PolynomialRing -- the class of all ordered monoid rings

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 Macaulay2Doc/doc_rings.m2:186:0.