XPBWPolynomial(VarSet, R)ΒΆ

xlpoly.spad line 756

This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. Author: Michel Petitot (petitot@lifl.fr).

0: %
from AbelianMonoid
1: %
from MagmaWithUnit
*: (%, %) -> %
from Magma
*: (%, R) -> %
from XFreeAlgebra(VarSet, R)
*: (Integer, %) -> %
from AbelianGroup
*: (NonNegativeInteger, %) -> %
from AbelianMonoid
*: (PoincareBirkhoffWittLyndonBasis VarSet, R) -> %
from FreeModuleCategory(R, PoincareBirkhoffWittLyndonBasis VarSet)
*: (PositiveInteger, %) -> %
from AbelianSemiGroup
*: (R, %) -> %
from LeftModule R
*: (R, PoincareBirkhoffWittLyndonBasis VarSet) -> %
from FreeModuleCategory(R, PoincareBirkhoffWittLyndonBasis VarSet)
*: (VarSet, %) -> %
from XFreeAlgebra(VarSet, R)
+: (%, %) -> %
from AbelianSemiGroup
-: % -> %
from AbelianGroup
-: (%, %) -> %
from AbelianGroup
<: (%, %) -> Boolean if R has OrderedAbelianMonoid
from PartialOrder
<=: (%, %) -> Boolean if R has OrderedAbelianMonoid
from PartialOrder
=: (%, %) -> Boolean
from BasicType
>: (%, %) -> Boolean if R has OrderedAbelianMonoid
from PartialOrder
>=: (%, %) -> Boolean if R has OrderedAbelianMonoid
from PartialOrder
^: (%, 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)
coefficient: (%, PoincareBirkhoffWittLyndonBasis VarSet) -> R
from FreeModuleCategory(R, PoincareBirkhoffWittLyndonBasis VarSet)
coefficients: % -> List R
from FreeModuleCategory(R, PoincareBirkhoffWittLyndonBasis VarSet)
coerce: % -> OutputForm
from CoercibleTo OutputForm
coerce: % -> XDistributedPolynomial(VarSet, R)
coerce(p) returns p as a distributed polynomial.
coerce: % -> XRecursivePolynomial(VarSet, R)
coerce(p) returns p as a recursive polynomial.
coerce: FreeMonoid VarSet -> %
from RetractableTo FreeMonoid VarSet
coerce: Integer -> %
from NonAssociativeRing
coerce: LiePolynomial(VarSet, R) -> %
coerce(p) returns p.
coerce: PoincareBirkhoffWittLyndonBasis VarSet -> %
from RetractableTo PoincareBirkhoffWittLyndonBasis VarSet
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)
construct: List Record(k: PoincareBirkhoffWittLyndonBasis VarSet, c: R) -> %
from IndexedDirectProductCategory(R, PoincareBirkhoffWittLyndonBasis VarSet)
constructOrdered: List Record(k: PoincareBirkhoffWittLyndonBasis VarSet, c: R) -> %
from IndexedDirectProductCategory(R, PoincareBirkhoffWittLyndonBasis VarSet)
degree: % -> NonNegativeInteger
from XPolynomialsCat(VarSet, R)
exp: (%, NonNegativeInteger) -> % if R has Module Fraction Integer
exp(p, n) returns the exponential of p (truncated up to order n).
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
latex: % -> String
from SetCategory
leadingCoefficient: % -> R
from IndexedDirectProductCategory(R, PoincareBirkhoffWittLyndonBasis VarSet)
leadingMonomial: % -> %
from IndexedDirectProductCategory(R, PoincareBirkhoffWittLyndonBasis VarSet)
leadingSupport: % -> PoincareBirkhoffWittLyndonBasis VarSet
from IndexedDirectProductCategory(R, PoincareBirkhoffWittLyndonBasis VarSet)
leadingTerm: % -> Record(k: PoincareBirkhoffWittLyndonBasis VarSet, c: R)
from IndexedDirectProductCategory(R, PoincareBirkhoffWittLyndonBasis VarSet)
leftPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
leftPower: (%, PositiveInteger) -> %
from Magma
leftRecip: % -> Union(%, failed)
from MagmaWithUnit
LiePolyIfCan: % -> Union(LiePolynomial(VarSet, R), failed)
LiePolyIfCan(p) return p if p is a Lie polynomial.
linearExtend: (PoincareBirkhoffWittLyndonBasis VarSet -> R, %) -> R
from FreeModuleCategory(R, PoincareBirkhoffWittLyndonBasis VarSet)
listOfTerms: % -> List Record(k: PoincareBirkhoffWittLyndonBasis VarSet, c: R)
from IndexedDirectProductCategory(R, PoincareBirkhoffWittLyndonBasis VarSet)
log: (%, NonNegativeInteger) -> % if R has Module Fraction Integer
log(p, n) returns the logarithm of p (truncated up to order n).
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)
max: (%, %) -> % if R has OrderedAbelianMonoid
from OrderedSet
maxdeg: % -> FreeMonoid VarSet
from XPolynomialsCat(VarSet, R)
min: (%, %) -> % if R has OrderedAbelianMonoid
from OrderedSet
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: (R, PoincareBirkhoffWittLyndonBasis VarSet) -> %
from IndexedDirectProductCategory(R, PoincareBirkhoffWittLyndonBasis VarSet)
monomial?: % -> Boolean
from XFreeAlgebra(VarSet, R)
monomials: % -> List %
from FreeModuleCategory(R, PoincareBirkhoffWittLyndonBasis VarSet)
numberOfMonomials: % -> NonNegativeInteger
from IndexedDirectProductCategory(R, PoincareBirkhoffWittLyndonBasis VarSet)
one?: % -> Boolean
from MagmaWithUnit
opposite?: (%, %) -> Boolean
from AbelianMonoid
product: (%, %, NonNegativeInteger) -> %
product(a, b, n) returns a*b (truncated up to order n).
quasiRegular: % -> %
from XFreeAlgebra(VarSet, R)
quasiRegular?: % -> Boolean
from XFreeAlgebra(VarSet, R)
recip: % -> Union(%, failed)
from MagmaWithUnit
reductum: % -> %
from IndexedDirectProductCategory(R, PoincareBirkhoffWittLyndonBasis VarSet)
retract: % -> FreeMonoid VarSet
from RetractableTo FreeMonoid VarSet
retract: % -> PoincareBirkhoffWittLyndonBasis VarSet
from RetractableTo PoincareBirkhoffWittLyndonBasis VarSet
retractIfCan: % -> Union(FreeMonoid VarSet, failed)
from RetractableTo FreeMonoid VarSet
retractIfCan: % -> Union(PoincareBirkhoffWittLyndonBasis VarSet, failed)
from RetractableTo PoincareBirkhoffWittLyndonBasis 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: (%, %) -> %
from XFreeAlgebra(VarSet, R)
sh: (%, NonNegativeInteger) -> %
from XFreeAlgebra(VarSet, R)
smaller?: (%, %) -> Boolean if R has Comparable
from Comparable
subtractIfCan: (%, %) -> Union(%, failed)
from CancellationAbelianMonoid
sup: (%, %) -> % if R has OrderedAbelianMonoidSup
from OrderedAbelianMonoidSup
support: % -> List PoincareBirkhoffWittLyndonBasis VarSet
from FreeModuleCategory(R, PoincareBirkhoffWittLyndonBasis VarSet)
totalDegree: % -> NonNegativeInteger if PoincareBirkhoffWittLyndonBasis VarSet has coerce: PoincareBirkhoffWittLyndonBasis VarSet -> Vector NonNegativeInteger
from FreeModuleCategory(R, PoincareBirkhoffWittLyndonBasis VarSet)
trunc: (%, NonNegativeInteger) -> %
from XPolynomialsCat(VarSet, R)
varList: % -> List VarSet
from XFreeAlgebra(VarSet, R)
zero?: % -> Boolean
from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianProductCategory R

AbelianSemiGroup

Algebra R

BasicType

BiModule(%, %)

BiModule(R, R)

CancellationAbelianMonoid

CoercibleTo OutputForm

Comparable if R has Comparable

FreeModuleCategory(R, PoincareBirkhoffWittLyndonBasis VarSet)

IndexedDirectProductCategory(R, PoincareBirkhoffWittLyndonBasis VarSet)

LeftModule %

LeftModule R

Magma

MagmaWithUnit

Module R

Monoid

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors if R has noZeroDivisors

OrderedAbelianMonoid if R has OrderedAbelianMonoid

OrderedAbelianMonoidSup if R has OrderedAbelianMonoidSup

OrderedAbelianSemiGroup if R has OrderedAbelianMonoid

OrderedCancellationAbelianMonoid if R has OrderedAbelianMonoidSup

OrderedSet if R has OrderedAbelianMonoid

PartialOrder if R has OrderedAbelianMonoid

RetractableTo FreeMonoid VarSet

RetractableTo PoincareBirkhoffWittLyndonBasis VarSet

RightModule %

RightModule R

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

unitsKnown

XAlgebra R

XFreeAlgebra(VarSet, R)

XPolynomialsCat(VarSet, R)