LieAlgebra R

xlpoly.spad line 299 [edit on github]

• R: CommutativeRing

The category of Lie Algebras. It is used by the following domains of non-commutative algebra: LiePolynomial and XPBWPolynomial. Author : Michel Petitot (petitot@lifl.fr).

0: %

from AbelianMonoid

*: (%, R) -> %

from RightModule R

*: (Integer, %) -> %

from AbelianGroup

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

*: (R, %) -> %

from LeftModule R

+: (%, %) -> %

from AbelianSemiGroup

-: % -> %

from AbelianGroup

-: (%, %) -> %

from AbelianGroup

/: (%, R) -> % if R has Field

x/r returns the division of x by r.

=: (%, %) -> Boolean

from BasicType

~=: (%, %) -> Boolean

from BasicType

coerce: % -> OutputForm

from CoercibleTo OutputForm

construct: (%, %) -> %

construct(x, y) returns the Lie bracket of x and y.

latex: % -> String

from SetCategory

opposite?: (%, %) -> Boolean

from AbelianMonoid

sample: %

from AbelianMonoid

subtractIfCan: (%, %) -> Union(%, failed)

from CancellationAbelianMonoid

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

BasicType

BiModule(R, R)

CancellationAbelianMonoid

CoercibleTo OutputForm

LeftModule R

Module R

RightModule R

SetCategory