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).

* : (%, R) -> %

from RightModule(R)

* : (R, %) -> %

from LeftModule(R)

* : (Integer, %) -> %

from AbelianGroup

* : (NonNegativeInteger, %) -> %

from AbelianMonoid

* : (PositiveInteger, %) -> %

from AbelianSemiGroup

+ : (%, %) -> %

from AbelianSemiGroup

- : % -> %

from AbelianGroup

- : (%, %) -> %

from AbelianGroup

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

x/r returns the division of x by r.

0 : () -> %

from AbelianMonoid

= : (%, %) -> 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

~= : (%, %) -> Boolean

from BasicType

CancellationAbelianMonoid

SetCategory

CoercibleTo(OutputForm)

AbelianMonoid

RightModule(R)

AbelianSemiGroup

BiModule(R, R)

Module(R)

LeftModule(R)

BasicType

AbelianGroup