LieExponentials(VarSet, R, Order)ΒΆ

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).

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.

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

TwoSidedRecip

unitsKnown