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# AssociativeAlgebras : Index

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

- 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