XPolynomialsCat(vl, R)ΒΆ

xpoly.spad line 107

The Category of polynomial rings with non-commutative variables. The coefficient ring may be non-commutative too. However coefficients commute with variables.

0: %
from AbelianMonoid
1: %
from MagmaWithUnit
*: (%, %) -> %
from Magma
*: (%, R) -> %
from XFreeAlgebra(vl, R)
*: (Integer, %) -> %
from AbelianGroup
*: (NonNegativeInteger, %) -> %
from AbelianMonoid
*: (PositiveInteger, %) -> %
from AbelianSemiGroup
*: (R, %) -> %
from LeftModule R
*: (vl, %) -> %
from XFreeAlgebra(vl, 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(vl, R)
coef: (%, FreeMonoid vl) -> R
from XFreeAlgebra(vl, R)
coerce: % -> OutputForm
from CoercibleTo OutputForm
coerce: FreeMonoid vl -> %
from RetractableTo FreeMonoid vl
coerce: Integer -> %
from NonAssociativeRing
coerce: R -> %
from XAlgebra R
coerce: vl -> %
from XFreeAlgebra(vl, R)
commutator: (%, %) -> %
from NonAssociativeRng
constant: % -> R
from XFreeAlgebra(vl, R)
constant?: % -> Boolean
from XFreeAlgebra(vl, R)
degree: % -> NonNegativeInteger
degree(p) returns the degree of p. Note that the degree of a word is its length.
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(vl, R)
lquo: (%, FreeMonoid vl) -> %
from XFreeAlgebra(vl, R)
lquo: (%, vl) -> %
from XFreeAlgebra(vl, R)
map: (R -> R, %) -> %
from XFreeAlgebra(vl, R)
maxdeg: % -> FreeMonoid vl
maxdeg(p) returns the greatest leading word in the support of p.
mindeg: % -> FreeMonoid vl
from XFreeAlgebra(vl, R)
mindegTerm: % -> Record(k: FreeMonoid vl, c: R)
from XFreeAlgebra(vl, R)
mirror: % -> %
from XFreeAlgebra(vl, R)
monom: (FreeMonoid vl, R) -> %
from XFreeAlgebra(vl, R)
monomial?: % -> Boolean
from XFreeAlgebra(vl, R)
one?: % -> Boolean
from MagmaWithUnit
opposite?: (%, %) -> Boolean
from AbelianMonoid
quasiRegular: % -> %
from XFreeAlgebra(vl, R)
quasiRegular?: % -> Boolean
from XFreeAlgebra(vl, R)
recip: % -> Union(%, failed)
from MagmaWithUnit
retract: % -> FreeMonoid vl
from RetractableTo FreeMonoid vl
retractIfCan: % -> Union(FreeMonoid vl, failed)
from RetractableTo FreeMonoid vl
rightPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
rightPower: (%, PositiveInteger) -> %
from Magma
rightRecip: % -> Union(%, failed)
from MagmaWithUnit
rquo: (%, %) -> %
from XFreeAlgebra(vl, R)
rquo: (%, FreeMonoid vl) -> %
from XFreeAlgebra(vl, R)
rquo: (%, vl) -> %
from XFreeAlgebra(vl, R)
sample: %
from AbelianMonoid
sh: (%, %) -> % if R has CommutativeRing
from XFreeAlgebra(vl, R)
sh: (%, NonNegativeInteger) -> % if R has CommutativeRing
from XFreeAlgebra(vl, R)
subtractIfCan: (%, %) -> Union(%, failed)
from CancellationAbelianMonoid
trunc: (%, NonNegativeInteger) -> %
trunc(p, n) returns the polynomial p truncated at order n.
varList: % -> List vl
from XFreeAlgebra(vl, 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 vl

RightModule %

RightModule R

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

unitsKnown

XAlgebra R

XFreeAlgebra(vl, R)