PathSignatures : Index

• A family of paths on a cone
• adjointWord -- image of a word through the shuffle algebra homomorphism induced by a polynomial map
• adjointWord(NCRingElement,NCPolynomialRing,List) -- image of a word through the shuffle algebra homomorphism induced by a polynomial map
• ambient -- exported from the NCALgebra package.
• ambient(NCPolynomialRing) -- exported from the NCALgebra package.
• antipode(NCRingElement) -- The antipode of a tensor
• Array _ NCPolynomialRing -- create a word from an array
• CAxisTensor -- the signature tensor of the canonical axis path at a given level
• CAxisTensor(ZZ,NCPolynomialRing) -- the signature tensor of the canonical axis path at a given level
• CMonTensor -- the signature tensor of the canonical monomial path at a given level
• CMonTensor(ZZ,NCPolynomialRing) -- the signature tensor of the canonical monomial path at a given level
• coefficientRing(Path)
• Computing Path Varieties
• concatPath -- concatenation of paths
• concatPath(Path,Path) -- concatenation of paths
• dim(Path)
• getCoefficientRing
• getCoefficientRing(Path)
• getDimension
• getDimension(Path)
• getNumberOfPieces
• getNumberOfPieces(Path)
• getPieces
• getPieces(Path)
• halfshuffle -- compute the half-shuffle of an ordered pair of words
• halfshuffle(NCRingElement,NCRingElement) -- compute the half-shuffle of an ordered pair of words
• inner -- compute the inner product of two tensors.
• inner(NCRingElement,NCRingElement) -- compute the inner product of two tensors.
• lie -- lie bracket of two elements
• lieBasis -- basis element corresponding to a Lyndon word in a Lie algebra
• lieBasis(Array,NCPolynomialRing) -- basis element corresponding to a Lyndon word in a Lie algebra
• lieBasis(List,NCPolynomialRing) -- basis element corresponding to a Lyndon word in a Lie algebra
• linPath -- constructor of single piece polynomial path
• linPath(List) -- constructor of single piece polynomial path
• lyndonShuffle -- compute the representation of a tensor as a shuffle polynomial in Lyndon words
• lyndonShuffle(NCRingElement) -- compute the representation of a tensor as a shuffle polynomial in Lyndon words
• lyndonWords -- compute all Lyndon words of at most a given length on a given number of letters
• lyndonWords(ZZ,ZZ) -- compute all Lyndon words of at most a given length on a given number of letters
• Matrix * NCRingElement -- Diagonal matrix action on a tensor.
• matrixAction -- Diagonal matrix action on a tensor.
• matrixAction(Matrix,NCRing,NCRing) -- Diagonal matrix action on a tensor.
• matrixAction(Matrix,NCRingElement,NCRing) -- Diagonal matrix action on a tensor.
• NCPolynomialRing -- exported from the NCAlgebra package, used to encode tensor algebras
• NCRingElement -- exported from the NCAlgebra package, used to encode tensors
• NCRingElement ** NCRingElement -- shuffle product of two words
• NCRingElement >> NCRingElement -- compute the half-shuffle of an ordered pair of words
• NCRingElement @ NCRingElement -- compute the inner product of two tensors.
• NCRingElement @ ZZ -- k-th level component of a tensor.
• NCRingElement ⧢ NCRingElement -- shuffle product of two words
• net(Path)
• Path
• Path ** Path -- concatenation of paths
• Path ^ ZZ
• Path _ List
• Path _ Sequence
• Path _ ZZ
• PathSignatures -- a package for working with signatures of algebraic paths
• Polynomial paths of degree m
• polyPath -- constructor of single piece polynomial path
• polyPath(List) -- constructor of single piece polynomial path
• pwLinPath -- constructor of a piecewise linear path from a matrix
• pwLinPath(Matrix) -- constructor of a piecewise linear path from a matrix
• sgnVolTensor -- The signed volume tensor in a free associative algebra.
• sgnVolTensor(NCPolynomialRing) -- The signed volume tensor in a free associative algebra.
• shuffle -- shuffle product of two words
• shuffle(NCRingElement,NCRingElement) -- shuffle product of two words
• sig -- compute the signature of a piecewise polynomial path.
• sig(Path,List) -- compute the signature of a piecewise polynomial path.
• sig(Path,NCRingElement) -- compute the signature of a piecewise polynomial path.
• sig(Path,ZZ) -- compute the signature of a piecewise polynomial path.
• sig(Path,ZZ,NCRing) -- compute the signature of a piecewise polynomial path.
• substitute(Path,Ring) -- changes the coefficient ring of a path
• tensorArray -- k-th level component of a tensor.
• tensorArray(NCRingElement) -- k-th level component of a tensor.
• tensorArray(NCRingElement,ZZ) -- k-th level component of a tensor.
• tensorExp -- Compute a component of the exponential of a tensor.
• tensorExp(NCRingElement,ZZ) -- Compute a component of the exponential of a tensor.
• tensorLog -- Compute a component of the logarithm of a tensor.
• tensorLog(NCRingElement,ZZ) -- Compute a component of the logarithm of a tensor.
• tensorParametrization -- Constructs the morphism that maps a word to its coefficient in the given tensor.
• tensorParametrization(...,CoefficientRing=>...) -- Constructs the morphism that maps a word to its coefficient in the given tensor.
• tensorParametrization(...,VarWordTable=>...) -- Constructs the morphism that maps a word to its coefficient in the given tensor.
• tensorParametrization(NCRingElement) -- Constructs the morphism that maps a word to its coefficient in the given tensor.
• The universal variety and toric coordinates
• VarWordTable -- Constructs the morphism that maps a word to its coefficient in the given tensor.
• wordAlgebra -- create a free algebra over a given alphabet
• wordAlgebra(List) -- create a free algebra over a given alphabet
• wordAlgebra(ZZ) -- create a free algebra over a given alphabet
• wordFormat -- display a tensor in word notation
• wordFormat(NCRingElement) -- display a tensor in word notation
• wordString -- a string representing a word in wordFormat
• wordString(NCRingElement) -- a string representing a word in wordFormat