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)

* : (%, %) -> %

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

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

~= : (%, %) -> Boolean

from BasicType

CancellationAbelianMonoid

SetCategory

NonAssociativeRng

CoercibleTo(OutputForm)

AbelianMonoid

RightModule(R)

AbelianSemiGroup

BiModule(R, R)

Module(R)

LeftModule(R)

Magma

NonAssociativeSemiRng

BasicType

AbelianGroup