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”).
- 0: %
from AbelianMonoid
- *: (NonNegativeInteger, %) -> %
from AbelianMonoid
- *: (PositiveInteger, %) -> %
from AbelianSemiGroup
- +: (%, %) -> %
from AbelianSemiGroup
- <=: (%, %) -> Boolean
from PartialOrder
- <: (%, %) -> Boolean
from PartialOrder
- >=: (%, %) -> Boolean
from PartialOrder
- >: (%, %) -> Boolean
from PartialOrder
- coerce: % -> OutputForm
from CoercibleTo OutputForm
- inf: (%, %) -> %
inf(x, y)returns the largest element which can be subtracted fromxandy.
- latex: % -> String
from SetCategory
- max: (%, %) -> %
from OrderedSet
- min: (%, %) -> %
from OrderedSet
- opposite?: (%, %) -> Boolean
from AbelianMonoid
- sample: %
from AbelianMonoid
- smaller?: (%, %) -> Boolean
from Comparable
- subtractIfCan: (%, %) -> Union(%, failed)
- sup: (%, %) -> %
sup(x, y)returns the least element from which bothxandycan be subtracted.
- zero?: % -> Boolean
from AbelianMonoid