LiePolynomial(VarSet, R)

xlpoly.spad line 449 [edit on github]

• VarSet : OrderedSet
• R : CommutativeRing

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

* : (%, R) -> %

from RightModule(R)

* : (R, %) -> %

from LeftModule(R)

* : (Integer, %) -> %

from AbelianGroup

* : (NonNegativeInteger, %) -> %

from AbelianMonoid

* : (PositiveInteger, %) -> %

from AbelianSemiGroup

+ : (%, %) -> %

from AbelianSemiGroup

- : % -> %

from AbelianGroup

- : (%, %) -> %

from AbelianGroup

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

from LieAlgebra(R)

0 : () -> %

from AbelianMonoid

= : (%, %) -> Boolean

from BasicType

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.

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 : VarSet -> %

from FreeLieAlgebra(VarSet, R)

coerce : % -> OutputForm

from CoercibleTo(OutputForm)

coerce : % -> XDistributedPolynomial(VarSet, R)

from FreeLieAlgebra(VarSet, R)

coerce : % -> XRecursivePolynomial(VarSet, R)

from FreeLieAlgebra(VarSet, R)

construct : (%, %) -> %

from LieAlgebra(R)

construct : (%, LyndonWord(VarSet)) -> %

construct(x, y) returns the Lie bracket [x, y].

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

from IndexedProductCategory(R, LyndonWord(VarSet))

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].

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

from IndexedProductCategory(R, LyndonWord(VarSet))

degree : % -> NonNegativeInteger

from FreeLieAlgebra(VarSet, R)

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

from FreeLieAlgebra(VarSet, R)

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

from FreeLieAlgebra(VarSet, R)

latex : % -> String

from SetCategory

leadingCoefficient : % -> R

from IndexedProductCategory(R, LyndonWord(VarSet))

leadingMonomial : % -> %

from IndexedProductCategory(R, LyndonWord(VarSet))

leadingSupport : % -> LyndonWord(VarSet)

from IndexedProductCategory(R, LyndonWord(VarSet))

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

from IndexedProductCategory(R, LyndonWord(VarSet))

linearExtend : (Mapping(R, LyndonWord(VarSet)), %) -> 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 : (Mapping(R, R), %) -> %

from IndexedProductCategory(R, LyndonWord(VarSet))

mirror : % -> %

from FreeLieAlgebra(VarSet, R)

monomial : (R, LyndonWord(VarSet)) -> %

from IndexedProductCategory(R, LyndonWord(VarSet))

monomial? : % -> Boolean

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")

from CancellationAbelianMonoid

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

~= : (%, %) -> Boolean

from BasicType

FreeLieAlgebra(VarSet, R)

SetCategory

BiModule(R, R)

IndexedDirectProductCategory(R, LyndonWord(VarSet))

CancellationAbelianMonoid

IndexedProductCategory(R, LyndonWord(VarSet))

LeftModule(R)

RightModule(R)

Module(R)

AbelianGroup

LieAlgebra(R)

AbelianSemiGroup

FreeModuleCategory(R, LyndonWord(VarSet))

Comparable

AbelianMonoid

BasicType

CoercibleTo(OutputForm)

AbelianProductCategory(R)