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> Given the recent discussion of mathematics on this list, I

> thought you might find the following paper interesting:

__>
http://www.chess3d.com/desum.htm
__> It tries to answer the question
"Given a polynomial of one

> variable to whatever degree, is it possible to find the

> polynomial that when summed equals the polynomial given?"

Actually, what the author calls the Desummation operator

(and signifies with a backwards summation sign) is already

known in mathematics as the difference operator, and is

symbolized by a capital delta. So, for example, Delta(x^2)

equals 2x-1. The author of the web page explains this

very well, and gives good examples.

I'm sure that Newton and Wallis knew how to calculate the

difference of a polynomial the very first time that they

seriously thought about it, and I once saw credit being

given to someone in 1711 for one of the nicest theorems,

namely how you can do the reverse operation (e.g., a

mechanical way to go from 2x+1 to x^2 + C for any polynomial.

But vast amounts about all this were known by 1851 when Boole

wrote "The Calculus of Finite Differences". A wonderful

modern reference, though probably not containing everything

in Boole's book, is Knuth's "Concrete Mathematics".

Lee Corbin

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