OrderedAbelianGroup

catdef.spad line 911 [edit on github]

Ordered sets which are also abelian groups, such that the addition preserves the ordering.

0: %

from AbelianMonoid

*: (Integer, %) -> %

from AbelianGroup

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

+: (%, %) -> %

from AbelianSemiGroup

-: % -> %

from AbelianGroup

-: (%, %) -> %

from AbelianGroup

<=: (%, %) -> Boolean

from PartialOrder

<: (%, %) -> Boolean

from PartialOrder

=: (%, %) -> Boolean

from BasicType

>=: (%, %) -> Boolean

from PartialOrder

>: (%, %) -> Boolean

from PartialOrder

~=: (%, %) -> Boolean

from BasicType

abs: % -> %

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

negative?(x) tests whether x is strictly less than 0.

opposite?: (%, %) -> Boolean

from AbelianMonoid

positive?: % -> Boolean

positive?(x) tests whether x is strictly greater than 0.

sample: %

from AbelianMonoid

sign: % -> Integer

sign(x) is 1 if x is positive, -1 if x is negative, 0 if x equals 0.

smaller?: (%, %) -> Boolean

from Comparable

subtractIfCan: (%, %) -> Union(%, failed)

from CancellationAbelianMonoid

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

BasicType

CancellationAbelianMonoid

CoercibleTo OutputForm

Comparable

OrderedAbelianMonoid

OrderedAbelianSemiGroup

OrderedCancellationAbelianMonoid

OrderedSet

PartialOrder

SetCategory