PoincareBirkhoffWittLyndonBasis(VarSet)

xlpoly.spad line 647 [edit on github]

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
coerce : VarSet -> %

coerce(v) return v

coerce : LyndonWord(VarSet) -> %
from CoercibleFrom(LyndonWord(VarSet))
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)
first : % -> LyndonWord(VarSet)

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

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))
retractIfCan : % -> Union(LyndonWord(VarSet), "failed")
from RetractableTo(LyndonWord(VarSet))
retractable? : % -> Boolean

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

smaller? : (%, %) -> Boolean
from Comparable
varList : % -> List(VarSet)

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

~= : (%, %) -> Boolean
from BasicType

CoercibleFrom(LyndonWord(VarSet))

CoercibleTo(OutputForm)

Comparable

RetractableTo(LyndonWord(VarSet))

OrderedSet

SetCategory

BasicType

PartialOrder