Inclusion of matrix normal forms code into CoqEAL about coqeal HOT 10 CLOSED

I'm sympathetic to (all?) results eventually ending up in MathComp proper, but I think we are talking a different time scale than just moving the matrix code to CoqEAL. For example, I don't think we want MathComp to depend on or include Paramcoq? In my mind, the best location for Paramcoq would actually be Coq itself.

It would be nice to see some documented "MathComp inclusion process" to get a sense of what kind of quality and reusability is needed before opening MathComp PRs. I think it has been said before that finmap is the closest in quality to MathComp itself, yet it is planned to live on for quite a while separately, right?

@proux01 I think this should be a straightforward transfer, I will open a CoqEAL PR adding files to theory and we can take it from there.

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no one got time yet to look at it on the mathcomp side math-comp/math-comp#756 ;-) ).

now I did...

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I agree with including this development in CoqEAL.

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The theory part doesn't depend on paramcoq, only the refinement part that should remain in CoqEAL anyway IMHO.

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That also sounds a good idea to me.
@palmskog let me know if you need any help with the inclusion.

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Actually, I believe all of this should eventually land inside mathcomp, (including coqeal-theory)

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Indeed, a large part of coqeal-theory looks like an antichamber of mathcomp.
But that requires some work (I once attempted to move just some results in ssrcomplement.v but no one got time yet to look at it on the mathcomp side math-comp/math-comp#756 ;-) ).

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For example, I don't think we want MathComp to depend on or include Paramcoq? In my mind, the best location for Paramcoq would actually be Coq itself.

That's why I was talking about coqeal-theory, which has no dependency on paramcoq.

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I agree with @proux01 and this extends to the part on matrix canonical forms.

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I think we are talking a different time scale than just moving the matrix code to CoqEAL

Yes, of course, my comment was in no way trying to delay that.

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