FreeNilpotentLie(n, class, R)
fnla.spad line 159
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Generate the Free Lie Algebra over a ring R with identity; A P. Hall basis is generated by a package call to HallBasis.
- * : (%, %) -> %
- from Magma
- * : (%, R) -> %
- from RightModule(R)
- * : (R, %) -> %
- from LeftModule(R)
- * : (Integer, %) -> %
- from AbelianGroup
- * : (NonNegativeInteger, %) -> %
- from AbelianMonoid
- * : (PositiveInteger, %) -> %
- from AbelianSemiGroup
- + : (%, %) -> %
- from AbelianSemiGroup
- - : % -> %
- from AbelianGroup
- - : (%, %) -> %
- from AbelianGroup
- 0 : () -> %
- from AbelianMonoid
- = : (%, %) -> Boolean
- from BasicType
- ^ : (%, PositiveInteger) -> %
- from Magma
- 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
- 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
- ~= : (%, %) -> Boolean
- from BasicType
BiModule(R, R)
CancellationAbelianMonoid
NonAssociativeAlgebra(R)
BasicType
Magma
RightModule(R)
Module(R)
AbelianGroup
AbelianSemiGroup
SetCategory
LeftModule(R)
AbelianMonoid
NonAssociativeRng
NonAssociativeSemiRng
CoercibleTo(OutputForm)