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height of an algebraic number
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(Definition)
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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:
Then the height  of the algebraic number is given by:
This is a quantity which is used in the proof of the existence of transcendental numbers.
- 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.
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"height of an algebraic number" is owned by kidburla2003.
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Cross-references: proof of the existence of transcendental numbers, relatively prime, root, degree, polynomial, algebraic number
There are 13 references to this entry.
This is version 14 of height of an algebraic number, born on 2003-01-31, modified 2004-04-12.
Object id is 3954, canonical name is HeightOfAnAlgebraicNumber2.
Accessed 3765 times total.
Classification:
| AMS MSC: | 03E10 (Mathematical logic and foundations :: Set theory :: Ordinal and cardinal numbers) |
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Pending Errata and Addenda
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