AbelianProductCategory(A)

indexedp.spad line 1 [edit on github]

• A : Type

This category represents products with coordinatewise additive operations.

* : (Integer, %) -> % if A has AbelianGroup

from AbelianGroup

* : (NonNegativeInteger, %) -> % if A has AbelianMonoid

from AbelianMonoid

* : (PositiveInteger, %) -> % if A has AbelianMonoid

from AbelianSemiGroup

+ : (%, %) -> % if A has AbelianMonoid

from AbelianSemiGroup

- : % -> % if A has AbelianGroup

from AbelianGroup

- : (%, %) -> % if A has AbelianGroup

from AbelianGroup

0 : () -> % if A has AbelianMonoid

from AbelianMonoid

= : (%, %) -> Boolean if A has AbelianMonoid

from BasicType

coerce : % -> OutputForm if A has AbelianMonoid

from CoercibleTo(OutputForm)

latex : % -> String if A has AbelianMonoid

from SetCategory

opposite? : (%, %) -> Boolean if A has AbelianMonoid

from AbelianMonoid

sample : () -> % if A has AbelianMonoid

from AbelianMonoid

subtractIfCan : (%, %) -> Union(%, "failed") if A has CancellationAbelianMonoid

from CancellationAbelianMonoid

zero? : % -> Boolean if A has AbelianMonoid

from AbelianMonoid

~= : (%, %) -> Boolean if A has AbelianMonoid

from BasicType

CoercibleTo(OutputForm)

AbelianMonoid

AbelianSemiGroup

BasicType

SetCategory

CancellationAbelianMonoid

AbelianGroup