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Re: [Axiom-developer] Bernoulli puzzle

From: Raymond Rogers
Subject: Re: [Axiom-developer] Bernoulli puzzle
Date: Tue, 21 Oct 2014 12:25:45 -0400
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    Yes I learned some time ago that maintenance can be devastating.  I am a little at odds
with your theory but not too much; and I will try to conform to your styles.  Along that
vein: can you point me to the current tools you recommend and examples of how you are
currently doing documentation?   They seem to have drifted a little over the years.

BTW: my ideal is "The Elements of Programming Style," by Kernighan and Plauger.
After a particularlly upsetting run in, with myself, regarding "clever" coding I found this to
be an exceptional guide.  Clarity is typically more important than cleverness or one or two
machine cycles.

"although YOU understand the code you write, nobody else does. "
Even when I was younger and clever that wasn't true after six months :):)  I guess I might
be schizoid but after six months and then looking at some "clever" math or programing I typically
have to start from scratch (really sad).


On 10/20/2014 06:20 PM, address@hidden wrote:

A little off topic; but I have developed an alternate way of dealing
with polynomial sequences like Bernoulli polynomials that are
generated by generating functions. It involves casting the sequences
in matrices and apply Pascal Matrices and Umbral calculus.  It makes
some known relations obvious and casts a different viewpoint on
others.  It might allow some kind of Polynomial sequence algebra or
some such.  It does have the advantage of automatically converting
some (actually most) sequences to others by symbolic/parametrized
methods.  If anybody is interested let me know and I will write up the
application to Bernoulli polynomials as a special case.
That would be an interesting generalization. Axiom implements several
number theory algorithms with generating functions. If they were all
just "cover calls" to a common method it would be useful.

If you were to write something like that I'm begging you to write 
a fair amount of natural language explanation. I lost a whole weekend
trying to reverse-engineer the bernoulli code so I can document it. 
Without Waldek's help I'd still be struggling. Please consider that,
although YOU understand the code you write, nobody else does. Few
people, myself included, have heard of Unbral calculus.


The primary use of conversation is to satisfy the impulse to talk
George Santanyana

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