ASKSAGE: Sage Q&A Forum - Individual question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Mon, 24 Dec 2018 10:29:23 -0600Computing heights of large degree algebraic numbershttp://ask.sagemath.org/question/44772/computing-heights-of-large-degree-algebraic-numbers/I have an irreducible polynomial of large degree (I would like to go up to degree ~1000), and I would like to compute the height of its roots. Currently I am doing this:
def irreducible_root_height(f):
K.<y> = NumberField(f)
h = y.global_height()
return h
This is rather slow because I have to construct the number field. Is there a way to find the height without constructing the number field?
I tried to use the functionality with general algebraic numbers, but there doesn't seem to be a way to define an arbitrary root of a polynomial in QQbar. It also looks like computing the height of something in QQbar works by computing a number field, so this wouldn't be any faster.Mon, 24 Dec 2018 10:29:23 -0600http://ask.sagemath.org/question/44772/computing-heights-of-large-degree-algebraic-numbers/