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[Axiom-developer] lattice

From: daly
Subject: [Axiom-developer] lattice
Date: Fri, 5 Sep 2014 01:22:35 -0500



The orange text are books or papers which I've already scanned for
references. An underlined text points to an online source for the
document (not hosted by me). There are roughly 800 references so
far. I re-worked the page so it is automatically generated from a
bibtex-like format, letting mouse-over show the citation.

The idea is to form the closure of the references, so to speak.
Some sources have most of their references already on the page.
Others have an almost disjoint set. In fact, it seems that there
are two distinct clades, one European and one American. A few
researchers, like Davenport, seem to cover both.

Since the goal of the effort is to collect algorithms I am reviewing
books and papers that contain algorithms. I'm also implementing at
least some of them in Spad in an as-yet unpublished Volume 14. One
glitch I've found is algebraic. For instance, I have a Maple 
algorithm over the Integers that uses division, making it more
of a challenge to implement in Axiom since Integer does not support
division. Another algorithm (coset enumeration, Sims) doesn't seem
to fit easily anywhere.

Another struggle along the way is to get some sense of the history of
an algorithm, e.g. Ritt -> Risch -> Rothstein -> Trager -> Bronstein ...
with a lot of side complications about Norman, Davenport, Moses, ... 

There needs to be an ordering by area, by algorithm, and by
improvements (with citations) as well as by researcher. And since
this is algebra, ordered by domain (Ring, Commutative Ring, Integral
domain, Unique Factorization domain, Euclidean domain, Field) and
finite variations, etc. I am unsure what is a reasonable taxonomy.

I see more web pages and more struggles about how to display
these relationships.

This has the character of a jigsaw puzzle with multiple solutions.

Where is Knuth when we need him?


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