S000184


Coefficients of the minimal polynomial having a Salem number under 1.3 as a root, sorted.

1, 0, 0, -1, -1, -1, 0, 0, 1, 1, 1, 0, -1, -1, -1, -1, -1, 0, 1, 1, 1, 0, 0, 0, -1, -1, -1, 0, 0, 0, 1, 1, 0, 0, -1, 0, -1, 0, -1, 0, 0, 1, 1, 0, -1, 0, 0, -1, 0, 0, -1, 0, 1, 1, 0, -1, -1, 0, 1, 0, -1, -1, 0, 1, 1, -1, 1, -1, 0, 0, -1, 0, 0, -1, 1, -1, 1, 1, 0

1

S000184

These polynomials are sorted by degree and then the Salam number they produce. The degree of the n-th polynomial is given in S000183. These polynomials are symmetric.

T. D. Noe, Plot of polynomial coefficients (1095 terms)

T. D. Noe, Table of polynomial coefficients (1095 terms)

Example: the polynomials begin
1, 0, 0, -1, -1, -1, 0, 0, 1
1, 1, 0, -1, -1, -1, -1, -1, 0, 1, 1

(Mma) {let the coefficients of the i-th polynomial be in the array t[[i]]. Then the i-th Salem number is computed by} p = t[[i]]; poly = p.x^Range[0, Length[p] - 1]; NRoots[poly == 0, x, PrecisionGoal -> 15][[-1, 2]]

Cf. S000181-S000183.

sign,tabf

T. D. Noe, Aug 06 2014

© Tony D Noe 2014-2015