LeftModule R

catdef.spad line 811 [edit on github]

• R: SemiRng

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

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