SemiRingΒΆ
catdef.spad line 1379 [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
- ^: (%, NonNegativeInteger) -> %
from MagmaWithUnit
- ^: (%, PositiveInteger) -> %
from Magma
- antiCommutator: (%, %) -> %
- coerce: % -> OutputForm
from CoercibleTo OutputForm
- 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
- zero?: % -> Boolean
from AbelianMonoid
BiModule(%, %)
CancellationAbelianMonoid if % has AbelianGroup