NonAssociativeRngΒΆ

naalgc.spad line 137

NonAssociativeRng is a basic ring-type structure, not necessarily commutative or associative, and not necessarily with unit. Axioms x*(y+z) = x*y + x*z (x+y)*z = x*z + y*z Common Additional Axioms noZeroDivisors ab = 0 => a=0 or b=0

0: %
from AbelianMonoid
*: (%, %) -> %
from Magma
*: (Integer, %) -> %
from AbelianGroup
*: (NonNegativeInteger, %) -> %
from AbelianMonoid
*: (PositiveInteger, %) -> %
from AbelianSemiGroup
+: (%, %) -> %
from AbelianSemiGroup
-: % -> %
from AbelianGroup
-: (%, %) -> %
from AbelianGroup
=: (%, %) -> Boolean
from BasicType
^: (%, PositiveInteger) -> %
from Magma
~=: (%, %) -> Boolean
from BasicType
antiCommutator: (%, %) -> %
from NonAssociativeSemiRng
associator: (%, %, %) -> %
associator(a, b, c) returns (a*b)*c-a*(b*c).
coerce: % -> OutputForm
from CoercibleTo OutputForm
commutator: (%, %) -> %
commutator(a, b) returns a*b-b*a.
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
latex: % -> String
from SetCategory
leftPower: (%, PositiveInteger) -> %
from Magma
opposite?: (%, %) -> Boolean
from AbelianMonoid
rightPower: (%, PositiveInteger) -> %
from Magma
sample: %
from AbelianMonoid
subtractIfCan: (%, %) -> Union(%, failed)
from CancellationAbelianMonoid
zero?: % -> Boolean
from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

BasicType

CancellationAbelianMonoid

CoercibleTo OutputForm

Magma

NonAssociativeSemiRng

SetCategory