Quote:
Originally Posted by kubus
Here are my calculations.
We can represent 2,1378M as y^{13}+xy^{6}+1,
where y=2^{53} and x=2^{27}.
2,26L is yx+1.
Now dividing y^{13}+xy^{6}+1 by yx+1 and taking advantage of an equality x^{2}=2y we get
A(y)+xB(y), where
A(y)=y^{12}+y^{11}y^{10}y^{9}+y^{8}+y^{7}y^{6}+y^{5}+y^{4}y^{3}y^{2}+y+1
B(y)=y^{11}y^{9}+y^{7}+y^{4}y^{2}+1
A(y) and B(y) are symmetrical so we reduce the coeffs by representing poly with root z=2^{27}+2^{26}. We get 12th degree polynomial and in fact this is trilliwig's formula %9.
wblipp, I don't understand how to "pull out" 2,2M, too.
kubus

Yes, I was looking for formula %9. I was hoping that it might be
symmetric. It is not, but I thought that if it isn't, it might have a
representation as a sextic not in (z+1/z), but rather [with Z = 2^53]
in (z + 2/z). It seems that it does, but the constant is much too large.
Perhaps we might try a sextic in (z + k/z) for some other value of k?