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 GNU Scientific Library Reference Manual - Third Edition (v1.12) by M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, P. Alken, M. Booth, F. RossiPaperback (6"x9"), 592 pages, 60 figuresISBN 0954612078RRP £24.95 ($39.95) ## 6.6 Examples To demonstrate the use of the general polynomial solver we will take the polynomial P(x) = x^5 - 1 which has the following roots, 1, e^{2\pi i /5}, e^{4\pi i /5}, e^{6\pi i /5}, e^{8\pi i /5}  The following program will find these roots. #include <stdio.h> #include <gsl/gsl_poly.h> int main (void) { int i; /* coefficients of P(x) = -1 + x^5 */ double a[6] = { -1, 0, 0, 0, 0, 1 }; double z[10]; gsl_poly_complex_workspace * w = gsl_poly_complex_workspace_alloc (6); gsl_poly_complex_solve (a, 6, w, z); gsl_poly_complex_workspace_free (w); for (i = 0; i < 5; i++) { printf ("z%d = %+.18f %+.18f\n", i, z[2*i], z[2*i+1]); } return 0; }  The output of the program is, $ ./a.out
z0 = -0.809016994374947451 +0.587785252292473137
z1 = -0.809016994374947451 -0.587785252292473137
z2 = +0.309016994374947451 +0.951056516295153642
z3 = +0.309016994374947451 -0.951056516295153642
z4 = +1.000000000000000000 +0.000000000000000000


which agrees with the analytic result, z_n = \exp(2 \pi n i/5).

 ISBN 0954612078 GNU Scientific Library Reference Manual - Third Edition (v1.12) See the print edition