AssociativeAlgebras : Index

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