FreeMagma(VarSet)

xlpoly.spad line 1 [edit on github]

This type is the basic representation of parenthesized words (binary trees over arbitrary symbols) useful in LiePolynomial. Author: Michel Petitot (petitot@lifl.fr).

* : (%, %) -> %

x*y returns the tree [x, y].

< : (%, %) -> Boolean
from PartialOrder
<= : (%, %) -> Boolean
from PartialOrder
= : (%, %) -> Boolean
from BasicType
> : (%, %) -> Boolean
from PartialOrder
>= : (%, %) -> Boolean
from PartialOrder
coerce : VarSet -> %
from CoercibleFrom(VarSet)
coerce : % -> FreeMonoid(VarSet)

coerce(x) returns the element of FreeMonoid(VarSet) corresponding to x by removing parentheses.

coerce : % -> OutputForm
from CoercibleTo(OutputForm)
first : % -> VarSet

first(x) returns the first entry of the tree x.

latex : % -> String
from SetCategory
left : % -> %

left(x) returns left subtree of x or error if retractable?(x) is true.

length : % -> PositiveInteger

length(x) returns the number of entries in x.

lexico : (%, %) -> Boolean

lexico(x, y) returns true iff x is smaller than y w.r.t. the lexicographical ordering induced by VarSet. N.B. This operation does not take into account the tree structure of its arguments. Thus this is not a total ordering.

max : (%, %) -> %
from OrderedSet
min : (%, %) -> %
from OrderedSet
mirror : % -> %

mirror(x) returns the reversed word of x. That is x itself if retractable?(x) is true and mirror(z) * mirror(y) if x is y*z.

rest : % -> %

rest(x) return x without the first entry or error if retractable?(x) is true.

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

retractable?(x) tests if x is a tree with only one entry.

right : % -> %

right(x) returns right subtree of x or error if retractable?(x) is true.

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

varList(x) returns the list of distinct entries of x.

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

RetractableTo(VarSet)

CoercibleTo(OutputForm)

Comparable

OrderedSet

SetCategory

BasicType

PartialOrder

CoercibleFrom(VarSet)