Re: [Axiom-mail] positive definite matrix predicate

[Konstantin L. Metlov]

> Definitely avoid subdomains. They require support from the interpreter.
> There are only 2 subdomains that have been properly implemented in Axiom,
> PositiveInteger and NonNegativeInteger and both required a lot of effort.
Even if what I really want is just check the predicate ?

From what I've read in "The AXIOM System" J.H. Davenport it seemed like the 
right feature to use for this... Yes, I understand that only the interpreter 
would automatically identify the matrix in its output as, let's say, 
Hermitean. In the SPAD code I'd write that my function requires a Hermitian 
matrix and will have to make an explicit coercion (which would check the 
predicate and ensure it is a Hermitian indeed or signal an error that it is 
not). For all the other purposes Hermitean matrix would be just a 
SquareMatrix.

I was thinking about defining a domain, but the problem, which turned this 
idea down, that this domain would not be closed. Yes, the sum of Hermitian 
(and positive definite) matrices is Hermitian (positive definite) too, but 
their product is only Hermitian if they commute. This seemed (on my current, 
almost non-existant, level of knowledge of Axiom) to be hard to capture by a 
type system... at least by a static one. The type of the result of the 
multiplication would depend on whether two particular matrices commute.

May be it is impossible to represent in Axiom ? Which would explain why it 
does not have these basic notions built into its matrix algebra...

With the best regards,
                         Konstantin.

p.s. Is this feature (subdomains) going to be removed ?