Gabriel Dos Reis <g...@cs.tamu.edu> writes:
[...]
| I am concerned with the operations defined by DirectProduct and their
| semantics. For the specific case at hand, I don't care about the
| default implementation in Algebra since DirectProduct explicitly
| overwrites it, saying that the scalar value 1 should be regarded the same
| as the vecor [1,1,1,1], for example.
|
| My contention is that many of the operations in DirectProduct have
| fishy semantics.
|
| coerce: R -> %
|
| is one of them. Another one (I hope NOT under discussion at this point) is
|
| *: (%,%) -> %
|
| which multiplies the vector componentwise!
By the way, this category membership assertion in DirectProductCategory
if R has CancellationAbelianMonoid then CancellationAbelianMonoid
is clearly wrong with the implementation of multiplication in DirectProduct.
In DirectProduct(2,INT), take
a := [1,0]
b := [0,1]
c := [0,2]
you have a * b = a * c = [0,0], but you clearly don't have b = c
Many operations in DirectProduct just have the wrong semantics.
I will start fixing that in OpenAxiom.
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