OrderedAbelianSemiGroup

catdef.spad line 927 [edit on github]

Ordered sets which are also abelian semigroups, such that the addition preserves the ordering. :code:` x < y => x+z < y+z`

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

+: (%, %) -> %

from AbelianSemiGroup

<=: (%, %) -> Boolean

from PartialOrder

<: (%, %) -> Boolean

from PartialOrder

=: (%, %) -> Boolean

from BasicType

>=: (%, %) -> Boolean

from PartialOrder

>: (%, %) -> Boolean

from PartialOrder

~=: (%, %) -> Boolean

from BasicType

abs: % -> % if % has AbelianGroup

abs(x) returns the absolute value of x.

coerce: % -> OutputForm

from CoercibleTo OutputForm

latex: % -> String

from SetCategory

max: (%, %) -> %

from OrderedSet

min: (%, %) -> %

from OrderedSet

negative?: % -> Boolean if % has SetWithZero

from OrderedSet

positive?: % -> Boolean if % has SetWithZero

from OrderedSet

sign: % -> Integer if % has SetWithZero

from OrderedSet

smaller?: (%, %) -> Boolean

from Comparable

AbelianSemiGroup

BasicType

CoercibleTo OutputForm

Comparable

OrderedSet

PartialOrder

SetCategory