# QuotientRing -- the class of all quotient rings

## Methods that use a quotient ring :

• ambient(QuotientRing), see ambient(Ring) -- ambient polynomial ring
• codim(QuotientRing) -- compute the codimension
• 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) (missing documentation)
• 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
• 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) (missing documentation)

## For the programmer

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