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.