数学

Emathema:在线的方程自动求解平台

  • 杨乐 ,
  • 柳银萍 ,
  • 李志斌
展开
  • 华东师范大学 计算机科学技术系, 上海 200062
杨乐,男,硕士研究生,研究方向为计算机符号计算及其应用.E-mail:yangle20081982@163.com

收稿日期: 2016-09-28

  网络出版日期: 2017-05-18

基金资助

国家自然科学基金(11435005)

Emathema: An online automated computing platform for equations

  • YANG Le ,
  • LIU Yin-ping ,
  • LI Zhi-bin
Expand
  • Department of Computer Science and Technology, East China Normal University, Shanghai 200062, China

Received date: 2016-09-28

  Online published: 2017-05-18

摘要

微分方程在现代科技、工程领域中的作用日益显著,本课题组多年来在微分方程可积性和解析求解方面做了很多机械化工作,研发出了一系列Maple应用软件.基于这些应用软件、计算机代数系统Maple及一些开源技术,课题组研发了一个在线的开放的方程自动求解平台Emathema,为用户提供便捷的代数计算和绘图服务.在此平台上,用户不仅可调用已嵌入的Maple外部应用软件求解非线性代数和微分方程(组),而且在交互方式下可进行几乎所有和方程相关的简单符号计算,所有的计算结果均以可视化的方式输出.

本文引用格式

杨乐 , 柳银萍 , 李志斌 . Emathema:在线的方程自动求解平台[J]. 华东师范大学学报(自然科学版), 2017 , (3) : 20 -28 . DOI: 10.3969/j.issn.1000-5641.2017.03.002

Abstract

Differential equations are playing more and more important role in modern science and technologies, engineering. On solving and integrability analysis of differential equations, our research group developed a dozen different off-line related software based on Maple. On the basis of these Maple packages, Maple and some open-source technologies, an online automated computing platform for equations called Emathema was proposed and implemented. Emathema can provide convenient and efficient online computing and graphing services for users. On this platform, users can not only solve nonlinear algebraic and differential equations using external Maple packages, but also execute almost all simple symbolic computations related to equations in the interactive mode. For each input, Emathema outputs the computing result visually.

参考文献

[1] WANG P, GRAY S, KAJLER N, et al. IAMC architecture and prototyping: A progress report [C]//Proceedings of the 2001 International Symposium on Symbolic and Algebraic Computation. ACM, 2001: 337-344.
[2] Wolfram Research Inc. webMathematica [EB/OL]. (2002-06-18)[2016-09-15]. http://www.wolfram.com/products/webmathematica/.
[3] PÉREZ F, GRANGER B E. IPython: A system for interactive scientific computing [J]. Computing in Science & Engineering, 2007, 9(3): 21-29.
[4] PAU C, SCHREINER W. Distributed Mathematica [M/OL]. (2000-07-01)[2016-09-15]. http://www.risc.jku.at/software/distmath/report/index.html.
[5] WU Y W, LIAO W D, WANG P, et al. An internet accessible grid computing system: Grid-Elimino[C]//Proceedings of IAMC. 2003: 1-8.
[6] FUJIMOTO M, SUZUKI M. AsirPad—a computer algebra system with a pen-based interface on PDA[C]//Proceedings of 7th Asian Symposium on Computer Mathematics (ASCM2005). Korea Institute for Advanced Study, 2005: 259-262.
[7] HOY M B. Wolfram | Alpha: A brief introduction [J]. Medical Reference Services Quarterly, 2010, 29(1): 67-74.
[8] MELIS E, ANDRÈS E, BÜDENBENDER J, et al. ActiveMath: A generic and adaptive web-based learning environment [J]. International Journal of Artificial Intelligence in Education (IJAIED), 2001, 12: 385-407.
[9] Maplesoft Inc.Maple TA [EB/OL]. (2003-04-03)[2016-09-10]. http://www.maplesoft.com.cn/products/mapleta/.
[10] AL-SHOMRANI S,WANG P. DMAS: A web-based distributed mathematics assessment system [C]//Proceedings of the International Conference on Learning. 2008: 3-6.
[11] YANG L, SU W, WANG K J, et al. iMathema: A novel online intelligent computing system oriented to common scientific computations[C]//Proceedings of the Second International Conference on Innovative Computing and Cloud Computing. ACM, 2013: 10-16.
[12] POLYANIN A D. EqWorld (The World of Mathematical Equations) [EB/OL]. (2004-04-12)[2016-09-01]. http://eqworld.ipmnet.ru.
[13] Equation Sheet.com [EB/OL]. (2007-04-23)[2016-09-10]. http://equationsheet.com/sheets/Equations-13.html.
[14] Oxford Centre for Nonlinear Partial Differential Equations. OxPDE [EB/OL]. (2007-05-10)[2016-09-03]. http://www.maths.ox.ac.uk/groups/oxpde.
[15] 华东师范大学偏微分方程中心 [EB/OL]. (2010-09-05)[2016-09-01]. http://www.cpde.ecnu.edu.cn/.
[16] The PHP Group. PHP: Hypertext preprocessor [EB/OL]. (2001-05-13)[2016-09-01]. http://php.net.
[17] W3C Recommendation. Mathematical Markup Language (MathML) version 3 [EB/OL]. (2010-10-20)[2016-09-01]. http://www.w3.org/TR/MathML3/.
[18] GRAY J. ASCIIMathML: Now everyone can type MathML [J]. MSOR Connections, 2007, 7(3): 26-30.
[19] CERVONE D. MathJax: A platform for mathematics on the Web [J]. Notices of the AMS, 2012, 59(2): 312-316.
[20] ASLESON R, SCHUTTA N T. Foundations of Ajax [M]. Berkeley: Apress Press. 2005.
[21] jQuery main website. jQuery: The write less, do more, Javascript library [EB/OL]. (2009-05-10)[2016-09-02]. http://jquery.com/.
[22] LI Z B, LIU Y P. RATH: A Maple package for finding travelling solitary wave solutions to nonlinear evolution equations [J]. Computer Physics Communications, 2002, 148(2): 256-266.
[23] LI Z B, LIU Y P. RAEEM: A Maple package for finding a series of exact traveling wave solutions for nonlinear evolution equation [J]. Computer Physics Communications, 2004, 163(3): 191-201.
[24] LI Z B, LIU Y P, QIAN H F. A method and its implementation for constructing Bäcklund transformations to nonlinear evolution equations [J]. Computer Mathematics, 2008: 188-198.
[25] LIN Y Z, LI Z B, LIU Y P. Symbolic computation of analytic approximate solutions for nonlinear fractional differential equations [J]. Computer Physics Communications, 2013, 184(1): 130-141.
[26] WANG D M. An implementation of the characteristic set method in Maple [M]//Automated Practical Reasoning. Wien: Springer-Verlag, 1995: 187-201.
[27] WANG D M. Epsilon: A library of software tools for polynomial elimination [J]. Mathematical Software, 2002: 379-389.
[28] WANG D K. Wsolve: A Maple package for solving system of polynomial equations [EB/OL]. (2004-05-10)[2016-09-04]. http://www.mmrc.iss.ac.cn/dwang/wsolve.html.
[29] LIU Y P, YAO R X, LI Z B, et al. An online computing and knowledge platform for differential equations[C]//Proceedings of the 5th International Congress on Mathematical Software. Springer International Publishing, 2016: 181-188.
文章导航

/