SemiRingΒΆ

catdef.spad line 1366 [edit on github]

The category of associative semirings, not necessarily commutative, with 0 and 1.

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

*: (%, %) -> %

from LeftModule %

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

from AbelianGroup

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

+: (%, %) -> %

from AbelianSemiGroup

-: % -> % if % has AbelianGroup

from AbelianGroup

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

from AbelianGroup

=: (%, %) -> Boolean

from BasicType

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, 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: (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower: (%, PositiveInteger) -> %

from Magma

leftRecip: % -> Union(%, failed)

from MagmaWithUnit

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

recip: % -> Union(%, failed)

from MagmaWithUnit

rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

sample: %

from AbelianMonoid

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

from CancellationAbelianMonoid

zero?: % -> Boolean

from AbelianMonoid

AbelianMonoid

AbelianSemiGroup

BasicType

BiModule(%, %)

CancellationAbelianMonoid if % has AbelianGroup

CoercibleTo OutputForm

LeftModule %

Magma

MagmaWithUnit

Monoid

NonAssociativeSemiRing

NonAssociativeSemiRng

RightModule %

SemiGroup

SemiRng

SetCategory