OrderedAbelianGroup

catdef.spad line 911 [edit on github]

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

* : (Integer, %) -> %: from AbelianGroup

* : (NonNegativeInteger, %) -> %: from AbelianMonoid

* : (PositiveInteger, %) -> %: from AbelianSemiGroup

+ : (%, %) -> %: from AbelianSemiGroup

- : % -> %: from AbelianGroup

- : (%, %) -> %: from AbelianGroup

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

OrderedCancellationAbelianMonoid

CancellationAbelianMonoid

CoercibleTo(OutputForm)

OrderedAbelianMonoid

OrderedAbelianSemiGroup

AbelianSemiGroup