FreeMagma VarSetΒΆ

xlpoly.spad line 1

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
from CoercibleTo OutputForm
coerce: VarSet -> %
from RetractableTo VarSet
first: % -> VarSet
first(x) returns the first entry of the tree x.
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
latex: % -> String
from SetCategory
left: % -> %
left(x) returns left subtree of x or error if retractable? <l–free-magma_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? <l–free-magma_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? <l–free-magma_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? <l–free-magma_retractable?>`(``x`) is true.
smaller?: (%, %) -> Boolean
from Comparable
varList: % -> List VarSet
varList(x) returns the list of distinct entries of x.

BasicType

CoercibleTo OutputForm

Comparable

OrderedSet

PartialOrder

RetractableTo VarSet

SetCategory