OrderedMonoid

catdef.spad line 1037 [edit on github]

Ordered sets which are also monoids, such that multiplication preserves the ordering.

* : (%, %) -> %

from Magma

1 : () -> %

from MagmaWithUnit

< : (%, %) -> Boolean

from PartialOrder

<= : (%, %) -> Boolean

from PartialOrder

= : (%, %) -> Boolean

from BasicType

> : (%, %) -> Boolean

from PartialOrder

>= : (%, %) -> Boolean

from PartialOrder

^ : (%, NonNegativeInteger) -> %

from MagmaWithUnit

^ : (%, PositiveInteger) -> %

from Magma

coerce : % -> OutputForm

from CoercibleTo(OutputForm)

latex : % -> String

from SetCategory

leftPower : (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower : (%, PositiveInteger) -> %

from Magma

leftRecip : % -> Union(%, "failed")

from MagmaWithUnit

max : (%, %) -> %

from OrderedSet

min : (%, %) -> %

from OrderedSet

one? : % -> Boolean

from MagmaWithUnit

recip : % -> Union(%, "failed")

from MagmaWithUnit

rightPower : (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower : (%, PositiveInteger) -> %

from Magma

rightRecip : % -> Union(%, "failed")

from MagmaWithUnit

sample : () -> %

from MagmaWithUnit

smaller? : (%, %) -> Boolean

from Comparable

~= : (%, %) -> Boolean

from BasicType

MagmaWithUnit

CoercibleTo(OutputForm)

OrderedSemiGroup

Comparable

OrderedSet

SemiGroup

SetCategory

Magma

Monoid

BasicType

PartialOrder