back to list

Graham-style recurrence polynomials, degree four

🔗Gene Ward Smith <gwsmith@svpal.org>

8/31/2003 3:14:54 PM

Here they are for degree four. I took out everything where the large
root was a power of two, but I might have well have removed all the
ones where it was an integer, since they look pretty useless.

1.220744 x^4-x-1
1.324718 x^4-x^2-x
1.353210 x^4-x-2
1.380278 x^4-x^3-1
1.395337 x^4-2*x-1
1.465571 x^4-x^3-x
1.494530 x^4-2*x-2
1.521380 x^4-x^2-2*x
1.533751 x^4-x-4
1.543689 x^4-x^3-2
1.618034 x^4-2*x^2-x
1.618034 x^4-x^3-x^2
1.642935 x^4-2*x-4
1.663252 x^4-4*x-1
1.695621 x^4-x^3-2*x
1.727754 x^4-4*x-2
1.748403 x^4-x^3-4
1.767868 x^4-x-8
1.769292 x^4-2*x^2-2*x
1.796322 x^4-x^2-4*x
1.835087 x^4-4*x-4
1.849421 x^4-2*x-8
2.040042 x^4-8*x-1
2.077216 x^4-8*x-2
2.106919 x^4-2*x^3-1
2.114908 x^4-4*x^2-x
2.144700 x^4-8*x-4
2.166313 x^4-x^2-8*x
2.190328 x^4-2*x^3-2
2.205569 x^4-2*x^3-x
2.214320 x^4-4*x^2-2*x
2.259801 x^4-8*x-8
2.320233 x^4-2*x^3-4
2.330746 x^4-2*x^2-8*x
2.359304 x^4-2*x^3-2*x
2.382976 x^4-4*x^2-4*x
2.394859 x^4-x^3-8*x
2.414214 x^4-2*x^3-x^2
2.507450 x^4-2*x^3-8
2.561553 x^4-x^3-4*x^2
2.594313 x^4-2*x^3-4*x
2.649436 x^4-4*x^2-8*x
2.732051 x^4-2*x^3-2*x^2
2.888969 x^4-8*x^2-x
2.931142 x^4-2*x^3-8*x
2.945995 x^4-8*x^2-2*x
3.000000 x^4-3*x^3
3.051374 x^4-8*x^2-4*x
3.236068 x^4-2x^3-4*x^2
3.236068 x^4-8*x^2-8*x
3.372281 x^4-x^3-8*x^2
3.414214 x^4-4*x^3+2*x^2
3.709275 x^4-4*x^3+4*x
3.732051 x^4-4*x^3+x^2
3.861009 x^4-4*x^3+8
3.866198 x^4-4*x^3+2*x
3.934317 x^4-4*x^3+4
3.935432 x^4-4*x^3+x
3.967988 x^4-4*x^3+2
3.984188 x^4-4*x^3+1
4.015445 x^4-4*x^3-1
4.030545 x^4-4*x^3-2
4.059780 x^4-4*x^3-4
4.060647 x^4-4*x^3-x
4.114825 x^4-4*x^3-8
4.117942 x^4-4*x^3-2*x
4.224170 x^4-4*x^3-4*x
4.236068 x^4-4*x^3-x^2
4.411139 x^4-4*x^3-8*x
4.449490 x^4-4*x^3-2*x^2
4.828427 x^4-4*x^3-4*x^2
5.000000 x^4-5*x^3
5.464102 x^4-4*x^3-8*x^2
6.000000 x^4-6*x^3
6.828427 x^4-8*x^3+8*x^2
7.000000 x^4-7*x^3
7.464102 x^4-8*x^3+4*x^2
7.741657 x^4-8*x^3+2*x^2
7.870865 x^4-8*x^3+8*x
7.872983 x^4-8*x^3+x^2
7.936496 x^4-8*x^3+4*x
7.968502 x^4-8*x^3+2*x
7.984283 x^4-8*x^3+8
7.984314 x^4-8*x^3+x
7.992164 x^4-8*x^3+4
7.996088 x^4-8*x^3+2
7.998045 x^4-8*x^3+1
8.001952 x^4-8*x^3-1
8.003901 x^4-8*x^3-2
8.007790 x^4-8*x^3-4
8.015534 x^4-8*x^3-8
8.015564 x^4-8*x^3-x
8.031009 x^4-8*x^3-2*x
8.061549 x^4-8*x^3-4*x
8.121294 x^4-8*x^3-8*x
8.123106 x^4-8*x^3-x^2
8.242641 x^4-8*x^3-2*x^2
8.472136 x^4-8*x^3-4*x^2
8.898979 x^4-8*x^3-8*x^2
9.000000 x^4-9*x^3
10.000000 x^4-10*x^3
12.000000 x^4-12*x^3