# FreeMagma VarSetΒΆ

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

~=: (%, %) -> Boolean

from BasicType

coerce: % -> FreeMonoid VarSet

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

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

from CoercibleFrom VarSet

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

retractable?: % -> Boolean

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

retractIfCan: % -> Union(VarSet, failed)

from RetractableTo VarSet

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`.

BasicType

CoercibleFrom VarSet

Comparable

OrderedSet

PartialOrder

RetractableTo VarSet

SetCategory