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)#
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 degreea
– 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]