolynomialRing)` -- see isSkewCommutative -- whether a ring has skew commuting variables
- `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(Monoid) -- get values used for optional arguments
- `precision(PolynomialRing)` -- see precision
- presentation(PolynomialRing,QuotientRing) -- presentation of a quotient ring
- `selectVariables(List,PolynomialRing)` -- see selectVariables -- make a subring of a polynomial ring generated by selected variables
- `isWeylAlgebra(PolynomialRing)` -- see Weyl algebras

## For the programmer

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

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Macaulay2Doc/doc_rings.m2:186:0.