AbelianGroupΒΆ

catdef.spad line 1

The class of abelian groups, i.e. additive monoids where each element has an additive inverse.

0: %
from AbelianMonoid
*: (Integer, %) -> %
n*x is the product of x by the integer n.
*: (NonNegativeInteger, %) -> %
from AbelianMonoid
*: (PositiveInteger, %) -> %
from AbelianSemiGroup
+: (%, %) -> %
from AbelianSemiGroup
-: % -> %
-x is the additive inverse of x.
-: (%, %) -> %
x-y is the difference of x and y i.e. x + (-y).
=: (%, %) -> Boolean
from BasicType
~=: (%, %) -> Boolean
from BasicType
coerce: % -> OutputForm
from CoercibleTo OutputForm
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
latex: % -> String
from SetCategory
opposite?: (%, %) -> Boolean
from AbelianMonoid
sample: %
from AbelianMonoid
subtractIfCan: (%, %) -> Union(%, failed)
from CancellationAbelianMonoid
zero?: % -> Boolean
from AbelianMonoid

AbelianMonoid

AbelianSemiGroup

BasicType

CancellationAbelianMonoid

CoercibleTo OutputForm

SetCategory