This type supports distributed multivariate polynomials whose variables do not commute. The coefficient ring may be non-commutative too. However, coefficients and variables commute.

(1) -> )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 --------------------------------

 ?*? : (vl, %) -> %                    ?*? : (R, %) -> %
 ?*? : (%, R) -> %                     ?*? : (Integer, %) -> %
 ?*? : (%, %) -> %                     ?*? : (PositiveInteger, %) -> %
 ?+? : (%, %) -> %                     -? : % -> %
 ?-? : (%, %) -> %                     ?=? : (%, %) -> Boolean
 1 : () -> %                           0 : () -> %
 ?^? : (%, PositiveInteger) -> %       annihilate? : (%, %) -> Boolean
 antiCommutator : (%, %) -> %          associator : (%, %, %) -> %
 coef : (%, %) -> R                    coef : (%, FreeMonoid(vl)) -> R
 coefficients : % -> List(R)           coerce : vl -> %
 coerce : FreeMonoid(vl) -> %          coerce : R -> %
 coerce : Integer -> %                 coerce : % -> OutputForm
 commutator : (%, %) -> %              constant : % -> R
 constant? : % -> Boolean              degree : % -> NonNegativeInteger
 latex : % -> String                   lquo : (%, %) -> %
 lquo : (%, FreeMonoid(vl)) -> %       lquo : (%, vl) -> %
 map : ((R -> R), %) -> %              maxdeg : % -> FreeMonoid(vl)
 mindeg : % -> FreeMonoid(vl)          mirror : % -> %
 monomial? : % -> Boolean              monomials : % -> List(%)
 one? : % -> Boolean                   opposite? : (%, %) -> Boolean
 quasiRegular : % -> %                 quasiRegular? : % -> Boolean
 recip : % -> Union(%,"failed")        retract : % -> FreeMonoid(vl)
 retract : % -> R                      rquo : (%, %) -> %
 rquo : (%, FreeMonoid(vl)) -> %       rquo : (%, vl) -> %
 sample : () -> %                      varList : % -> List(vl)
 zero? : % -> Boolean                  ?~=? : (%, %) -> Boolean
 ?*? : (NonNegativeInteger, %) -> %
 ?^? : (%, 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
 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 : (%, NonNegativeInteger) -> %
 leftPower : (%, PositiveInteger) -> %
 leftRecip : % -> Union(%,"failed")
 linearExtend : ((FreeMonoid(vl) -> R), %) -> R if R has COMRING
 listOfTerms : % -> List(Record(k: FreeMonoid(vl),c: R))
 mindegTerm : % -> Record(k: FreeMonoid(vl),c: R)
 monomial : (R, FreeMonoid(vl)) -> %
 numberOfMonomials : % -> NonNegativeInteger
 plenaryPower : (%, PositiveInteger) -> % if R has COMRING
 reductum : % -> % if FreeMonoid(vl) has COMPAR
 retractIfCan : % -> Union(FreeMonoid(vl),"failed")
 retractIfCan : % -> Union(R,"failed")
 rightPower : (%, NonNegativeInteger) -> %
 rightPower : (%, PositiveInteger) -> %
 rightRecip : % -> Union(%,"failed")
 sh : (%, NonNegativeInteger) -> % if R has COMRING
 sh : (%, %) -> % if R has COMRING
 smaller? : (%, %) -> Boolean if R has COMPAR and FreeMonoid(vl) has COMPAR
 subtractIfCan : (%, %) -> Union(%,"failed")
 support : % -> List(FreeMonoid(vl))
 trunc : (%, NonNegativeInteger) -> %