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.
Note
This 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]