Re: [Axiom-mail] positive definite matrix predicate
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 ? ___ Axiom-mail mailing list Axiom-mail@nongnu.org http://lists.nongnu.org/mailman/listinfo/axiom-mail
Re: [Axiom-mail] positive definite matrix predicate
Konstantin L. Metlov wrote: 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... I don't think it is impossible to represent in the algebra. The usual way to restrict a result is to define a retractIfCan or coerceIfCan function that will attempt to return a restricted result. If the retraction (of type Union(restrictedtype,failed)) returns failed then the wider result is used. With the best regards, Konstantin. p.s. Is this feature (subdomains) going to be removed ? No. Subdomains will continue to exist. ___ Axiom-mail mailing list Axiom-mail@nongnu.org http://lists.nongnu.org/mailman/listinfo/axiom-mail ___ Axiom-mail mailing list Axiom-mail@nongnu.org http://lists.nongnu.org/mailman/listinfo/axiom-mail
Re: [Axiom-mail] positive definite matrix predicate
Konstantin Hello ! I have a lot of questions :-) Trying to implement a certain special function in Axiom (Epstein zeta, to be precise), which depends on a positive definite matrix argument. How do I properly implement the test that the matrix is positive definite? I do not see this test anywhere. The only mention of the subject seems to be in MHROWRED ModulareHermitianRowReduction but I do not see a test for this condition. Did I overlook a standard predicate, which tests for this ? I do not think you overlooked anything. Should I perform the test in my function (which, since such a test seems to be quite basis, may potentially lead to duplication of code in future) and potentially fail ? Write your own test but give some thought to making it general. If I add such predicate to MatrixCategory (which looks like a proper place for such a basic thing), what are the conditions for the patch to be accepted ? I'm not sure if this should be defined at the category level. That complicates the problem because now you have to figure out all of the places where matrix category is used and check that your category-level function is valid (e.g. over complex domains?). You could look at MATLIN MatrixLinearAlgebraFunctions and add it there at the level of generality you need. Does your code work over IntegralDomains? EuclideanDomains? Fields?, etc. There are no conditions for a patch to be accepted but I need to be fairly confident that the patch doesn't break anything, and that the patch works as users expect. This is helped along by having lots of simple test cases sent along with the patch. Even better is a set of explanations of the function (which I'd otherwise have to create that documentation which takes time for me to learn). Tim ___ Axiom-mail mailing list Axiom-mail@nongnu.org http://lists.nongnu.org/mailman/listinfo/axiom-mail
