RngΒΆ

catdef.spad line 1375 [edit on github]

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