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) -> %