QuotientRing -- the class of all quotient rings

Functions and methods returning a quotient ring:

• coimage(RingMap) -- see coimage -- coimage of a map
• graphRing(RingMap) -- the coordinate ring of the graph of the regular map corresponding to a ring map
• Ring / Ideal -- make a quotient ring
• Ring / List -- see Ring / Ideal -- make a quotient ring
• Ring / Module -- see Ring / Ideal -- make a quotient ring
• Ring / RingElement -- see Ring / Ideal -- make a quotient ring
• Ring / Sequence -- see Ring / Ideal -- make a quotient ring
• singularLocus(Ideal) -- see singularLocus -- singular locus
• singularLocus(Ring) -- see singularLocus -- singular locus

Methods that use a quotient ring:

• ambient(QuotientRing) -- see ambient(Ring) -- ambient polynomial ring
• codim(QuotientRing) -- compute the codimension
• degreeGroup(QuotientRing) -- see degreeGroup -- the degree group of a ring or monoid
• degrees(QuotientRing) -- see degrees(Ring) -- degrees of generators
• describe(QuotientRing) -- see describe -- real description
• dim(QuotientRing) -- see dim(Ring) -- compute the Krull dimension
• flattenRing(QuotientRing) -- see flattenRing -- write a ring as a (quotient of a) polynomial ring
• heft(QuotientRing) -- see heft -- heft vector of ring or monoid
• hilbertSeries(QuotientRing) -- see hilbertSeries(PolynomialRing) -- compute the Hilbert series of a ring
• ideal(QuotientRing) -- see ideal(Ring) -- get the defining ideal
• isAffineRing(QuotientRing) -- see isAffineRing -- whether something is an affine ring
• isHomogeneous(QuotientRing) -- see isHomogeneous -- whether something is homogeneous (graded)
• isQuotientOf(Ring,QuotientRing) -- see isQuotientOf(Ring,Ring) -- whether one ring is a quotient of another
• isQuotientOf(Type,QuotientRing) -- see isQuotientOf(Type,Ring) -- whether one ring is a quotient of a ring of a given type
• isQuotientRing(QuotientRing) -- see isQuotientRing -- whether something is a quotient ring
• isSkewCommutative(QuotientRing) -- see isSkewCommutative -- whether a ring has skew commuting variables
• newRing(QuotientRing) -- see newRing -- make a copy of a ring, with some features changed
• numgens(QuotientRing) -- see numgens(Ring) -- number of generators of a polynomial ring
• options(QuotientRing) -- see options(Monoid) -- get values used for optional arguments
• precision(QuotientRing) -- see precision
• presentation(PolynomialRing,QuotientRing) -- presentation of a quotient ring
• presentation(QuotientRing) -- see presentation(PolynomialRing,QuotientRing) -- presentation of a quotient ring
• trim(QuotientRing) -- see trim -- minimize generators and relations
• isWeylAlgebra(QuotientRing) -- see Weyl algebras

For the programmer

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

The source of this document is in Macaulay2Doc/doc_rings.m2:194:0.