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> < ^ Subject:

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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