Thread: 7- table
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Old 2008-07-25, 11:16   #38
R.D. Silverman
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"Bob Silverman"
Nov 2003
North of Boston

52·13·23 Posts

Originally Posted by fivemack View Post
Hi Raman.

The calculation of M should be modulo the number you're trying to factor - ie 10^25 N = (10^50+1) mod cofactor. But as xilman pointed out you just fill in the numerator and denominator in the Y0 and Y1 fields.

The idea of substituting y+1/y is to take advantage of the symmetry of the octic; you write {octic} = x^4 * quartic(x+1/x) for some suitably-chosen quartic, and the 10^50+1 and 10^25 are from (x + 1/x) written as (x^2+1)/x.
The reason this works is that *reversing* the coefficients of any polynomial
results in a homomorphism of its splitting field, sending a root r of the
polynomial to 1/r. Thus, if the coefficients of the polynomial are the same
when reversed, we can replace the polynomial with one whose roots are
r + 1/r and get an isomorphic field.
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