XRecursivePolynomial(VarSet, R)ΒΆ

xpoly.spad line 393

This type supports multivariate polynomials whose variables do not commute. The representation is recursive. The coefficient ring may be non-commutative. Coefficients and variables commute.

0: %
from AbelianMonoid
1: %
from MagmaWithUnit
*: (%, %) -> %
from Magma
*: (%, R) -> %
from XFreeAlgebra(VarSet, R)
*: (Integer, %) -> %
from AbelianGroup
*: (NonNegativeInteger, %) -> %
from AbelianMonoid
*: (PositiveInteger, %) -> %
from AbelianSemiGroup
*: (R, %) -> %
from LeftModule R
*: (VarSet, %) -> %
from XFreeAlgebra(VarSet, R)
+: (%, %) -> %
from AbelianSemiGroup
-: % -> %
from AbelianGroup
-: (%, %) -> %
from AbelianGroup
=: (%, %) -> Boolean
from BasicType
^: (%, NonNegativeInteger) -> %
from MagmaWithUnit
^: (%, PositiveInteger) -> %
from Magma
~=: (%, %) -> Boolean
from BasicType
annihilate?: (%, %) -> Boolean
from Rng
antiCommutator: (%, %) -> %
from NonAssociativeSemiRng
associator: (%, %, %) -> %
from NonAssociativeRng
characteristic: () -> NonNegativeInteger
from NonAssociativeRing
coef: (%, %) -> R
from XFreeAlgebra(VarSet, R)
coef: (%, FreeMonoid VarSet) -> R
from XFreeAlgebra(VarSet, R)
coerce: % -> OutputForm
from CoercibleTo OutputForm
coerce: FreeMonoid VarSet -> %
from RetractableTo FreeMonoid VarSet
coerce: Integer -> %
from NonAssociativeRing
coerce: R -> %
from XAlgebra R
coerce: VarSet -> %
from XFreeAlgebra(VarSet, R)
commutator: (%, %) -> %
from NonAssociativeRng
constant: % -> R
from XFreeAlgebra(VarSet, R)
constant?: % -> Boolean
from XFreeAlgebra(VarSet, R)
degree: % -> NonNegativeInteger
from XPolynomialsCat(VarSet, R)
expand: % -> XDistributedPolynomial(VarSet, R)
expand(p) returns p in distributed form.
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
latex: % -> String
from SetCategory
leftPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
leftPower: (%, PositiveInteger) -> %
from Magma
leftRecip: % -> Union(%, failed)
from MagmaWithUnit
lquo: (%, %) -> %
from XFreeAlgebra(VarSet, R)
lquo: (%, FreeMonoid VarSet) -> %
from XFreeAlgebra(VarSet, R)
lquo: (%, VarSet) -> %
from XFreeAlgebra(VarSet, R)
map: (R -> R, %) -> %
from XFreeAlgebra(VarSet, R)
maxdeg: % -> FreeMonoid VarSet
from XPolynomialsCat(VarSet, R)
mindeg: % -> FreeMonoid VarSet
from XFreeAlgebra(VarSet, R)
mindegTerm: % -> Record(k: FreeMonoid VarSet, c: R)
from XFreeAlgebra(VarSet, R)
mirror: % -> %
from XFreeAlgebra(VarSet, R)
monom: (FreeMonoid VarSet, R) -> %
from XFreeAlgebra(VarSet, R)
monomial?: % -> Boolean
from XFreeAlgebra(VarSet, R)
one?: % -> Boolean
from MagmaWithUnit
opposite?: (%, %) -> Boolean
from AbelianMonoid
quasiRegular: % -> %
from XFreeAlgebra(VarSet, R)
quasiRegular?: % -> Boolean
from XFreeAlgebra(VarSet, R)
recip: % -> Union(%, failed)
from MagmaWithUnit
RemainderList: % -> List Record(k: VarSet, c: %)
RemainderList(p) returns the regular part of p as a list of terms.
retract: % -> FreeMonoid VarSet
from RetractableTo FreeMonoid VarSet
retractIfCan: % -> Union(FreeMonoid VarSet, failed)
from RetractableTo FreeMonoid VarSet
rightPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
rightPower: (%, PositiveInteger) -> %
from Magma
rightRecip: % -> Union(%, failed)
from MagmaWithUnit
rquo: (%, %) -> %
from XFreeAlgebra(VarSet, R)
rquo: (%, FreeMonoid VarSet) -> %
from XFreeAlgebra(VarSet, R)
rquo: (%, VarSet) -> %
from XFreeAlgebra(VarSet, R)
sample: %
from AbelianMonoid
sh: (%, %) -> % if R has CommutativeRing
from XFreeAlgebra(VarSet, R)
sh: (%, NonNegativeInteger) -> % if R has CommutativeRing
from XFreeAlgebra(VarSet, R)
subtractIfCan: (%, %) -> Union(%, failed)
from CancellationAbelianMonoid
trunc: (%, NonNegativeInteger) -> %
from XPolynomialsCat(VarSet, R)
unexpand: XDistributedPolynomial(VarSet, R) -> %
unexpand(p) returns p in recursive form.
varList: % -> List VarSet
from XFreeAlgebra(VarSet, R)
zero?: % -> Boolean
from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

Algebra R if R has CommutativeRing

BasicType

BiModule(%, %)

BiModule(R, R)

CancellationAbelianMonoid

CoercibleTo OutputForm

LeftModule %

LeftModule R

Magma

MagmaWithUnit

Module R if R has CommutativeRing

Monoid

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors if R has noZeroDivisors

RetractableTo FreeMonoid VarSet

RightModule %

RightModule R

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

unitsKnown

XAlgebra R

XFreeAlgebra(VarSet, R)

XPolynomialsCat(VarSet, R)