I think I found an answer within Axiom itself:
(1) -> sqrt(-1.0)
1) ->
>> Error detected within library code:
negative sqrt
This is, probably, what I should do. It was really a question of how to fail:
at type conversion or during the computation itself. This example shows that
in the case of Float Axiom fails during the computation. My computation will
involve floats and is similar to this example. This way to fail is simple and
makes it unnecessary to define categories. I should, probably, simply add
predicates to SquareMatrixCategory to test for hermitiannes (symmetricity, if
its real) and positive definiteness to avoid duplicate code in future.
On the other hand:
(1) -> sqrt(-1)
(1) ->
+---+
(1) \|- 1
Type: AlgebraicNumber
(2) -> sqrt(-1)::Complex(Float)
(2) ->
(2) %i
Type: Complex Float
Shouldn't it be consistent with the former ?
With the best regards,
Konstantin.
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