RingElement -- the class of all ring elements handled by the engine

RingElement -- the class of all ring elements handled by the engine

See also:

The type RingElement is a member of the class Type. Each object of class RingElement is called a ring element. Each ring element is also a member of class MutableHashTable.

Making a ring element :

- RingElement

Ideal _ ZZ

Matrix _ (...) -- get an entry

Ring _ String -- get a variable by name

Ring _ ZZ -- get a variable by number

Ring _ {...} -- make a monomial from a list of exponents

RingElement % GroebnerBasis

RingElement % RingElement

RingElement * RingElement

RingElement + RingElement

RingElement - RingElement

RingElement / RingElement

RingElement // RingElement

RingElement ^ ZZ

RingElement _ MonoidElement

RingElement _ RingElement -- get a coefficient

RingElement _ ZZ

RingMap RingElement

ZZ _ EngineRing

ZZ _ Ring

contract(RingElement,RingElement)

det Matrix

diff(RingElement,RingElement)

gcd(RingElement,RingElement)

homogenize(RingElement,RingElement)

homogenize(RingElement,RingElement,{...})

leadCoefficient RingElement

leadCoefficient Vector

leadComponent Vector

leadTerm RingElement

leadTerm Vector

lift(RingElement,Ring)

lift(RingElement,RingElement)

promote(MonoidElement,Ring)

promote(MonoidElement,RingElement)

promote(QQ,RingElement)

promote(RingElement,Ring)

promote(RingElement,RingElement)

promote(ZZ,EngineRing)

pseudoRemainder(RingElement,RingElement)

random Ring -- random element of a ring

random(ZZ,Ring) -- a random ring element of a given degree

random({...},Ring) -- a random ring element of a given degree

someTerms(RingElement,ZZ,ZZ)

substitute(RingElement,Matrix)

substitute(RingElement,Ring)

substitute(RingElement,{...})

trace Matrix

Methods for using a ring element :

ChainComplexMap + RingElement

ChainComplexMap - RingElement

ChainComplexMap == RingElement

GradedModuleMap + RingElement

GradedModuleMap - RingElement

GradedModuleMap == RingElement

Ideal : RingElement

Matrix % RingElement -- reduce the columns modulo of a ring element

Matrix ** RingElement

Matrix + RingElement

Matrix ++ RingElement

Matrix - RingElement

Matrix // RingElement -- factor a map through a multiplication map

Matrix == RingElement

Matrix | RingElement

Matrix || RingElement

Module / RingElement

Module : RingElement

QQ % RingElement

QQ * RingElement

QQ + RingElement

QQ - RingElement

QQ / RingElement

QQ // RingElement

Ring / RingElement

RingElement % Ideal

RingElement % Matrix

RingElement % QQ

RingElement % ZZ

RingElement * ChainComplexMap

RingElement * GradedModuleMap

RingElement * Ideal

RingElement * Matrix

RingElement * Module

RingElement * QQ

RingElement * Vector

RingElement * ZZ

RingElement ** Matrix

RingElement ** RingElement

RingElement + ChainComplexMap

RingElement + GradedModuleMap

RingElement + Matrix

RingElement + QQ

RingElement + ZZ

RingElement ++ Matrix

RingElement ++ RingElement

RingElement ++ ZZ

RingElement - ChainComplexMap

RingElement - GradedModuleMap

RingElement - Matrix

RingElement - QQ

RingElement - ZZ

RingElement / QQ

RingElement / ZZ

RingElement // GroebnerBasis

RingElement // Matrix

RingElement // QQ

RingElement // ZZ

RingElement == ChainComplexMap

RingElement == GradedModuleMap

RingElement == Matrix

RingElement == RingElement

RingElement == ZZ

RingElement ? RingElement

RingElement | Matrix

RingElement | RingElement

RingElement || Matrix

RingElement || RingElement

ZZ % RingElement

ZZ * RingElement

ZZ + RingElement

ZZ ++ RingElement

ZZ - RingElement

ZZ / RingElement

ZZ // RingElement

ZZ == RingElement

annihilator RingElement

baseName RingElement

coefficients RingElement

coefficients({...},RingElement)

cokernel RingElement

content RingElement

contract(Matrix,RingElement)

contract(RingElement,Matrix)

contract(RingElement,Vector)

contract(Vector,RingElement)

degree RingElement

diff RingElement -- differentiate a ring element

diff(Matrix,RingElement)

diff(RingElement,Matrix)

diff(RingElement,Vector)

diff(Vector,RingElement)

divideByVariable(Matrix,RingElement)

divideByVariable(Matrix,RingElement,ZZ)

exponents RingElement

expression RingElement

gcdCoefficients(RingElement,RingElement)

homogenize(Ideal,RingElement)

homogenize(Matrix,RingElement)

homogenize(Matrix,RingElement,{...})

homogenize(Module,RingElement)

homogenize(Module,RingElement,{...})

homogenize(Vector,RingElement)

homogenize(Vector,RingElement,{...})

ideal RingElement

image RingElement

index RingElement

isHomogeneous RingElement

isUnit RingElement

kernel RingElement

leadMonomial RingElement

lift(RingElement,QQ)

lift(RingElement,ZZ)

liftable(RingElement,Ring)

listForm RingElement

map(Module,Module,RingElement) -- make a map

map(Module,RingElement) -- make a map

net RingElement

promote(ZZ,RingElement)

quotient(Ideal,RingElement)

quotient(Module,RingElement)

saturate(Ideal,RingElement)

saturate(Module,RingElement)

size RingElement

standardForm RingElement

substitute(RingElement,Option)

terms RingElement

toString RingElement