Rng

catdef.spad line 1389 [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.

* : (%, %) -> %

from Magma

* : (Integer, %) -> %

from AbelianGroup

* : (NonNegativeInteger, %) -> %

from AbelianMonoid

* : (PositiveInteger, %) -> %

from AbelianSemiGroup

+ : (%, %) -> %

from AbelianSemiGroup

- : % -> %

from AbelianGroup

- : (%, %) -> %

from AbelianGroup

0 : () -> %

from AbelianMonoid

= : (%, %) -> Boolean

from BasicType

^ : (%, PositiveInteger) -> %

from Magma

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

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

~= : (%, %) -> Boolean

from BasicType

SemiRng

NonAssociativeRng

CoercibleTo(OutputForm)

AbelianSemiGroup

BiModule(%, %)

BasicType

AbelianMonoid

AbelianGroup

SemiGroup

LeftModule(%)

RightModule(%)

Magma

NonAssociativeSemiRng

CancellationAbelianMonoid

SetCategory