OrderedAbelianMonoidSup

catdef.spad line 941 [edit on github]

This domain is an OrderedAbelianMonoid with a sup operation added. The purpose of the sup operator in this domain is to act as a supremum with respect to the partial order imposed by -, rather than with respect to the total > order (since that is "max").

* : (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)

inf : (%, %) -> %: inf(x, y) returns the largest element which can be subtracted from x and y.

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

sup : (%, %) -> %: sup(x, y) returns the least element from which both x and y can be subtracted.

zero? : % -> Boolean: from AbelianMonoid

~= : (%, %) -> Boolean: from BasicType

OrderedCancellationAbelianMonoid

CancellationAbelianMonoid

CoercibleTo(OutputForm)

OrderedAbelianMonoid

OrderedAbelianSemiGroup

AbelianSemiGroup