Enumeration of totally real fields: PHC interface¶
AUTHORS:
- John Voight (2007-09-19): initial version 
- sage.rings.number_field.totallyreal_phc.coefficients_to_power_sums(n, m, a)[source]¶
- Take the list - a, representing a list of initial coefficients of a (monic) polynomial of degree \(n\), and return 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. - 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] - >>> from sage.all import * >>> from sage.rings.number_field.totallyreal_phc import coefficients_to_power_sums >>> coefficients_to_power_sums(Integer(3),Integer(2),[Integer(1),Integer(5),Integer(7)]) [3, -7, 39] >>> coefficients_to_power_sums(Integer(5),Integer(4),[Integer(1),Integer(5),Integer(7),Integer(9),Integer(8)]) [5, -8, 46, -317, 2158]