# PoincareBirkhoffWittLyndonBasis VarSetΒΆ

This domain provides the internal representation of polynomials in non-commutative variables written over the Poincare-Birkhoff-Witt basis. See the XPBWPolynomial domain constructor. See Free Lie Algebras by C. Reutenauer (Oxford science publications). Author: Michel Petitot (petitot@lifl.fr).

1: %

1 returns the empty list.

<=: (%, %) -> Boolean

from PartialOrder

<: (%, %) -> Boolean

from PartialOrder

=: (%, %) -> Boolean

from BasicType

>=: (%, %) -> Boolean

from PartialOrder

>: (%, %) -> Boolean

from PartialOrder

~=: (%, %) -> Boolean

from BasicType

coerce: % -> FreeMonoid VarSet

coerce([l1]*[l2]*...[ln]) returns the word l1*l2*...*ln, where [l_i] is the backeted form of the Lyndon word l_i.

coerce: % -> OutputForm
coerce: LyndonWord VarSet -> %

from CoercibleFrom LyndonWord VarSet

coerce: VarSet -> %

coerce(v) return v

first: % -> LyndonWord VarSet

first([l1]*[l2]*...[ln]) returns the Lyndon word l1.

hash: % -> SingleInteger

from SetCategory

hashUpdate!: (HashState, %) -> HashState

from SetCategory

latex: % -> String

from SetCategory

length: % -> NonNegativeInteger

length([l1]*[l2]*...[ln]) returns the length of the word l1*l2*...*ln.

listOfTerms: % -> List LyndonWord VarSet

listOfTerms([l1]*[l2]*...[ln]) returns the list of words l1, l2, .... ln.

max: (%, %) -> %

from OrderedSet

min: (%, %) -> %

from OrderedSet

rest: % -> %

rest([l1]*[l2]*...[ln]) returns the list l2, .... ln.

retract: % -> LyndonWord VarSet

from RetractableTo LyndonWord VarSet

retractable?: % -> Boolean

retractable?([l1]*[l2]*...[ln]) returns true iff n equals 1.

retractIfCan: % -> Union(LyndonWord VarSet, failed)

from RetractableTo LyndonWord VarSet

smaller?: (%, %) -> Boolean

from Comparable

varList: % -> List VarSet

varList([l1]*[l2]*...[ln]) returns the list of variables in the word l1*l2*...*ln.

BasicType

CoercibleFrom LyndonWord VarSet

Comparable

OrderedSet

PartialOrder

RetractableTo LyndonWord VarSet

SetCategory