RngΒΆ

catdef.spad line 1376

The category of associative rings, not necessarily commutative, and not necessarily with a 1. This is a combination of an abelian group and a semigroup, with multiplication distributing over addition.

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
annihilate?: (%, %) -> Boolean
annihilate?(x,y) holds when the product of x and y is 0.
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
rightPower: (%, PositiveInteger) -> %
from Magma
sample: %
from AbelianMonoid
subtractIfCan: (%, %) -> Union(%, failed)
from CancellationAbelianMonoid
zero?: % -> Boolean
from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

BasicType

BiModule(%, %)

CancellationAbelianMonoid

CoercibleTo OutputForm

LeftModule %

Magma

NonAssociativeRng

NonAssociativeSemiRng

RightModule %

SemiGroup

SemiRng

SetCategory