David Joyner wrote:
>
> One example I've been trying to illustrate in my undergraduate
> algebra class is the following:
>
> (a) the coefficients of X^i in the power series expansion
> of 1/(1 + X^3 + X^4) (mod 2), [...]
>
> GAP does all these, but (a) is the hardest. [...] It is
> so slow that it is almost impractical for classroom use [...]

This series may be quickly computed using the Newton iteration
for inversion of a power series. Here it nicely specializes to

f  (X)  =  1
 0 

f  (X)  =  f (X^2) (1 + X^3 + X^4)   mod  X^2^(n+1)
 n+1        n

which may be quickly computed via additions and shifts.

What is the source of this problem?

-Bill Dubuque

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