OrderedAbelianMonoidSupΒΆ

catdef.spad line 935

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 BasicType
>: (%, %) -> Boolean
from PartialOrder
>=: (%, %) -> Boolean
from PartialOrder
~=: (%, %) -> Boolean
from BasicType
coerce: % -> OutputForm
from CoercibleTo OutputForm
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
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

AbelianMonoid

AbelianSemiGroup

BasicType

CancellationAbelianMonoid

CoercibleTo OutputForm

Comparable

OrderedAbelianMonoid

OrderedAbelianSemiGroup

OrderedCancellationAbelianMonoid

OrderedSet

PartialOrder

SetCategory