NonAssociativeAlgebra RΒΆ

naalgc.spad line 190

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
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
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