FreeNilpotentLie(n, class, R)ΒΆ
fnla.spad line 159 [edit on github]
class: NonNegativeInteger
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
- ^: (%, PositiveInteger) -> %
from Magma
- antiCommutator: (%, %) -> %
- associator: (%, %, %) -> %
from NonAssociativeRng
- coerce: % -> OutputForm
from CoercibleTo OutputForm
- commutator: (%, %) -> %
from NonAssociativeRng
- deepExpand: % -> OutputForm
deepExpand(x)rewrites all terms ofxas commutators of generators.
- dimension: () -> NonNegativeInteger
dimension()is the rank of this Lie algebra
- generator: NonNegativeInteger -> %
generator(i)is theith Hall Basis element
- 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)
- zero?: % -> Boolean
from AbelianMonoid
BiModule(R, R)
Module R