Emathema: An online automated computing platform for equations

doi:10.3969/j.issn.1000-5641.2017.03.002

Abstract

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.

Key words: symbolic computation, online computing platform, Maple package, differential equation

CLC Number:

YANG Le, LIU Yin-ping, LI Zhi-bin. Emathema: An online automated computing platform for equations[J]. Journal of East China Normal University(Natural Sc, 2017, (3): 20-28.

References

[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.