LieExponentials(VarSet, R, Order)

xlpoly.spad line 982 [edit on github]

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).

* : (%, %) -> %
from Magma
/ : (%, %) -> %
from Group
1 : () -> %
from MagmaWithUnit
= : (%, %) -> Boolean
from BasicType
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.

^ : (%, Integer) -> %
from Group
^ : (%, NonNegativeInteger) -> %
from MagmaWithUnit
^ : (%, PositiveInteger) -> %
from Magma
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.

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.

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.

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

SetCategory

Group

CoercibleTo(OutputForm)

MagmaWithUnit

SemiGroup

TwoSidedRecip

Magma

unitsKnown

Monoid

BasicType