height of an algebraic number
Suppose we have an algebraic number^{} such that the polynomial^{} of smallest degree it is a root of (with the co-efficients relatively prime) is given by:
$$\sum _{i=0}^{n}{a}_{i}{x}^{i}.$$ |
Then the height $h$ of the algebraic number is given by:
$$h=n+\sum _{i=0}^{n}|{a}_{i}|.$$ |
This is a quantity which is used in the proof of the existence of transcendental numbers^{}.
References
- 1 Shaw, R. Mathematics Society Notes, 1st edition. King’s School Chester, 2003.
- 2 Stewart, I. Galois Theory^{}, 3rd edition. Chapman and Hall, 2003.
- 3 Baker, A. Transcendental Number Theory, 1st edition. Cambridge University Press, 1975.
Title | height of an algebraic number |
---|---|
Canonical name | HeightOfAnAlgebraicNumber |
Date of creation | 2013-03-22 13:24:34 |
Last modified on | 2013-03-22 13:24:34 |
Owner | kidburla2003 (1480) |
Last modified by | kidburla2003 (1480) |
Numerical id | 17 |
Author | kidburla2003 (1480) |
Entry type | Definition |
Classification | msc 03E10 |
Synonym | height |
Related topic | AlgebraicNumbersAreCountable |