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

From: Martin Rubey
Subject: [Axiom-developer] Re: pfaffian.input.pamphlet
Date: 28 Sep 2007 08:23:54 +0200
User-agent: Gnus/5.09 (Gnus v5.9.0) Emacs/21.4

address@hidden writes:

> Martin,
> Attached is a pamphlet file documenting Pfaffian along with regression
> test cases. I've added it to axiom and am running a regression test 
> cycle now.
> Tim

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.

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.


> ========================================================================
> \documentclass{article}
> \usepackage{amsfonts}
> \usepackage{axiom}
> \begin{document}
> \title{\$SPAD/src/input pfaffian}
> \author{Timothy Daly, Gunter Rote, Martin Rubey}
\author{Timothy Daly, G√ľnter Rote, Martin Rubey}


> \bibitem{9} ``Skew-Symmetric Determinants'', 
> The American Mathematical Monthly, vol. 61, no.2., 1954, p.116, 
> S. Parameswaran Online-Subscription

 author = {G\"{u}nter Rote},
 title = {Division-free algorithms for the determinant and the Pfaffian:
 algebraic and combinatorial approaches},
 book = {Computational Discrete Mathematics: advanced lectures},
 year = {2001},
 isbn = {3-540-42775-9},
 pages = {119--135},
 publisher = {Springer-Verlag New York, Inc.},
 address = {New York, NY, USA},
 eprint = 

> \end{thebibliography}
> \end{document}

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