| 1 | ||
|
Editor: Bill Page
Time: 2008/05/08 17:34:49 GMT-7 |
||
| Note: new | ||
changed: - \begin{axiom} )sh AlgebraGivenByStructuralConstants \end{axiom}
axiom)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. Issue )edit /usr/local/lib/axiom/target/x86_64-unknown-linux/../../src/algebra/ALGSC.spad to see algebra source code for ALGSC
------------------------------- Operations -------------------------------- ?*? : (SquareMatrix(n,R),%) -> % ?*? : (R,%) -> % ?*? : (%,R) -> % ?*? : (%,%) -> % ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % ?-? : (%,%) -> % -? : % -> % ?=? : (%,%) -> Boolean 0 : () -> % 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 rightDiscriminant : Vector % -> 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 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 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