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fricas
)sh GenericNonAssociativeAlgebra
GenericNonAssociativeAlgebra(R: CommutativeRing,n: PositiveInteger,ls: List(Symbol),gamma: Vector(Matrix(R))) is a domain constructor Abbreviation for GenericNonAssociativeAlgebra is GCNAALG This constructor is not exposed in this frame. ------------------------------- Operations -------------------------------- ?*? : (%,%) -> % ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % ?-? : (%,%) -> % -? : % -> % ?=? : (%,%) -> Boolean 0 : () -> % ?^? : (%,PositiveInteger) -> % alternative? : () -> Boolean antiAssociative? : () -> Boolean antiCommutative? : () -> Boolean antiCommutator : (%,%) -> % associative? : () -> Boolean associator : (%,%,%) -> % basis : () -> Vector(%) coerce : % -> OutputForm commutative? : () -> Boolean commutator : (%,%) -> % flexible? : () -> Boolean generic : Vector(%) -> % generic : Vector(Symbol) -> % generic : Symbol -> % generic : () -> % hash : % -> SingleInteger jacobiIdentity? : () -> Boolean jordanAdmissible? : () -> Boolean jordanAlgebra? : () -> Boolean latex : % -> String leftAlternative? : () -> Boolean lieAdmissible? : () -> Boolean lieAlgebra? : () -> Boolean powerAssociative? : () -> Boolean rank : () -> PositiveInteger rightAlternative? : () -> Boolean sample : () -> % someBasis : () -> Vector(%) zero? : % -> Boolean ?~=? : (%,%) -> Boolean ?*? : (SquareMatrix(n,Fraction(Polynomial(R))),%) -> % ?*? : (Fraction(Polynomial(R)),%) -> % ?*? : (%,Fraction(Polynomial(R))) -> % ?*? : (NonNegativeInteger,%) -> % apply : (Matrix(Fraction(Polynomial(R))),%) -> % associatorDependence : () -> List(Vector(Fraction(Polynomial(R)))) if Fraction(Polynomial(R)) has INTDOM coerce : Vector(Fraction(Polynomial(R))) -> % conditionsForIdempotents : () -> List(Polynomial(R)) if R has INTDOM conditionsForIdempotents : Vector(%) -> List(Polynomial(R)) if R has INTDOM conditionsForIdempotents : () -> List(Polynomial(Fraction(Polynomial(R)))) conditionsForIdempotents : Vector(%) -> List(Polynomial(Fraction(Polynomial(R)))) convert : Vector(Fraction(Polynomial(R))) -> % convert : % -> Vector(Fraction(Polynomial(R))) coordinates : Vector(%) -> Matrix(Fraction(Polynomial(R))) coordinates : % -> Vector(Fraction(Polynomial(R))) coordinates : (Vector(%),Vector(%)) -> Matrix(Fraction(Polynomial(R))) coordinates : (%,Vector(%)) -> Vector(Fraction(Polynomial(R))) ?.? : (%,Integer) -> Fraction(Polynomial(R)) generic : (Vector(Symbol),Vector(%)) -> % generic : (Symbol,Vector(%)) -> % genericLeftDiscriminant : () -> Fraction(Polynomial(R)) if R has INTDOM genericLeftMinimalPolynomial : % -> SparseUnivariatePolynomial(Fraction(Polynomial(R))) if R has INTDOM genericLeftNorm : % -> Fraction(Polynomial(R)) if R has INTDOM genericLeftTrace : % -> Fraction(Polynomial(R)) if R has INTDOM genericLeftTraceForm : (%,%) -> Fraction(Polynomial(R)) if R has INTDOM genericRightDiscriminant : () -> Fraction(Polynomial(R)) if R has INTDOM genericRightMinimalPolynomial : % -> SparseUnivariatePolynomial(Fraction(Polynomial(R))) if R has INTDOM genericRightNorm : % -> Fraction(Polynomial(R)) if R has INTDOM genericRightTrace : % -> Fraction(Polynomial(R)) if R has INTDOM genericRightTraceForm : (%,%) -> Fraction(Polynomial(R)) if R has INTDOM hashUpdate! : (HashState,%) -> HashState leftCharacteristicPolynomial : % -> SparseUnivariatePolynomial(Fraction(Polynomial(R))) leftDiscriminant : () -> Fraction(Polynomial(R)) leftDiscriminant : Vector(%) -> Fraction(Polynomial(R)) leftMinimalPolynomial : % -> SparseUnivariatePolynomial(Fraction(Polynomial(R))) if Fraction(Polynomial(R)) has INTDOM leftNorm : % -> Fraction(Polynomial(R)) leftPower : (%,PositiveInteger) -> % leftRankPolynomial : () -> SparseUnivariatePolynomial(Fraction(Polynomial(R))) if R has INTDOM leftRankPolynomial : () -> SparseUnivariatePolynomial(Polynomial(Fraction(Polynomial(R)))) if Fraction(Polynomial(R)) has FIELD leftRecip : % -> Union(%,"failed") if Fraction(Polynomial(R)) has INTDOM leftRegularRepresentation : % -> Matrix(Fraction(Polynomial(R))) leftRegularRepresentation : (%,Vector(%)) -> Matrix(Fraction(Polynomial(R))) leftTrace : % -> Fraction(Polynomial(R)) leftTraceMatrix : () -> Matrix(Fraction(Polynomial(R))) leftTraceMatrix : Vector(%) -> Matrix(Fraction(Polynomial(R))) leftUnit : () -> Union(%,"failed") if Fraction(Polynomial(R)) has INTDOM leftUnits : () -> Union(Record(particular: %,basis: List(%)),"failed") noncommutativeJordanAlgebra? : () -> Boolean plenaryPower : (%,PositiveInteger) -> % recip : % -> Union(%,"failed") if Fraction(Polynomial(R)) has INTDOM represents : Vector(Fraction(Polynomial(R))) -> % represents : (Vector(Fraction(Polynomial(R))),Vector(%)) -> % rightCharacteristicPolynomial : % -> SparseUnivariatePolynomial(Fraction(Polynomial(R))) rightDiscriminant : () -> Fraction(Polynomial(R)) rightDiscriminant : Vector(%) -> Fraction(Polynomial(R)) rightMinimalPolynomial : % -> SparseUnivariatePolynomial(Fraction(Polynomial(R))) if Fraction(Polynomial(R)) has INTDOM rightNorm : % -> Fraction(Polynomial(R)) rightPower : (%,PositiveInteger) -> % rightRankPolynomial : () -> SparseUnivariatePolynomial(Fraction(Polynomial(R))) if R has INTDOM rightRankPolynomial : () -> SparseUnivariatePolynomial(Polynomial(Fraction(Polynomial(R)))) if Fraction(Polynomial(R)) has FIELD rightRecip : % -> Union(%,"failed") if Fraction(Polynomial(R)) has INTDOM rightRegularRepresentation : % -> Matrix(Fraction(Polynomial(R))) rightRegularRepresentation : (%,Vector(%)) -> Matrix(Fraction(Polynomial(R))) rightTrace : % -> Fraction(Polynomial(R)) rightTraceMatrix : () -> Matrix(Fraction(Polynomial(R))) rightTraceMatrix : Vector(%) -> Matrix(Fraction(Polynomial(R))) rightUnit : () -> Union(%,"failed") if Fraction(Polynomial(R)) has INTDOM rightUnits : () -> Union(Record(particular: %,basis: List(%)),"failed") structuralConstants : () -> Vector(Matrix(Fraction(Polynomial(R)))) structuralConstants : Vector(%) -> Vector(Matrix(Fraction(Polynomial(R)))) subtractIfCan : (%,%) -> Union(%,"failed") unit : () -> Union(%,"failed") if Fraction(Polynomial(R)) has INTDOM




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