FreeLieAlgebra(VarSet, R)ΒΆ

xlpoly.spad line 325

The category of free Lie algebras. It is used by domains of non-commutative algebra: LiePolynomial and XPBWPolynomial. Author: Michel Petitot (petitot@lifl.fr)

0: %
from AbelianMonoid
*: (%, R) -> %
from RightModule R
*: (Integer, %) -> %
from AbelianGroup
*: (NonNegativeInteger, %) -> %
from AbelianMonoid
*: (PositiveInteger, %) -> %
from AbelianSemiGroup
*: (R, %) -> %
from LeftModule R
+: (%, %) -> %
from AbelianSemiGroup
-: % -> %
from AbelianGroup
-: (%, %) -> %
from AbelianGroup
/: (%, R) -> % if R has Field
from LieAlgebra R
=: (%, %) -> Boolean
from BasicType
~=: (%, %) -> Boolean
from BasicType
coef: (XRecursivePolynomial(VarSet, R), %) -> R
coef(x, y) returns the scalar product of x by y, the set of words being regarded as an orthogonal basis.
coerce: % -> OutputForm
from CoercibleTo OutputForm
coerce: % -> XDistributedPolynomial(VarSet, R)
coerce(x) returns x as distributed polynomial.
coerce: % -> XRecursivePolynomial(VarSet, R)
coerce(x) returns x as a recursive polynomial.
coerce: VarSet -> %
coerce(x) returns x as a Lie polynomial.
construct: (%, %) -> %
from LieAlgebra R
degree: % -> NonNegativeInteger
degree(x) returns the greatest length of a word in the support of x.
eval: (%, List VarSet, List %) -> %
eval(p, [x1, ..., xn], [v1, ..., vn]) replaces xi by vi in p.
eval: (%, VarSet, %) -> %
eval(p, x, v) replaces x by v in p.
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
latex: % -> String
from SetCategory
LiePoly: LyndonWord VarSet -> %
LiePoly(l) returns the bracketed form of l as a Lie polynomial.
lquo: (XRecursivePolynomial(VarSet, R), %) -> XRecursivePolynomial(VarSet, R)
lquo(x, y) returns the left simplification of x by y.
mirror: % -> %
mirror(x) returns Sum(r_i mirror(w_i)) if x is Sum(r_i w_i).
opposite?: (%, %) -> Boolean
from AbelianMonoid
rquo: (XRecursivePolynomial(VarSet, R), %) -> XRecursivePolynomial(VarSet, R)
rquo(x, y) returns the right simplification of x by y.
sample: %
from AbelianMonoid
subtractIfCan: (%, %) -> Union(%, failed)
from CancellationAbelianMonoid
trunc: (%, NonNegativeInteger) -> %
trunc(p, n) returns the polynomial p truncated at order n.
varList: % -> List VarSet
varList(x) returns the list of distinct entries of x.
zero?: % -> Boolean
from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

BasicType

BiModule(R, R)

CancellationAbelianMonoid

CoercibleTo OutputForm

LeftModule R

LieAlgebra R

Module R

RightModule R

SetCategory