By Johannes Buchmann, Michael J. Jacobson Jr., Stefan Neis, Patrick Theobald, Damian Weber (auth.), B. Heinrich Matzat, Gert-Martin Greuel, Gerhard Hiss (eds.)

This ebook comprises 22 lectures offered on the ultimate convention of the German learn application "Algorithmic quantity thought and Algebra 1991-1997", backed by way of the Deutsche Forschungsgemeinschaft. the aim of this study application and the assembly was once to assemble builders of desktop algebra software program and researchers utilizing computational easy methods to achieve perception into experimental difficulties and theoretical questions in algebra and quantity thought. The e-book provides an outline on algorithmic equipment and effects acquired in this interval regularly in algebraic quantity thought, commutative algebra and algebraic geometry, and workforce and illustration conception. the various articles illustrate the present country of the pc algebra platforms constructed with help from the examine software, for instance KANT and LiDIA for algebraic quantity conception, SINGULAR, REDLOG and INVAR for commutative algebra and invariant thought respectively, and hole, SYSYPHOS and CHEVIE for team and illustration theory.

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**Additional info for Algorithmic Algebra and Number Theory: Selected Papers From a Conference Held at the University of Heidelberg in October 1997**

**Sample text**

4, Cor. 6). In some cases, dealt with in sect. 6, we are able to determine the torsion of the Mordell-Weil group and the possible isogenies between such curves. The results of this paper had their origin in calculations of Hecke operators in spaces of automorphic forms over function fields. These were performed in the framework of the "Schwerpunktprogramm Algorithmische Zahlentheorie und Algebra" of Deutsche Forschungsgemeinschaft (DFG), whose support is gratefully acknowledged. B. H. Matzat et al.

3 Hyperelliptic curves of genus 3 with real multiplication 41 y2 = x 8 + 4x7 _ 8x 6 _ 66x 5 - 120x4 - 56x 3 + 53x 2 + 36x - 16 ( -1) . 2 16 . 3 216 . 56 . 3 y2 = 19x. 116 - + 9202x' - 10962x 3 + 7844x 2 3040x - + 475 2X2 - X - 1 + 282x4 + 176x 3 - 123x 2 - 170x + 25 Hyperelliptic curves of genus 4 with real multiplication N 47 Curve y2 Ll. 76 . 176 = x'D + 6x 9 + 11x. _ + 24x 7 + 19x 6 + 16x 5 llx 6 - 14xs - 40x 4 - _ 13x' - 30x 3 42x 3 - - 38x 2 - 28x - 11 48x 2 - 28x - 7 References 1. J. Antoniadis, M.

Proofs of these facts are given by specifying several series of ElK which give rise to the stated conductors, and examining the possible output of Tate's algorithm. They do not give particular insight why for p = 3 some conductors are missing. Second, we consider curves ElK over the global field K = IF'q (T) of characteristic two or three which are Tate curves at the infinite place and whose finite ramification is concentrated in one rational place (without restriction, the place corresponding to T = 0).