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# Edit detail for XDistributedPolynomial revision 1 of 1

 1 Editor: Bill Page Time: 2018/07/06 22:46:02 GMT+0 Note:

changed:
-
This type supports distributed multivariate polynomials
whose variables do not commute.
The coefficient ring may be non-commutative too.
However, coefficients and variables commute.
\begin{axiom}
)sh XDistributedPolynomial
\end{axiom}



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) -> %