OrderedAbelianMonoidSup

catdef.spad line 935 [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 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