# Enumeration of Totally Real Fields: PHC interface¶

AUTHORS:

– John Voight (2007-10-10):
• 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 (m-1)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 (2007-09-19)

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]