SemiRng

catdef.spad line 1371 [edit on github]

The category of associative semirings, not necessarily commutative, and not necessarily with a 1.

* : (%, %) -> %

from LeftModule(%)

* : (Integer, %) -> % if % has AbelianGroup

from AbelianGroup

* : (NonNegativeInteger, %) -> % if % has AbelianMonoid

from AbelianMonoid

* : (PositiveInteger, %) -> %

from AbelianSemiGroup

+ : (%, %) -> %

from AbelianSemiGroup

- : % -> % if % has AbelianGroup

from AbelianGroup

- : (%, %) -> % if % has AbelianGroup

from AbelianGroup

0 : () -> % if % has AbelianMonoid

from AbelianMonoid

= : (%, %) -> Boolean

from BasicType

^ : (%, PositiveInteger) -> %

from Magma

antiCommutator : (%, %) -> %

from NonAssociativeSemiRng

coerce : % -> OutputForm

from CoercibleTo(OutputForm)

latex : % -> String

from SetCategory

leftPower : (%, PositiveInteger) -> %

from Magma

opposite? : (%, %) -> Boolean if % has AbelianMonoid

from AbelianMonoid

rightPower : (%, PositiveInteger) -> %

from Magma

sample : () -> % if % has AbelianMonoid

from AbelianMonoid

subtractIfCan : (%, %) -> Union(%, "failed") if % has AbelianGroup

from CancellationAbelianMonoid

zero? : % -> Boolean if % has AbelianMonoid

from AbelianMonoid

~= : (%, %) -> Boolean

from BasicType

LeftModule(%)

BasicType

CoercibleTo(OutputForm)

BiModule(%, %)

RightModule(%)

SemiGroup

SetCategory

Magma

NonAssociativeSemiRng

CancellationAbelianMonoid

AbelianSemiGroup