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 Topics FrontPage SandBox SandBoxNonAssociativeAlgebra AlgebraGivenByStructuralConstants <-- You are here. fricas)sh AlgebraGivenByStructuralConstants AlgebraGivenByStructuralConstants(R: Field,n: PositiveInteger,ls: List(Symbol),gamma: Vector(Matrix(R))) is a domain constructor Abbreviation for AlgebraGivenByStructuralConstants is ALGSC This constructor is exposed in this frame. ------------------------------- Operations -------------------------------- ?*? : (SquareMatrix(n,R),%) -> % ?*? : (R,%) -> % ?*? : (%,R) -> % ?*? : (%,%) -> % ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % ?-? : (%,%) -> % -? : % -> % ?=? : (%,%) -> Boolean 0 : () -> % ?^? : (%,PositiveInteger) -> % alternative? : () -> Boolean antiAssociative? : () -> Boolean antiCommutative? : () -> Boolean antiCommutator : (%,%) -> % apply : (Matrix(R),%) -> % associative? : () -> Boolean associator : (%,%,%) -> % basis : () -> Vector(%) coerce : Vector(R) -> % coerce : % -> OutputForm commutative? : () -> Boolean commutator : (%,%) -> % convert : Vector(R) -> % convert : % -> Vector(R) coordinates : % -> Vector(R) ?.? : (%,Integer) -> R flexible? : () -> Boolean hash : % -> SingleInteger jacobiIdentity? : () -> Boolean jordanAdmissible? : () -> Boolean jordanAlgebra? : () -> Boolean latex : % -> String leftAlternative? : () -> Boolean leftDiscriminant : () -> R leftDiscriminant : Vector(%) -> R leftNorm : % -> R leftTrace : % -> R leftTraceMatrix : () -> Matrix(R) lieAdmissible? : () -> Boolean lieAlgebra? : () -> Boolean powerAssociative? : () -> Boolean rank : () -> PositiveInteger represents : Vector(R) -> % rightAlternative? : () -> Boolean rightDiscriminant : () -> R rightNorm : % -> R rightTrace : % -> R rightTraceMatrix : () -> Matrix(R) sample : () -> % someBasis : () -> Vector(%) zero? : % -> Boolean ?~=? : (%,%) -> Boolean ?*? : (NonNegativeInteger,%) -> % associatorDependence : () -> List(Vector(R)) if R has INTDOM conditionsForIdempotents : () -> List(Polynomial(R)) conditionsForIdempotents : Vector(%) -> List(Polynomial(R)) coordinates : Vector(%) -> Matrix(R) coordinates : (Vector(%),Vector(%)) -> Matrix(R) coordinates : (%,Vector(%)) -> Vector(R) hashUpdate! : (HashState,%) -> HashState leftCharacteristicPolynomial : % -> SparseUnivariatePolynomial(R) leftMinimalPolynomial : % -> SparseUnivariatePolynomial(R) if R has INTDOM leftPower : (%,PositiveInteger) -> % leftRankPolynomial : () -> SparseUnivariatePolynomial(Polynomial(R)) if R has FIELD leftRecip : % -> Union(%,"failed") if R has INTDOM leftRegularRepresentation : % -> Matrix(R) leftRegularRepresentation : (%,Vector(%)) -> Matrix(R) leftTraceMatrix : Vector(%) -> Matrix(R) leftUnit : () -> Union(%,"failed") if R has INTDOM leftUnits : () -> Union(Record(particular: %,basis: List(%)),"failed") if R has INTDOM noncommutativeJordanAlgebra? : () -> Boolean plenaryPower : (%,PositiveInteger) -> % recip : % -> Union(%,"failed") if R has INTDOM represents : (Vector(R),Vector(%)) -> % rightCharacteristicPolynomial : % -> SparseUnivariatePolynomial(R) rightDiscriminant : Vector(%) -> R rightMinimalPolynomial : % -> SparseUnivariatePolynomial(R) if R has INTDOM rightPower : (%,PositiveInteger) -> % rightRankPolynomial : () -> SparseUnivariatePolynomial(Polynomial(R)) if R has FIELD rightRecip : % -> Union(%,"failed") if R has INTDOM rightRegularRepresentation : % -> Matrix(R) rightRegularRepresentation : (%,Vector(%)) -> Matrix(R) rightTraceMatrix : Vector(%) -> Matrix(R) rightUnit : () -> Union(%,"failed") if R has INTDOM rightUnits : () -> Union(Record(particular: %,basis: List(%)),"failed") if R has INTDOM structuralConstants : () -> Vector(Matrix(R)) structuralConstants : Vector(%) -> Vector(Matrix(R)) subtractIfCan : (%,%) -> Union(%,"failed") unit : () -> Union(%,"failed") if R has INTDOM

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