LieExponentials(VarSet, R, Order)ΒΆ

xlpoly.spad line 986

Management of the Lie Group associated with a free nilpotent Lie algebra. Every Lie bracket with length greater than Order are assumed to be null. The implementation inherits from the XPBWPolynomial domain constructor: Lyndon coordinates are exponential coordinates of the second kind. Author: Michel Petitot (petitot@lifl.fr).

1: %
from MagmaWithUnit
*: (%, %) -> %
from Magma
/: (%, %) -> %
from Group
=: (%, %) -> Boolean
from BasicType
^: (%, Integer) -> %
from Group
^: (%, NonNegativeInteger) -> %
from MagmaWithUnit
^: (%, PositiveInteger) -> %
from Magma
~=: (%, %) -> Boolean
from BasicType
coerce: % -> OutputForm
from CoercibleTo OutputForm
coerce: % -> XDistributedPolynomial(VarSet, R)
coerce(g) returns the internal representation of g.
coerce: % -> XPBWPolynomial(VarSet, R)
coerce(g) returns the internal representation of g.
commutator: (%, %) -> %
from Group
conjugate: (%, %) -> %
from Group
exp: LiePolynomial(VarSet, R) -> %
exp(p) returns the exponential of p.
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
identification: (%, %) -> List Equation R
identification(g, h) returns the list of equations g_i = h_i, where g_i (resp. h_i) are exponential coordinates of g (resp. h).
inv: % -> %
from Group
latex: % -> String
from SetCategory
leftPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
leftPower: (%, PositiveInteger) -> %
from Magma
leftRecip: % -> Union(%, failed)
from MagmaWithUnit
listOfTerms: % -> List Record(k: PoincareBirkhoffWittLyndonBasis VarSet, c: R)
listOfTerms(p) returns the internal representation of p.
log: % -> LiePolynomial(VarSet, R)
log(p) returns the logarithm of p.
LyndonBasis: List VarSet -> List LiePolynomial(VarSet, R)
LyndonBasis(lv) returns the Lyndon basis of the nilpotent free Lie algebra.
LyndonCoordinates: % -> List Record(k: LyndonWord VarSet, c: R)
LyndonCoordinates(g) returns the exponential coordinates of g.
mirror: % -> %
mirror(g) is the mirror of the internal representation of g.
one?: % -> Boolean
from MagmaWithUnit
recip: % -> Union(%, failed)
from MagmaWithUnit
rightPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
rightPower: (%, PositiveInteger) -> %
from Magma
rightRecip: % -> Union(%, failed)
from MagmaWithUnit
sample: %
from MagmaWithUnit
varList: % -> List VarSet
varList(g) returns the list of variables of g.

BasicType

CoercibleTo OutputForm

Group

Magma

MagmaWithUnit

Monoid

SemiGroup

SetCategory

unitsKnown