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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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书目名称Discovering Mathematics with Magma
副标题Reducing the Abstrac
编辑Wieb Bosma,John Cannon
视频videohttp://file.papertrans.cn/282/281024/281024.mp4
概述First book on the well-known MAGMA symbolic computation system
丛书名称Algorithms and Computation in Mathematics
图书封面Titlebook: Discovering Mathematics with Magma; Reducing the Abstrac Wieb Bosma,John Cannon Book 2006 Springer-Verlag Berlin Heidelberg 2006 Magma.Perm
描述The appearance of this volume celebrates the ?rst decade of Magma, a new computeralgebrasystemlaunchedattheFirstMagmaConferenceonCom- tational Algebra held at Queen Mary and West?eld College, London, August 1993. This book introduces the reader to the role Magma plays in advanced mathematical research. Each paper examines how the computer can be used to gain insight into either a single problem or a small group of closely related problems. The intention is to present su?cient detail so that a reader can (a), gain insight into the mathematical questions that are the origin of the problems,and(b),developanunderstandingastohowsuchcomputations are speci?edinMagma.Itishopedthatthereaderwillcometoarealisationofthe important rolethatcomputational algebracanplayinmathematical research. Readers not primarily interested in using Magma will easily acquire the skills needed to undertake basic programming in Magma, while experienced Magma users can learn both mathematics and advanced computational methods in areas related to their own. The core of the volume comprises 14 papers. The authors were invited to submit articles on designated topics and these articles were then reviewed by referees. A
出版日期Book 2006
关键词Magma; Permutation; Signatur; algebra; algorithms; code; computer; computer algebra; computer algebra system
版次1
doihttps://doi.org/10.1007/978-3-540-37634-7
isbn_softcover978-3-642-07231-4
isbn_ebook978-3-540-37634-7Series ISSN 1431-1550
issn_series 1431-1550
copyrightSpringer-Verlag Berlin Heidelberg 2006
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Computing with the analytic Jacobian of a genus 2 curve,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.
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Graded rings and special K3 surfaces,as an application, construct 27 families of K3 surfaces that appear as degenerate cases of surfaces in the usual lists. These are displayed in Tables 1–3 and include both standard degenerations and new examples.
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Computer aided discovery of a fast algorithm for testing conjugacy in braid groups,id group. These investigations ultimately lead to the discovery of a new invariant of conjugacy classes in braid groups, to an efficient way of computing this invariant, and in particular to a much more powerful conjugacy test than the one which was originally to be implemented [11].
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Studying the Birch and Swinnerton-Dyer conjecture for modular abelian varieties using Magma,ssume the reader has proficiency working with elliptic curves, abelian varieties, modular forms, or modular symbols. The computations give evidence for the Birch and Swinnerton- Dyer conjecture and increase our explicit understanding of modular abelian varieties.
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