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KIAM Preprint  78, Moscow, 2011
Authors: Parusnikov V. I.
4-dimensional generalization of the continued fractions
Abstract:
Let Li(X), i=1,2, L1≠ L‾2, be two complex linear forms in R4, and Ki(X)=Li(X)L‾i(X) are positive quadratic forms. The root sets Li of forms Ki are two-dimensional planes in R4. Assume that L1L2=0 and that there are no integer points except 0 which lie at Li. We propose an algorithm of computation of integer points that give the best approximations to the sets of roots Li. If coefficients of forms Li lie in totally complex quaternary conjugated number fields ki, our algorithm often finds unities of ki. The algorithm was tested on the set of quaternary number fields specified by equations with small coefficients. The algorithm was successful more often than the best of known algorithms in totally real quaternary case - the Güting algorithm.
Publication language: russian,  pages: 16
Research direction:
Mathematical problems and theory of numerical methods
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About authors:
  • Parusnikov V. I.,  KIAM RAS