SemiRngΒΆ

catdef.spad line 1358

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