OrderedCancellationAbelianMonoid

catdef.spad line 993 [edit on github]

Ordered sets which are also abelian cancellation monoids, such that the addition preserves the ordering.

* : (NonNegativeInteger, %) -> %

from AbelianMonoid

* : (PositiveInteger, %) -> %

from AbelianSemiGroup

+ : (%, %) -> %

from AbelianSemiGroup

0 : () -> %

from AbelianMonoid

< : (%, %) -> Boolean

from PartialOrder

<= : (%, %) -> Boolean

from PartialOrder

= : (%, %) -> Boolean

from BasicType

> : (%, %) -> Boolean

from PartialOrder

>= : (%, %) -> Boolean

from PartialOrder

coerce : % -> OutputForm

from CoercibleTo(OutputForm)

latex : % -> String

from SetCategory

max : (%, %) -> %

from OrderedSet

min : (%, %) -> %

from OrderedSet

opposite? : (%, %) -> Boolean

from AbelianMonoid

sample : () -> %

from AbelianMonoid

smaller? : (%, %) -> Boolean

from Comparable

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

from CancellationAbelianMonoid

zero? : % -> Boolean

from AbelianMonoid

~= : (%, %) -> Boolean

from BasicType

BasicType

OrderedAbelianMonoid

OrderedAbelianSemiGroup

CoercibleTo(OutputForm)

AbelianMonoid

AbelianSemiGroup

Comparable

SetCategory

OrderedSet

CancellationAbelianMonoid

PartialOrder