By M. Pohst

ISBN-10: 0521330602

ISBN-13: 9780521330602

This vintage booklet provides an intensive advent to positive algebraic quantity concept, and is consequently particularly applicable as a textbook for a path on that topic. It additionally offers a accomplished examine contemporary examine. For experimental quantity theoreticians, the authors built new equipment and acquired new result of nice value for them. either machine scientists drawn to better mathematics and people educating algebraic quantity thought will locate the booklet of price.

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**Extra resources for Algorithmic Algebraic Number Theory (Encyclopedia of Mathematics and its Applications)**

**Example text**

Fourier Analysis on Finite Groups and Applications, London Mathematical Society Student Texts 4 (Cambridge University Press, Cambridge). T ONTI , E. (1976). Sulla struttura formale delle teorie fisiche. Rend. Sem. Mat. Fis. Milano 46, 163–257 (in Italian). ´ , H. (1992). Perspectives on information-based complexity. Bull. Amer. Math. , W O ZNIAKOWSKI Soc. 26, 29–52. T ROTTER , H. (1984). Eigenvalue distributions of large Hermitian matrices; Wigner’s semi-circle law and a theorem of Kac, Murdock and Szeg˝o.

Lie group symmetries. These are deeper symmetries than those described above, often involving the invariance of the system to a (nonlinear) Lie group of transformations. An important example (which arises naturally in mechanics) is the invariance of a system to the action of the rotation group SO(3). An excellent discussion of such symmetries is given in O LVER [1986]. The review article (I SERLES , M UNTHE -K AAS , N ØRSETT and Z ANNA [2000]) describes the numerical approach to computing solutions of ordinary differential equations with such symmetries.

By D. Luke). , S CHOENBERG , I. (1941). Fourier integrals and metric geometry. Trans. Amer. Math. Soc. 50, 226–251. , G ERHARD , J. (1999). Modern Computer Algebra (Cambridge University Press, New York). WATSON , G. (1998). Choice of norms for data fitting and function approximation. Acta Numerica 7, 337–377. W ERSCHULZ , A. (1991). The Computational Complexity of Differential and Integral Equations. An Information-Based Approach (Oxford University Press, New York). W ILKINSON , J. (1960). Error analysis of floating-point computation.

### Algorithmic Algebraic Number Theory (Encyclopedia of Mathematics and its Applications) by M. Pohst

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