LeftModule RΒΆ

catdef.spad line 807

The category of left modules over an rng (ring not necessarily with unit). This is an abelian group which supports left multiplication by elements of the rng.

0: % if R has AbelianMonoid
from AbelianMonoid
*: (Integer, %) -> % if R has AbelianGroup
from AbelianGroup
*: (NonNegativeInteger, %) -> % if R has AbelianMonoid
from AbelianMonoid
*: (PositiveInteger, %) -> %
from AbelianSemiGroup
*: (R, %) -> %
r*x returns the left multiplication of the module element x by the ring element r.
+: (%, %) -> %
from AbelianSemiGroup
-: % -> % if R has AbelianGroup
from AbelianGroup
-: (%, %) -> % if R has AbelianGroup
from AbelianGroup
=: (%, %) -> 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 if R has AbelianMonoid
from AbelianMonoid
sample: % if R has AbelianMonoid
from AbelianMonoid
subtractIfCan: (%, %) -> Union(%, failed) if R has AbelianGroup
from CancellationAbelianMonoid
zero?: % -> Boolean if R has AbelianMonoid
from AbelianMonoid

AbelianGroup if R has AbelianGroup

AbelianMonoid if R has AbelianMonoid

AbelianSemiGroup

BasicType

CancellationAbelianMonoid if R has AbelianGroup

CoercibleTo OutputForm

SetCategory