# LiePolynomial(VarSet, R)ΒΆ

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

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

*: (R, %) -> %

from LeftModule R

+: (%, %) -> %

from AbelianSemiGroup

-: % -> %

from AbelianGroup

-: (%, %) -> %

from AbelianGroup

/: (%, R) -> % if R has Field

from LieAlgebra R

=: (%, %) -> Boolean

from BasicType

~=: (%, %) -> 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
coerce: % -> XDistributedPolynomial(VarSet, R)

from FreeLieAlgebra(VarSet, R)

coerce: % -> XRecursivePolynomial(VarSet, R)

from FreeLieAlgebra(VarSet, R)

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 IndexedProductCategory(R, LyndonWord VarSet)

constructOrdered: List Record(k: LyndonWord VarSet, c: R) -> %

from IndexedProductCategory(R, LyndonWord VarSet)

degree: % -> NonNegativeInteger

from FreeLieAlgebra(VarSet, R)

eval: (%, List VarSet, List %) -> %

from FreeLieAlgebra(VarSet, R)

eval: (%, VarSet, %) -> %

from FreeLieAlgebra(VarSet, R)

latex: % -> String

from SetCategory

from IndexedProductCategory(R, LyndonWord VarSet)

from IndexedProductCategory(R, LyndonWord VarSet)

from IndexedProductCategory(R, LyndonWord VarSet)

leadingTerm: % -> Record(k: LyndonWord VarSet, c: R)

from IndexedProductCategory(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 IndexedProductCategory(R, LyndonWord VarSet)

mirror: % -> %

from FreeLieAlgebra(VarSet, R)

monomial?: % -> Boolean

from IndexedProductCategory(R, LyndonWord VarSet)

monomial: (R, LyndonWord VarSet) -> %

from IndexedProductCategory(R, LyndonWord VarSet)

monomials: % -> List %

from FreeModuleCategory(R, LyndonWord VarSet)

numberOfMonomials: % -> NonNegativeInteger

from IndexedDirectProductCategory(R, LyndonWord VarSet)

opposite?: (%, %) -> Boolean

from AbelianMonoid

reductum: % -> %

from IndexedProductCategory(R, 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)
support: % -> List LyndonWord VarSet

from FreeModuleCategory(R, LyndonWord VarSet)

trunc: (%, NonNegativeInteger) -> %

from FreeLieAlgebra(VarSet, R)

varList: % -> List VarSet

from FreeLieAlgebra(VarSet, R)

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

BasicType

BiModule(R, R)

CancellationAbelianMonoid

Comparable if R has Comparable

FreeLieAlgebra(VarSet, R)

FreeModuleCategory(R, LyndonWord VarSet)

IndexedDirectProductCategory(R, LyndonWord VarSet)

IndexedProductCategory(R, LyndonWord VarSet)

SetCategory