question on list comprehensions
Josiah Carlson
jcarlson at uci.edu
Sun Oct 17 20:42:19 EDT 2004
> Yes, as with integrals, the sum of an nth degree poly is (n+1)th degree.
> The n+2 coefficients for the sum from 0 to k can be determined by actually
> summing the poly for each of 0 to n+1 and equating the n+2 partial sume to
> the result poly (with powers evaluated) to get n+2 equations in n+2
> unknowns. Even with integral coefficients in the poly to be summed, the
> coefficients are generally non-integral rationals and can get pretty nasty
> to calculate, so for exact results, it may well be easier and faster to
> write and run a program.
As long as you can solve a k+1 degree polynomial with linear algebra
(via gaussian elimination, etc.), you can find:
sum([i**k for i in xrange(1, n+1)])
... with little issue (if you know the trick).
- Josiah
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