Zulip Chat Archive

Stream: Is there code for X?

Topic: The "house" of an algebraic integer


Michail Karatarakis (Dec 05 2023 at 15:22):

Do we want the "house" of an algebraic integer in mathlib (if it's not there) ?

Let KK be an algebraic number field of degree h,h, and let β1,,βh\beta_1, \ldots , \beta_h be an integer basis, so that every integer in KK has the unique representation a1β1++ahβha_1\beta_1 + \ldots + a_h\beta_h where a1,,aha_1, \ldots , a_h are rational integers.

If aa is an algebraic integer with a=a1β1++ahβh,a = a_1\beta_1 + \ldots + a_h\beta_h, then the ''house'' of aa is denoted by a\overline{| a |} and is the largest modulus of its conjugates a(i)a^{(i)} of a,a, that is a=max(1ih)a(i).\overline{| a |} = max_{(1 \leq i \leq h)} | a^{(i)} |.


Last updated: Dec 20 2023 at 11:08 UTC