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Old 2021-05-31, 03:09   #8
VBCurtis's Avatar
Feb 2005
Riverside, CA

52·7·29 Posts

Originally Posted by charybdis View Post
This isn't true: the skew compensates for c5 being much larger than c0, so we'd rather multiply c5 by 4 than multiply c0 by 8 even if c5 is huge. The algebraic norm for the polynomials we're considering is c5*a^5 + c0*b^5; the choice of skew ensures that the two terms are roughly the same size, so each coefficient has a similar contribution to the norms and multiplying one by 8 will be worse than multiplying the other by 4.
If you calculate some E-scores you'll see that they bear this out.
I tried this: I tried OP's 1281979*2^n+1, with n = 647. Multiplying by 8 to make a poly ending in +8 and Y0 = 2^130 had score 6.444e-12, while factoring out a 4 and making a poly ending in +1 with Y0 2^129 had score 7.02e-12.

10% is not a small difference. Thanks for the teaching moment!
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