SemiRngΒΆ

catdef.spad line 1357 [edit on github]

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

0: % if % has AbelianMonoid

from AbelianMonoid

*: (%, %) -> %

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

=: (%, %) -> Boolean

from BasicType

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

antiCommutator: (%, %) -> %

from NonAssociativeSemiRng

coerce: % -> OutputForm

from CoercibleTo OutputForm

hash: % -> SingleInteger

from SetCategory

hashUpdate!: (HashState, %) -> HashState

from SetCategory

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

AbelianSemiGroup

BasicType

BiModule(%, %)

CancellationAbelianMonoid if % has AbelianGroup

CoercibleTo OutputForm

LeftModule %

Magma

NonAssociativeSemiRng

RightModule %

SemiGroup

SetCategory