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NCRingElement -- Type of an element in a noncommutative ring

Description

This is the type of an element in a noncommutative graded ring. One can deal with these elements in much the same way as in the commutative case. See RingElement for details.

Methods that use an object of class NCRingElement:

  • baseName(NCRingElement) -- Returns the base name of a generator of an NCRing
  • coordinates(NCRingElement) -- see coordinates -- Computes coordinates relative to a given basis
  • degree(NCRingElement) -- Returns the degree of an NCRingElement
  • isCentral(NCRingElement) -- see isCentral -- Determines if an element is central
  • isCentral(NCRingElement,NCGroebnerBasis) -- see isCentral -- Determines if an element is central
  • isConstant(NCRingElement) -- Returns whether the NCRingElement is constant
  • isHomogeneous(NCRingElement) -- see isHomogeneous(NCIdeal) -- Determines whether the input defines a homogeneous object
  • isLeftRegular(NCRingElement,ZZ) -- see isLeftRegular -- Determines if a given (homogeneous) element is regular in a given degree
  • isRightRegular(NCRingElement,ZZ) -- see isLeftRegular -- Determines if a given (homogeneous) element is regular in a given degree
  • isNormal(NCRingElement) -- Determines if a given NCRingElement is normal
  • leadCoefficient(NCRingElement) -- Returns the lead monomial of an NCRingElement
  • leadMonomial(NCRingElement) -- Returns the lead monomial of an NCRingElement
  • leadTerm(NCRingElement) -- Returns the lead term of an NCRingElement
  • leftMultiplicationMap(NCRingElement,List,List) -- see leftMultiplicationMap -- Computes a matrix for left or right multiplication by a homogeneous element
  • leftMultiplicationMap(NCRingElement,ZZ) -- see leftMultiplicationMap -- Computes a matrix for left or right multiplication by a homogeneous element
  • leftMultiplicationMap(NCRingElement,ZZ,ZZ) -- see leftMultiplicationMap -- Computes a matrix for left or right multiplication by a homogeneous element
  • rightMultiplicationMap(NCRingElement,List,List) -- see leftMultiplicationMap -- Computes a matrix for left or right multiplication by a homogeneous element
  • rightMultiplicationMap(NCRingElement,ZZ) -- see leftMultiplicationMap -- Computes a matrix for left or right multiplication by a homogeneous element
  • rightMultiplicationMap(NCRingElement,ZZ,ZZ) -- see leftMultiplicationMap -- Computes a matrix for left or right multiplication by a homogeneous element
  • List * NCRingElement -- Scales a list by an NCRingElement on the right
  • monomials(NCRingElement) -- Returns the monomials appearing in the NCRingElement
  • ncIdeal(NCRingElement) -- see ncIdeal -- Define a two-sided ideal in a noncommutative ring
  • ncLeftIdeal(NCRingElement) -- see ncLeftIdeal -- Define a left ideal in a noncommutative ring
  • NCMatrix * NCRingElement -- Product of NCMatrices
  • ncRightIdeal(NCRingElement) -- see ncRightIdeal -- Define a right ideal in a noncommutative ring
  • NCRingElement % NCGroebnerBasis -- Reduces a NCRingElement by a NCGroebnerBasis
  • NCRingElement * List -- Scales a list by an NCRingElement on the left
  • NCRingElement * NCMatrix -- Product of NCMatrices
  • NCRingMap NCRingElement -- Apply an NCRingMap to an element or matrix
  • normalAutomorphism(NCRingElement) -- see normalAutomorphism -- Computes the automorphism determined by a normal homogeneous element
  • normalFormBergman(NCRingElement,NCGroebnerBasis) -- see normalFormBergman -- Calls Bergman for a normal form calculation
  • oreExtension(NCRing,NCRingMap,NCRingElement) -- see oreExtension -- Creates an Ore extension of a noncommutative ring
  • oreExtension(NCRing,NCRingMap,NCRingMap,NCRingElement) -- see oreExtension -- Creates an Ore extension of a noncommutative ring
  • oreIdeal(NCRing,NCRingMap,NCRingElement) -- see oreIdeal -- Creates the defining ideal of an Ore extension of a noncommutative ring
  • oreIdeal(NCRing,NCRingMap,NCRingMap,NCRingElement) -- see oreIdeal -- Creates the defining ideal of an Ore extension of a noncommutative ring
  • ring(NCRingElement) -- Returns the NCRing of an NCRingElement
  • size(NCRingElement) -- Returns the number of terms of an NCRingElement
  • sparseCoeffs(NCRingElement) -- see sparseCoeffs -- Converts ring elements into vectors over the coefficient ring
  • support(NCRingElement) -- Returns the variables appearing in the NCRingElement
  • terms(NCRingElement) -- Returns the terms of an NCRingElement
  • toString(NCRingElement) -- Converts an NCRingElement to a string

For the programmer

The object NCRingElement is a type, with ancestor classes HashTable < Thing.


The source of this document is in NCAlgebra/NCAlgebraDoc.m2:1115:0.