SemiRing

catdef.spad line 1380 [edit on github]

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

* : (%, %) -> %

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

0 : () -> %

from AbelianMonoid

1 : () -> %

from MagmaWithUnit

= : (%, %) -> Boolean

from BasicType

^ : (%, NonNegativeInteger) -> %

from MagmaWithUnit

^ : (%, PositiveInteger) -> %

from Magma

antiCommutator : (%, %) -> %

from NonAssociativeSemiRng

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

from CancellationAbelianMonoid

zero? : % -> Boolean

from AbelianMonoid

~= : (%, %) -> Boolean

from BasicType

RightModule(%)

Monoid

SemiGroup

CancellationAbelianMonoid

LeftModule(%)

BasicType

Magma

NonAssociativeSemiRng

NonAssociativeSemiRing

SetCategory

AbelianSemiGroup

AbelianMonoid

BiModule(%, %)

MagmaWithUnit

CoercibleTo(OutputForm)

SemiRng