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Re: [Axiom-developer] Bernoulli puzzle

From: daly
Subject: Re: [Axiom-developer] Bernoulli puzzle
Date: Mon, 20 Oct 2014 17:20:36 -0500


>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.


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