# FreeNilpotentLie(n, class, R)ΒΆ

Generate the Free Lie Algebra over a ring R with identity; A P. Hall basis is generated by a package call to HallBasis.

0: %

from AbelianMonoid

*: (%, %) -> %

from Magma

*: (%, R) -> %

from RightModule R

*: (Integer, %) -> %

from AbelianGroup

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

*: (R, %) -> %

from LeftModule R

+: (%, %) -> %

from AbelianSemiGroup

-: % -> %

from AbelianGroup

-: (%, %) -> %

from AbelianGroup

=: (%, %) -> Boolean

from BasicType

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

antiCommutator: (%, %) -> %
associator: (%, %, %) -> %
coerce: % -> OutputForm
commutator: (%, %) -> %
deepExpand: % -> OutputForm

deepExpand(x) rewrites all terms of x as commutators of generators.

dimension: () -> NonNegativeInteger

dimension() is the rank of this Lie algebra

generator: NonNegativeInteger -> %

generator(i) is the ith Hall Basis element

hash: % -> SingleInteger

from SetCategory

hashUpdate!: (HashState, %) -> HashState

from SetCategory

latex: % -> String

from SetCategory

leftPower: (%, PositiveInteger) -> %

from Magma

opposite?: (%, %) -> Boolean

from AbelianMonoid

plenaryPower: (%, PositiveInteger) -> %
rightPower: (%, PositiveInteger) -> %

from Magma

sample: %

from AbelianMonoid

shallowExpand: % -> OutputForm

shallowExpand(x) replaces elements of basis by commutators of other basis elements if possible.

subtractIfCan: (%, %) -> Union(%, failed)
zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

BasicType

BiModule(R, R)

CancellationAbelianMonoid

Magma

NonAssociativeRng

NonAssociativeSemiRng

SetCategory