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markh

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[资源] 利用mathematica探索Grassmann代数

见本版冷清, 特发资源, 顺便赚金币。

本人第一次接触到Grassmann代数是在某本多图书的fermion的路径积分中。 这种代数是fermion的反对易关系的表示形式, 初看起来比较突兀, 但在某些代数运算时比普通代数更加简单, 如微分积分, e指数表达式可以得到有限形式等。微分几何的外代数实际上也是Grassmann代数, 陈维桓的《微分几何初步》里面用置换构造出一个外代数, 结果是十分繁琐复杂。 当然上述都是粗浅的一些认识。 Grassmann代数作为一个数学分支, 内容不止是微分积分这么简单。 利用现代工具探索Grassmann代数就是本资源的主要内容。 遗憾的是本书尚未完成, 估计作者碰上了不可能完成的任务, 这也侧面反映了Grassmann代数还是有很多问题尚待解决。 希望各位搞数学的虫友把它解决。

附件分三部分, 1. 教科书; 2. mathematica的程序包; 3. 程序包的使用指南.

以下是资源介绍, cf
http://sites.google.com/site/gra ... rassmannalgebrabook

Grassmann Algebra: Exploring extended vector algebra with Mathematica
引用回帖:
The primary purpose of this book is to provide a readable account in modern notation of Grassmann's major algebraic contributions to mathematics and science. I would like it to be accessible to scientists and engineers, students and professionals alike. Consequently I have tried to avoid all mathematical terminology which does not make an essential contribution to understanding the basic concepts. The only assumption I have made about the reader's background is that they have some familiarity with basic vector algebra.   

引用回帖:
The secondary purpose of this book is to provide an environment for exploring Grassmann algebra. For general applications in higher dimensional spaces, computations by hand in any algebra become tedious, indeed limiting, thus restricting the hypotheses that can be explored. For this reason, the book is accompanied by a package for exploring the algebra written in a computer algebra system (Mathematica). You can read the book without using the package, or you can use the package to extend the examples in the text, experiment with hypotheses, or explore your own interests. You will need Mathematica to run the package.

版权声明, 请各位遵守.
引用回帖:
Copyright agreement  
The book is protected by copyright. It is a condition of your downloading it that you agree to use it for your own individual private study only. Parts of the book may not otherwise be copied or distributed in any way in whole or in part without the permission of the author. You may reference or quote small sections of the work as long as due acknowledgment is made.

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