NonAssociativeAlgebra R

naalgc.spad line 195 [edit on github]

• R: CommutativeRing

NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs). Axioms r*(a*b) = (r*a)*b = a*(r*b)

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

latex: % -> String

from SetCategory

leftPower: (%, PositiveInteger) -> %

from Magma

opposite?: (%, %) -> Boolean

from AbelianMonoid

plenaryPower: (%, PositiveInteger) -> %

plenaryPower(a, n) is recursively defined to be plenaryPower(a, n-1)*plenaryPower(a, n-1) for n>1 and a for n=1.

rightPower: (%, PositiveInteger) -> %

from Magma

sample: %

from AbelianMonoid

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

from CancellationAbelianMonoid

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

BasicType

BiModule(R, R)

CancellationAbelianMonoid

CoercibleTo OutputForm

LeftModule R

Magma

Module R

NonAssociativeRng

NonAssociativeSemiRng

RightModule R

SetCategory