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