PoincareBirkhoffWittLyndonBasis VarSetΒΆ

xlpoly.spad line 649

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
from CoercibleTo OutputForm
coerce: LyndonWord VarSet -> %
from RetractableTo 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

CoercibleTo OutputForm

Comparable

OrderedSet

PartialOrder

RetractableTo LyndonWord VarSet

SetCategory