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

This e-book comprises 22 lectures awarded on the ultimate convention of the German study software "Algorithmic quantity concept and Algebra 1991-1997", subsidized via the Deutsche Forschungsgemeinschaft. the aim of this learn application and the assembly used to be to compile builders of machine algebra software program and researchers utilizing computational tips on how to achieve perception into experimental difficulties and theoretical questions in algebra and quantity concept. The publication offers an summary on algorithmic tools and effects acquired in this interval frequently in algebraic quantity thought, commutative algebra and algebraic geometry, and crew and illustration conception. a few of the articles illustrate the present kingdom of the pc algebra platforms built with aid from the examine software, for instance KANT and LiDIA for algebraic quantity idea, SINGULAR, REDLOG and INVAR for commutative algebra and invariant idea respectively, and hole, SYSYPHOS and CHEVIE for crew and illustration theory.

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Mathematische Zeitschrijt, 227:337-366, 1998. 24. 1. Kiming and X. Wang. Examples of 2-dimensional odd Galois repesentations of As-type over Q satisfying the Artin conjecture. In G. Frey, editor, On Arlin's Conjecture for Odd 2-dimensional Representations, volume 1585 of Lecture Notes in Mathematics, pages 109-121, Berlin, Heidelberg, 1994. Springer-Verlag. 25. S. Lang. Survey of Diophantine Geometry. Springer-Verlag, Berlin, Heidelberg, 1997. 26. Q. Liu. Modeles minimaux des courbes de genre deux.

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37. David Mumford. Abelian Varieties. Oxford University Press, Oxford, 2 edition, 1974. 38. David Mumford. Curves and Their Jacobians. University of Michigan Press, Ann Arbor, 1975. 39. D. Mumford. Tata lectures on Theta I-III. Birkhauser Verlag, Ziirich, 1983. 40. A. Ogg. On the Weierstrass Points of Xo(N). Illinois J. Math. ,22(1):31-35, 1978. 41. C. Poor. On the hyperelliptic locus. Duke Math. J. , 76(3):809-884, 1994. 42. K. Ribet. On mod p Heeke operators and congruences between modular forms.

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