LiePolynomial(VarSet, R)ΒΆ

xlpoly.spad line 449

This type supports Lie polynomials in Lyndon basis see Free Lie Algebras by C. Reutenauer (Oxford science publications). Author: Michel Petitot (petitot@lifl.fr).

0: %
from AbelianMonoid
*: (%, R) -> %
from RightModule R
*: (Integer, %) -> %
from AbelianGroup
*: (LyndonWord VarSet, R) -> %
from FreeModuleCategory(R, LyndonWord VarSet)
*: (NonNegativeInteger, %) -> %
from AbelianMonoid
*: (PositiveInteger, %) -> %
from AbelianSemiGroup
*: (R, %) -> %
from LeftModule R
*: (R, LyndonWord VarSet) -> %
from FreeModuleCategory(R, LyndonWord VarSet)
+: (%, %) -> %
from AbelianSemiGroup
-: % -> %
from AbelianGroup
-: (%, %) -> %
from AbelianGroup
/: (%, R) -> % if R has Field
from LieAlgebra R
<: (%, %) -> 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
~=: (%, %) -> Boolean
from BasicType
coef: (XRecursivePolynomial(VarSet, R), %) -> R
from FreeLieAlgebra(VarSet, R)
coefficient: (%, LyndonWord VarSet) -> R
from FreeModuleCategory(R, LyndonWord VarSet)
coefficients: % -> List R
from FreeModuleCategory(R, LyndonWord VarSet)
coerce: % -> OutputForm
from CoercibleTo OutputForm
coerce: % -> XDistributedPolynomial(VarSet, R)
from FreeLieAlgebra(VarSet, R)
coerce: % -> XRecursivePolynomial(VarSet, R)
from FreeLieAlgebra(VarSet, R)
coerce: LyndonWord VarSet -> %
from RetractableTo LyndonWord VarSet
coerce: VarSet -> %
from FreeLieAlgebra(VarSet, R)
construct: (%, %) -> %
from LieAlgebra R
construct: (%, LyndonWord VarSet) -> %
construct(x, y) returns the Lie bracket [x, y].
construct: (LyndonWord VarSet, %) -> %
construct(x, y) returns the Lie bracket [x, y].
construct: (LyndonWord VarSet, LyndonWord VarSet) -> %
construct(x, y) returns the Lie bracket [x, y].
construct: List Record(k: LyndonWord VarSet, c: R) -> %
from IndexedDirectProductCategory(R, LyndonWord VarSet)
constructOrdered: List Record(k: LyndonWord VarSet, c: R) -> %
from IndexedDirectProductCategory(R, LyndonWord VarSet)
degree: % -> NonNegativeInteger
from FreeLieAlgebra(VarSet, R)
eval: (%, List VarSet, List %) -> %
from FreeLieAlgebra(VarSet, R)
eval: (%, VarSet, %) -> %
from FreeLieAlgebra(VarSet, R)
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
latex: % -> String
from SetCategory
leadingCoefficient: % -> R
from IndexedDirectProductCategory(R, LyndonWord VarSet)
leadingMonomial: % -> %
from IndexedDirectProductCategory(R, LyndonWord VarSet)
leadingSupport: % -> LyndonWord VarSet
from IndexedDirectProductCategory(R, LyndonWord VarSet)
leadingTerm: % -> Record(k: LyndonWord VarSet, c: R)
from IndexedDirectProductCategory(R, LyndonWord VarSet)
LiePoly: LyndonWord VarSet -> %
from FreeLieAlgebra(VarSet, R)
LiePolyIfCan: XDistributedPolynomial(VarSet, R) -> Union(%, failed)
LiePolyIfCan(p) returns p in Lyndon basis if p is a Lie polynomial, otherwise "failed" is returned.
linearExtend: (LyndonWord VarSet -> R, %) -> R
from FreeModuleCategory(R, LyndonWord VarSet)
listOfTerms: % -> List Record(k: LyndonWord VarSet, c: R)
from IndexedDirectProductCategory(R, LyndonWord VarSet)
lquo: (XRecursivePolynomial(VarSet, R), %) -> XRecursivePolynomial(VarSet, R)
from FreeLieAlgebra(VarSet, R)
map: (R -> R, %) -> %
from IndexedDirectProductCategory(R, LyndonWord VarSet)
max: (%, %) -> % if R has OrderedAbelianMonoid
from OrderedSet
min: (%, %) -> % if R has OrderedAbelianMonoid
from OrderedSet
mirror: % -> %
from FreeLieAlgebra(VarSet, R)
monomial: (R, LyndonWord VarSet) -> %
from IndexedDirectProductCategory(R, LyndonWord VarSet)
monomial?: % -> Boolean
from IndexedDirectProductCategory(R, LyndonWord VarSet)
monomials: % -> List %
from FreeModuleCategory(R, LyndonWord VarSet)
numberOfMonomials: % -> NonNegativeInteger
from IndexedDirectProductCategory(R, LyndonWord VarSet)
opposite?: (%, %) -> Boolean
from AbelianMonoid
reductum: % -> %
from IndexedDirectProductCategory(R, LyndonWord VarSet)
retract: % -> LyndonWord VarSet
from RetractableTo LyndonWord VarSet
retractIfCan: % -> Union(LyndonWord VarSet, failed)
from RetractableTo LyndonWord VarSet
rquo: (XRecursivePolynomial(VarSet, R), %) -> XRecursivePolynomial(VarSet, R)
from FreeLieAlgebra(VarSet, R)
sample: %
from AbelianMonoid
smaller?: (%, %) -> Boolean if R has Comparable
from Comparable
subtractIfCan: (%, %) -> Union(%, failed)
from CancellationAbelianMonoid
sup: (%, %) -> % if R has OrderedAbelianMonoidSup
from OrderedAbelianMonoidSup
support: % -> List LyndonWord VarSet
from FreeModuleCategory(R, LyndonWord VarSet)
totalDegree: % -> NonNegativeInteger if LyndonWord VarSet has coerce: LyndonWord VarSet -> Vector NonNegativeInteger
from FreeModuleCategory(R, LyndonWord VarSet)
trunc: (%, NonNegativeInteger) -> %
from FreeLieAlgebra(VarSet, R)
varList: % -> List VarSet
from FreeLieAlgebra(VarSet, R)
zero?: % -> Boolean
from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianProductCategory R

AbelianSemiGroup

BasicType

BiModule(R, R)

CancellationAbelianMonoid

CoercibleTo OutputForm

Comparable if R has Comparable

FreeLieAlgebra(VarSet, R)

FreeModuleCategory(R, LyndonWord VarSet)

IndexedDirectProductCategory(R, LyndonWord VarSet)

LeftModule R

LieAlgebra R

Module R

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 LyndonWord VarSet

RightModule R

SetCategory