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AssociativeAlgebras : Table of Contents
AssociativeAlgebras
-- Noncommutative algebra computations
Basic operations on noncommutative algebras
centralElements
-- Finds central elements in a given degree
Defining a noncommutative ring
Derivation
-- Derivation defined on a noncommutative algebra
endomorphismRingIdeal
-- Find the relations of an endomorphism ring
extAlgebra
-- Compute the Ext algebra of a ring
fourDimSklyanin
-- Defines a four-dimensional Sklyanin with given parameters
FreeAlgebra
-- Type of a free algebra
freeAlgebra
-- Create a FreeAlgebra
FreeAlgebra / Ideal
-- Type of a noncommutative ring
freeProduct
-- Define the free product of two algebras
homogDual
-- Computes the dual of a pure homogeneous ideal
isCentral
-- Determines if an element is central
isLeftRegular
-- Determines if a given (homogeneous) element is regular in a given degree
isNormal(RingElement)
-- Determines if an element of a noncommutative ring is normal
leftMultiplicationMap
-- Computes a matrix for left or right multiplication by a homogeneous element
leftQuadraticMatrix
-- Factors the quadratic ideal on the left or on the right.
lineSchemeFourDim
-- Compute the line scheme of a four-dimensional AS regular algebra
ncBasis
-- Returns a basis of an noncommutative ring in specified degrees.
NCGB
-- Compute a two-sided Groebner basis of an ideal to a specified degree
ncGraphIdeal
-- Compute the graph ideal of a ring map between noncommutative rings.
ncHilbertSeries
-- Computes the Hilbert series of a noncommutative ring
ncKernel
-- Compute the graph ideal of a ring map between noncommutative rings.
ncMatrixMult
-- Correctly multiplies matrices from noncommutative rings.
NCReductionTwoSided
-- Reduces the entries of an Matrix with respect to an ideal
normalAutomorphism
-- Computes the automorphism determined by a normal homogeneous element
normalElements
-- Finds normal elements
normalElements(RingMap,ZZ)
-- Finds elements normalized by a ring map
oppositeRing
-- Creates the opposite ring of a noncommutative ring
oreExtension
-- Creates an Ore extension of a noncommutative ring
oreIdeal
-- Creates the defining ideal of an Ore extension of a noncommutative ring
pointScheme
-- Compute the point scheme of the quadratic algebra B
qTensorProduct
-- Define the (q-)commuting tensor product
quadraticClosure
-- Creates the subideal generated by quadratic elements of a given ideal
rightKernel
-- Right kernel of a matrix
skewPolynomialRing
-- Defines a skew polynomial ring via a skewing matrix
skewPolynomialRing(Ring,RingElement,List)
-- Defines a skew polynomial ring via a scaling factor
threeDimSklyanin
-- Defines a three-dimensional Sklyanin with given parameters
toCommRing
-- Compute the abelianization of a Ring and returns a Ring.
toFreeAlgebraQuotient
-- Converts a Ring to a noncommutative ring
toRationalFunction
-- Attempt to find a rational function representation.