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 Topics FrontPage AboutAxiom AxiomDocumentation Axiom Algebra mathematical algorithms FriCAS Algebra NoncommutativePolynomials XDistributedPolynomial <-- You are here. This type supports distributed multivariate polynomials whose variables do not commute. The coefficient ring may be non-commutative too. However, coefficients and variables commute. fricas)sh XDistributedPolynomial XDistributedPolynomial(vl: OrderedSet,R: Ring) is a domain constructor Abbreviation for XDistributedPolynomial is XDPOLY This constructor is not exposed in this frame. ------------------------------- Operations -------------------------------- ?*? : (%, %) -> % ?*? : (Integer, %) -> % ?*? : (vl, %) -> % ?*? : (FreeMonoid(vl), R) -> % ?*? : (R, FreeMonoid(vl)) -> % ?*? : (%, R) -> % ?*? : (R, %) -> % ?*? : (PositiveInteger, %) -> % ?+? : (%, %) -> % ?-? : (%, %) -> % -? : % -> % ?=? : (%, %) -> Boolean 1 : () -> % 0 : () -> % ?^? : (%, PositiveInteger) -> % annihilate? : (%, %) -> Boolean antiCommutator : (%, %) -> % associator : (%, %, %) -> % coef : (%, FreeMonoid(vl)) -> R coef : (%, %) -> R coefficients : % -> List(R) coerce : Integer -> % coerce : R -> % coerce : FreeMonoid(vl) -> % coerce : vl -> % coerce : % -> OutputForm commutator : (%, %) -> % constant : % -> R constant? : % -> Boolean degree : % -> NonNegativeInteger hash : % -> SingleInteger latex : % -> String lquo : (%, vl) -> % lquo : (%, FreeMonoid(vl)) -> % lquo : (%, %) -> % map : ((R -> R), %) -> % maxdeg : % -> FreeMonoid(vl) mindeg : % -> FreeMonoid(vl) mirror : % -> % monom : (FreeMonoid(vl), R) -> % monomial? : % -> Boolean monomials : % -> List(%) one? : % -> Boolean opposite? : (%, %) -> Boolean quasiRegular : % -> % quasiRegular? : % -> Boolean recip : % -> Union(%,"failed") retract : % -> FreeMonoid(vl) rquo : (%, vl) -> % rquo : (%, FreeMonoid(vl)) -> % rquo : (%, %) -> % sample : () -> % varList : % -> List(vl) zero? : % -> Boolean ?~=? : (%, %) -> Boolean ?*? : (NonNegativeInteger, %) -> % ? Boolean if R has OAMON and FreeMonoid(vl) has ORDSET or R has OAMONS and FreeMonoid(vl) has ORDSET ?<=? : (%, %) -> Boolean if R has OAMON and FreeMonoid(vl) has ORDSET or R has OAMONS and FreeMonoid(vl) has ORDSET ?>? : (%, %) -> Boolean if R has OAMON and FreeMonoid(vl) has ORDSET or R has OAMONS and FreeMonoid(vl) has ORDSET ?>=? : (%, %) -> Boolean if R has OAMON and FreeMonoid(vl) has ORDSET or R has OAMONS and FreeMonoid(vl) has ORDSET ?^? : (%, NonNegativeInteger) -> % characteristic : () -> NonNegativeInteger coefficient : (%, FreeMonoid(vl)) -> R construct : List(Record(k: FreeMonoid(vl),c: R)) -> % constructOrdered : List(Record(k: FreeMonoid(vl),c: R)) -> % if FreeMonoid(vl) has COMPAR hashUpdate! : (HashState, %) -> HashState leadingCoefficient : % -> R if FreeMonoid(vl) has COMPAR leadingMonomial : % -> % if FreeMonoid(vl) has COMPAR leadingSupport : % -> FreeMonoid(vl) if FreeMonoid(vl) has COMPAR leadingTerm : % -> Record(k: FreeMonoid(vl),c: R) if FreeMonoid(vl) has COMPAR leftPower : (%, PositiveInteger) -> % leftPower : (%, NonNegativeInteger) -> % leftRecip : % -> Union(%,"failed") linearExtend : ((FreeMonoid(vl) -> R), %) -> R if R has COMRING listOfTerms : % -> List(Record(k: FreeMonoid(vl),c: R)) max : (%, %) -> % if R has OAMON and FreeMonoid(vl) has ORDSET or R has OAMONS and FreeMonoid(vl) has ORDSET min : (%, %) -> % if R has OAMON and FreeMonoid(vl) has ORDSET or R has OAMONS and FreeMonoid(vl) has ORDSET mindegTerm : % -> Record(k: FreeMonoid(vl),c: R) monomial : (R, FreeMonoid(vl)) -> % numberOfMonomials : % -> NonNegativeInteger reductum : % -> % if FreeMonoid(vl) has COMPAR retractIfCan : % -> Union(FreeMonoid(vl),"failed") rightPower : (%, PositiveInteger) -> % rightPower : (%, NonNegativeInteger) -> % rightRecip : % -> Union(%,"failed") sh : (%, %) -> % if R has COMRING sh : (%, NonNegativeInteger) -> % if R has COMRING smaller? : (%, %) -> Boolean if R has COMPAR and FreeMonoid(vl) has COMPAR or R has OAMON and FreeMonoid(vl) has ORDSET or R has OAMONS and FreeMonoid(vl) has ORDSET subtractIfCan : (%, %) -> Union(%,"failed") sup : (%, %) -> % if R has OAMONS and FreeMonoid(vl) has ORDSET support : % -> List(FreeMonoid(vl)) trunc : (%, NonNegativeInteger) -> %

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