|
|
|
Viewing Version
7
of
'height of an algebraic number'
|
[ view 'height of an algebraic number'
|
back to history
]
| Title of object: |
height of an algebraic number |
| Canonical Name: |
HeightOfAnAlgebraicNumber2 |
| Type: |
Definition |
| Created on: |
2003-01-31 15:34:12.649733-05 |
| Modified on: |
2003-02-07 08:53:14.111019-05 |
| Classification: |
msc:03E10 |
| Synonyms: |
height of an algebraic number=height |
Revision comment (for changes between this and next version):
Preamble:
% this is the default PlanetMath preamble. as your knowledge
% of TeX increases, you will probably want to edit this, but
% it should be fine as is for beginners.
% almost certainly you want these
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
% used for TeXing text within eps files
%\usepackage{psfrag}
% need this for including graphics (\includegraphics)
%\usepackage{graphicx}
% for neatly defining theorems and propositions
%\usepackage{amsthm}
% making logically defined graphics
%\usepackage{xypic}
% there are many more packages, add them here as you need them
% define commands here |
Content:
Suppose we have an algebraic number such that the polynomial of smallest degree it is a root of (with the co-efficients cancelled down as much as possible) is given by:
\sum_{i=1}^n a_i x^i
Then the height $h$ of the algebraic number is given by:
h = n + \sum_{i=1}^n |a_i|
$$ |
|
|
|
|
|
