FreeNilpotentLie(n, class, R)ΒΆ

fnla.spad line 159

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: (%, %) -> %
from NonAssociativeSemiRng
associator: (%, %, %) -> %
from NonAssociativeRng
coerce: % -> OutputForm
from CoercibleTo OutputForm
commutator: (%, %) -> %
from NonAssociativeRng
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) -> %
from NonAssociativeAlgebra R
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)
from CancellationAbelianMonoid
zero?: % -> Boolean
from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

BasicType

BiModule(R, R)

CancellationAbelianMonoid

CoercibleTo OutputForm

LeftModule R

Magma

Module R

NonAssociativeAlgebra R

NonAssociativeRng

NonAssociativeSemiRng

RightModule R

SetCategory