[top][index]
search for:

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

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 HashTable.

More general types (whose methods may also apply) :

  • HashTable -- the class of all hash tables
  • Types of ring element :

  • ZZZ
  • See also:

  • engine
  • Functions and methods returning a a ring element :

  • - RingElement
  • contract(RingElement,RingElement)
  • det Matrix -- determinant of a matrix
  • diff(RingElement,RingElement)
  • gcd(RingElement,RingElement)
  • homogenize(RingElement,RingElement)
  • homogenize(RingElement,RingElement,List)
  • Ideal _ ZZ
  • IndexedVariable _ Ring -- generator of a ring with a given name
  • leadCoefficient RingElement
  • leadCoefficient Vector
  • leadComponent Vector
  • leadTerm RingElement
  • leadTerm Vector
  • lift(RingElement,Ring)
  • lift(RingElement,RingElement)
  • Matrix _ (...) -- get an entry
  • promote(MonoidElement,Ring)
  • promote(MonoidElement,RingElement)
  • promote(QQ,RingElement)
  • promote(RingElement,Ring)
  • promote(RingElement,RingElement)
  • promote(RR,EngineRing)
  • promote(ZZ,EngineRing)
  • pseudoRemainder(RingElement,RingElement)
  • QQ _ Ring
  • random Ring -- random element of a ring
  • random({...},Ring) -- a random ring element of a given degree
  • random(ZZ,Ring) -- a random ring element of a given degree
  • Ring _ {...} -- make a monomial from a list of exponents
  • Ring _ String -- get a variable by name
  • Ring _ ZZ -- get a variable by number
  • RingElement % GroebnerBasis
  • RingElement % RingElement
  • RingElement * RingElement
  • RingElement + RingElement
  • RingElement - RingElement
  • RingElement / RingElement
  • RingElement // RingElement
  • RingElement ^ ZZ
  • RingElement _ {...}
  • RingElement _ MonoidElement
  • RingElement _ Ring -- generator of a ring with a given name
  • RingElement _ RingElement -- get a coefficient
  • RingElement _ ZZ
  • RingMap RingElement
  • RR _ EngineRing
  • someTerms(RingElement,ZZ,ZZ)
  • substitute(RingElement,List)
  • substitute(RingElement,Matrix)
  • substitute(RingElement,Ring)
  • Symbol _ Ring -- generator of a ring with a given name
  • trace Matrix
  • ZZ _ EngineRing
  • ZZ _ Ring
  • Methods for using a ring element :

  • annihilator RingElement
  • baseName RingElement
  • ChainComplexMap + RingElement
  • ChainComplexMap - RingElement
  • ChainComplexMap == RingElement
  • coefficients RingElement
  • coefficients(List,RingElement)
  • coefficients(ZZ,RingElement)
  • cokernel RingElement
  • content RingElement
  • contract(Matrix,RingElement)
  • contract(RingElement,Matrix)
  • contract(RingElement,Vector)
  • contract(Vector,RingElement)
  • degree RingElement
  • degreeLength 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)
  • dual(MonomialIdeal,RingElement) -- the Alexander dual
  • exponents RingElement
  • expression RingElement
  • fraction(RingElement,RingElement)
  • gcdCoefficients(RingElement,RingElement)
  • GradedModuleMap + RingElement
  • GradedModuleMap - RingElement
  • GradedModuleMap == RingElement
  • homogenize(Ideal,RingElement)
  • homogenize(Matrix,RingElement)
  • homogenize(Matrix,RingElement,List)
  • homogenize(Module,RingElement)
  • homogenize(Module,RingElement,List)
  • homogenize(Vector,RingElement)
  • homogenize(Vector,RingElement,List)
  • Ideal : RingElement
  • ideal RingElement
  • image RingElement
  • index RingElement
  • isConstant RingElement -- test whether something is constant
  • 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
  • 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
  • monomialIdeal RingElement
  • net RingElement
  • oldCoefficients RingElement
  • oldCoefficients(List,RingElement)
  • promote(ZZ,RingElement)
  • QQ % RingElement
  • QQ * RingElement
  • QQ ** RingElement
  • QQ + RingElement
  • QQ - RingElement
  • QQ / RingElement
  • QQ // RingElement
  • quotient(Ideal,RingElement)
  • quotient(Module,RingElement)
  • Ring / RingElement -- quotient ring
  • RingElement % Ideal
  • RingElement % Matrix
  • RingElement % MonomialIdeal
  • RingElement % QQ
  • RingElement % ZZ
  • RingElement * ChainComplexMap
  • RingElement * GradedModuleMap
  • RingElement * Ideal
  • RingElement * Matrix
  • RingElement * Module
  • RingElement * MonomialIdeal
  • RingElement * QQ
  • RingElement * RR
  • RingElement * Vector
  • RingElement * ZZ
  • RingElement ** Matrix
  • RingElement ** QQ
  • RingElement ** RingElement
  • RingElement ** ZZ
  • RingElement + ChainComplexMap
  • RingElement + GradedModuleMap
  • RingElement + Matrix
  • RingElement + QQ
  • RingElement + RR
  • RingElement + ZZ
  • RingElement ++ Matrix
  • RingElement ++ RingElement
  • RingElement ++ ZZ
  • RingElement - ChainComplexMap
  • RingElement - GradedModuleMap
  • RingElement - Matrix
  • RingElement - QQ
  • RingElement - RR
  • RingElement - ZZ
  • RingElement / QQ
  • RingElement / RR
  • RingElement / ZZ
  • RingElement // GroebnerBasis
  • RingElement // Matrix
  • RingElement // MonomialIdeal
  • RingElement // QQ
  • RingElement // RR
  • RingElement // ZZ
  • RingElement == ChainComplexMap
  • RingElement == GradedModuleMap
  • RingElement == Matrix
  • RingElement == RingElement
  • RingElement == ZZ
  • RingElement ? RingElement
  • RingElement [...] -- substitution of variables
  • RingElement | Matrix
  • RingElement | RingElement
  • RingElement || Matrix
  • RingElement || RingElement
  • RR * RingElement
  • RR + RingElement
  • RR - RingElement
  • RR / RingElement
  • RR // RingElement
  • saturate(Ideal,RingElement)
  • saturate(Module,RingElement)
  • size RingElement
  • standardForm RingElement
  • substitute(RingElement,Option)
  • terms RingElement
  • toString RingElement
  • ZZ % RingElement
  • ZZ * RingElement
  • ZZ ** RingElement
  • ZZ + RingElement
  • ZZ ++ RingElement
  • ZZ - RingElement
  • ZZ / RingElement
  • ZZ // RingElement
  • ZZ == RingElement

  • [top][index]
    search for: