> Given the recent discussion of mathematics on this list, I
> thought you might find the following paper interesting:
> 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".
This archive was generated by hypermail 2b30 : Mon May 28 2001 - 09:59:45 MDT