Enumeration of Totally Real Fields: PHC interface¶
AUTHORS:
 – John Voight (20071010):
 Zeroth attempt.

sage.rings.number_field.totallyreal_phc.
coefficients_to_power_sums
(n, m, a)¶ Takes the list a, representing a list of initial coefficients of a (monic) polynomial of degree n, and returns the power sums of the roots of f up to (m1)th powers.
INPUT:
 n – integer, the degree
 a – list of integers, the coefficients
OUTPUT:
list of integers.
NOTES:
Uses Newton’s relations, which are classical.
AUTHORS:
 John Voight (20070919)
EXAMPLES:
sage: from sage.rings.number_field.totallyreal_phc import coefficients_to_power_sums sage: coefficients_to_power_sums(3,2,[1,5,7]) [3, 7, 39] sage: coefficients_to_power_sums(5,4,[1,5,7,9,8]) [5, 8, 46, 317, 2158]