BiModule(R, S)

catdef.spad line 149 [edit on github]

• R : SemiRng
• S : SemiRng

A BiModule is both a left and right module with respect to potentially different rings.

* : (%, S) -> %

from RightModule(S)

* : (R, %) -> %

from LeftModule(R)

* : (Integer, %) -> % if S has AbelianGroup or R has AbelianGroup

from AbelianGroup

* : (NonNegativeInteger, %) -> % if S has AbelianMonoid or R has AbelianMonoid

from AbelianMonoid

* : (PositiveInteger, %) -> %

from AbelianSemiGroup

+ : (%, %) -> %

from AbelianSemiGroup

- : % -> % if S has AbelianGroup or R has AbelianGroup

from AbelianGroup

- : (%, %) -> % if S has AbelianGroup or R has AbelianGroup

from AbelianGroup

0 : () -> % if S has AbelianMonoid or R has AbelianMonoid

from AbelianMonoid

= : (%, %) -> Boolean

from BasicType

coerce : % -> OutputForm

from CoercibleTo(OutputForm)

latex : % -> String

from SetCategory

opposite? : (%, %) -> Boolean if S has AbelianMonoid or R has AbelianMonoid

from AbelianMonoid

sample : () -> % if S has AbelianMonoid or R has AbelianMonoid

from AbelianMonoid

subtractIfCan : (%, %) -> Union(%, "failed") if S has AbelianGroup or R has AbelianGroup

from CancellationAbelianMonoid

zero? : % -> Boolean if S has AbelianMonoid or R has AbelianMonoid

from AbelianMonoid

~= : (%, %) -> Boolean

from BasicType

CancellationAbelianMonoid

SetCategory

CoercibleTo(OutputForm)

AbelianMonoid

AbelianSemiGroup

LeftModule(R)

BasicType

RightModule(S)

AbelianGroup