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[Axiom-developer] Re: pfaffian.input.pamphlet

From: root
Subject: [Axiom-developer] Re: pfaffian.input.pamphlet
Date: Fri, 28 Sep 2007 02:46:35 -0400

>Many thanks.  Although I'm still unsure whether it wouldn't make more sense to
>just link to wikipedia.  It looks like duplicate effort to me.

In the longer term the documentation should explain the details of the
implementation as well as the theory. I didn't do that.

In the small it is duplicate effort but this algorithm should probably
go into the matrix domain. Eventually the documentation would end up
being more specific to the whole domain. 

In general all of the algorithms in Axiom have documentation
"somewhere" but my goal is to make the documentation an integral part
of the whole system architecture.

>Another tiny issue: this algorithm makes sense only for domains where there is
>no division or division is "slow", i.e., quotient fields.  For floats or prime
>fields there are much faster algorithms.

> It's just the same as with the determinant.  
> But I do not have the time to sort these things out.

If it lived in the algebra it would be reasonably straightforward to
have other pfaffian algorithms override this one for the specific domains
(e.g floats). Structurally that's exactly where Axiom wins.

I thought about putting it directly into Matrix but I'm busy with a
major rewrite of hyperdoc and wanted to capture it while I had the

And, as a bonus, I tripped across a bug and a puzzling limitation.

Thanks for sharing the algorithm.


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