# 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
• "degrees(QuotientRing)" -- see degrees(Ring) -- degrees of generators
• "degreesMonoid(QuotientRing)" -- see degreesMonoid -- get the monoid of degrees
• "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) -- returns the defining ideal
• "isAffineRing(QuotientRing)" -- see isAffineRing -- whether something is an affine ring
• isHomogeneous(QuotientRing) (missing documentation)
• "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
• "monoid(QuotientRing)" -- see monoid -- make or retrieve a monoid
• "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(Ring) -- 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
• "random(QuotientRing)" -- see random(Type) -- random element of a type
• "trim(QuotientRing)" -- see trim -- minimize generators and relations

## For the programmer

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