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Published in:
1993 | OriginalPaper | Chapter
Lattice Techniques
Author : Richard Zippel
Published in: Effective Polynomial Computation
Publisher: Springer US
Included in: Professional Book Archive
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Thus far we have considered diophantine approximation problems where we are trying to find good approximations to a single irrational number α.This can be expressed as determining integers p and q that minimize $$ \left| {q\alpha - p} \right|$$. Continued fraction techniques can be used to efficiently determine integers p and q satisfying 4.1$$ \left| {q\alpha - p} \right| \leqslant \frac{1}{q}.$$ This is a rewritten form of Proposition 5.