Titlebook: Discovering Mathematics with Magma; Reducing the Abstrac Wieb Bosma,John Cannon Book 2006 Springer-Verlag Berlin Heidelberg 2006 Magma.Perm

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Support varieties for modules,The support variety of a module over a group algebra is an affine variety that encodes many of the homological properties of the module. Although the definition of the support variety is given in terms of the cohomology ring of the group, it can be computed directly from the actions of the elementary abelian subgroups.

AUGUR

Cohomology and group extensions in Magma,We describe the theory and implementation of some new and more flexible . functions for computing cohomology groups of finite groups, and their application to the computation of group extensions.

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Computing the primitive permutation groups of degree less than 1000,In this chapter we describe how . was used to complete the classification of the primitive groups of degree less than 1000.

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Appendix: The Magma language,The following is a brief introduction to the . language. It is not a comprehensive description of the language, nor is it a programming tutorial (although, inevitably, it has much in common with one).

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fatty-streak

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Center for China and Globalization (CCG)e 1 over finite fields. After a brief review of the handling of both function and number fields in ., we give an introduction to computational class field theory focusing on applications: We show how to construct tables of small degree extensions and how to utilize the class field theory to find cur

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Center for China and Globalization (CCG)escribed Complex Multiplication. We treat 2 fields, one easy and one harder. Secondly we show how . can be used to find, and ultimately prove existence of, rational isogenies between the Jacobians of two genus 2 curves.