1. Computer Algebra System - Wikipedia, The Free Encyclopedia A computer algebra system (CAS) is a software program that facilitates symbolic mathematics. The core functionality of a CAS is manipulation of mathematical http://en.wikipedia.org/wiki/Computer_algebra_system

Computer algebra system From Wikipedia, the free encyclopedia Jump to: navigation search A computer algebra system CAS ) is a software program that facilitates symbolic mathematics . The core functionality of a CAS is manipulation of mathematical expressions in symbolic form. Contents Types of expressions Symbolic manipulations Other features History ... edit Types of expressions The expressions manipulated by the CAS typically include polynomials in multiple variables; standard functions of expressions ( sine exponential , etc.); various special functions ( erf Bessel functions , etc.); arbitrary functions of expressions; optimization; derivatives, integrals, simplifications, sums, and products of expressions; truncated series with expressions as coefficients, matrices of expressions, and so on. (This is a recursive definition.) edit Symbolic manipulations The symbolic manipulations supported typically include simplification to the smallest possible expression or some standard form, including automatic simplification with assumptions and simplification with constraints substitution of symbolic

2. COMPUTER ALGEBRA computer algebra, Algorithms, Systems and Applications computer algebra systems Peculiarities of programming in computer algebra systems http://kfe.fjfi.cvut.cz/~liska/ca/

Next: Contents COMPUTER ALGEBRA, Algorithms, Systems and Applications Richard Liska , Ladislav Drska, Jiri Limpouch, Milan Sinor, Michael Wester Franz Winkler For printing, the whole document in Postscript is available here (graphics outputs are missing). Contents Introduction What are algebraic calculations? Why do algebraic calculations? ... Richard Liska

3. Mathematics Archives - Topics In Mathematics - Computer Algebra KEYWORDS Conference Proceedings, Distance learning, Multimedia, Numerical integration and differentiation, computer algebra, Theorem proving, http://archives.math.utk.edu/topics/computerAlgebra.html

Topics in Mathematics Computer Algebra / Cryptology Genetic Algorithms Asian Technology Conference in Mathematics ADD. KEYWORDS: Conference Proceedings, Distance learning, Multimedia, Numerical integration and differentiation, Computer algebra, Theorem proving, Applications of Computer Algebra Systems (CAS), Graphing calculators Automatic Differentiation Bibliography Bibliography of the CATHODE (Computer Algebra Tools for Handling Ordinary Differential Equations) project A Bibliography of Computer Algebra Bibliography about the Maple Symbolic Algebra System ... Cryptologia ADD. KEYWORDS: Cryptology, Journal DOCUMENTA MATHEMATICA - Extra Volume ICM 1998 - Section: 14. Mathematical Aspects of Computer Science ADD. KEYWORDS: Articles SOURCE: DOCUMENTA MATHEMATICA, Proceedings of the International Congress of Mathematicians TECHNOLOGY: Postscript and DVI readers The Enigma Machine ADD. KEYWORDS: Software, History European Cryptography Resources Evolving Algebras ADD. KEYWORDS:

4. Axiom Computer Algebra System - Summary [Savannah] Savannah Free Software project for revival of Axiom as open source. http://savannah.nongnu.org/projects/axiom/

Login Status: Not Logged In Login New User This Page Clean Reload Printer Version Search in Projects People Cookbook Support Bugs Tasks Patches Hosted Projects Register New Project Full List Contributors Wanted Statistics Site Help User Docs: Cookbook User Docs: In Depth Guide Get Support Contact Us ... FAQ Developer Info Cryptographic software legal notice Anonymous CVS GNU Webmasters Documentation Organization Projects map www project GNU Project GNU GPL v3 Coming Events Free Software Directory Help GNU ... GNU Mirrors Axiom Computer Algebra System - Summary Group Main Main View Members Search ... Manage Show feedback again Membership Info Project Admins: Tim Daly David Mentr© Camm Maguire Juergen Weiss ... Dylan Thurston members View Members Group identification Id: System Name: axiom Name: Axiom Computer Algebra System Group Type: Search in this Group in Cookbook Support Bugs Tasks Patches This project is not part of the GNU Project. Axiom is a general purpose Computer Algebra system. It is useful for doing mathematics by computer and for research and development of mathematical algorithms. It defines a strongly typed, mathematically correct type hierarchy. It has a programming language and a built-in compiler. Axiom has been in development since 1973 and was sold as a commercial product. It has been released as free software.

5. UC Berkeley Computer Algebra Papers A paper written with John Chen on a Simple Graph Editor suitable for interfacing with a computer algebra system, August 2002 (code available on request). http://www.cs.berkeley.edu/~fateman/algebra.html

Here's an index to some recent and some older papers. A number of them have appeared in Proceedings of the International Symposium on Symbolic and Algebraic Computation (ISSAC), an annual conference usually co-sponsored by the Association for Computing Machinery's Special Interest Group on Symbolic and Algebraic Manipulation (SIGSAM), along with other cooperating organizations. More recently I've come to the conclusion that just posting papers here when I think they are "ripe" is useful: I can point to them, and search-engine web bots can find them. Formal publication has become less important scientifically, even though it continues to be required for certain kinds of academic recognition. If you wish to refer to material listed here that is not specifically marked as published, send me a note so I can tell you its current status; it could be that a more formal, archival version exists. Not all the papers are referenced from this page; you are free to browse the papers directory the most recent papers have the more recent dates! A paper that shows how one can save time computing with rational functions using poles and residues instead of numerators and denominators.

6. SAL- Mathematics - Computer Algebra Systems The major purpose of a computer algebra System (CAS) is to manipulate a formula symbolically using the computer. For example, expanding, factorizing, http://www.sai.msu.su/sal/A/1/

[an error occurred while processing this directive] The major purpose of a Computer Algebra System (CAS) is to manipulate a formula symbolically using the computer. For example, expanding, factorizing, root finding, or simplifying an algebraic polynomial are some of the common uses of CAS. However, many systems listed here have gone far beyond that and also offer other functionalities like numerical calculation, graphics, and simulations. They are included in this section because their very original, and still their most distinguishable capability is performing computer algebra. Search SAL: Computer Algebra Systems Commercial, Shareware, GPL Axiom a computer algebra system with powerful symbolic solver. bernina interactive program with interface to a computer algebra library. Computer Algebra Kit collection of small programs for computer algebra. CASA computer algebra software for constructive algebraic geometry in Maple. CoCoA a special-purpose system for doing Computations in Commutative Algebra. DrMath online symbolic math and computer algebra system.

7. Modern Computer Algebra Homepage computer algebra systems are gaining more and more importance in all areas of science and engineering. This textbook gives a thorough introduction to the http://www-math.uni-paderborn.de/mca/

Modern Computer Algebra Joachim von zur Gathen and Jürgen Gerhard Research Group Algorithmic Mathematics Department of Mathematics and Computer Science University of Paderborn , Germany Textbook, 2nd edition, Cambridge University Press US site Computer algebra systems are gaining more and more importance in all areas of science and engineering. This textbook gives a thorough introduction to the algorithmic basis of the mathematical engine in computer algebra systems. It is designed to accompany one- or two-semester courses for advanced undergraduate or graduate students in computer science or mathematics. Its comprehensiveness and authority make it also an essential reference for professionals in the area. Special features include: detailed study of algorithms including time analysis; implementation reports on several topics; complete proofs of the mathematical underpinnings; a wide variety of applications (among others, in chemistry, coding theory, cryptography, computational logic, and the design of calendars and musical scales). Some of this material has never appeared before in book form. Finally, a great deal of historical information and illustration enlivens the text. Besides many corrections and updates, Chapters 3 (Euclidean Algorithm), 15 (Hensel lifting), and 22 (Symbolic integration) were revised and extended in the 2nd edition.

8. Computer Algebra Group At SFU Part of the Centre for Experimental and Constructive Mathematics (CECM), Simon Fraser University, BC, Canada. Details of members, projects, meetings and http://www.cecm.sfu.ca/CAG/

Computer Algebra Group at SFU About Us Employment Opportunities Members ... Talks Text Size: MOCAA Seminar Series Upcoming conference dealines The Computer Algebra Group (CAG) at Simon Fraser University began in 1997. Members of the group are primarilly intested in the area known as Computer Algebra or Symbolic Computation. We use and develop software for the Maple and the Magma computer algebra systems. The CAG maintains a close relationship with Waterloo Maple, Inc., the producer of the computer algebra system Maple. The director of the CAG, Dr. Michael Monagan, is one of the authors of Maple. The current areas of research interest in our group include Simplification of algebraic formulae. Polynomial factorization and polynomial GCD computation. Symbolic summation and integration. Groebner bases and ideal theoretic computations. Symbolic solution of algebraic, ordinary and partial differential equations. High precision numerical differentation and integration. Numerical solution of analytic functions. Numerical solution of ordinary and partial differential equations. Recovery of formulae from floating point approxmations.

9. Computer Algebra In Mathematics Education This is the web site for computer algebra in Mathematics Education, an open, international organisation for those interested in the use of computer algebra http://www.lkl.ac.uk/came/

Curriculum Links Diary Reports Computer Algebra in Mathematics Education This is the web site for Computer Algebra in Mathematics Education , an open, international organisation for those interested in the use of computer algebra software in mathematics education. LATEST: Curriculum information - International overview of of CAS active curricula, assessment and qualifications Goals and history CAME was originally founded at ICME-8 in Seville in July 1996. CAME's goals are: to facilitate the dissemination and exchange of information on research and development in the use of computer algebra in mathematics education; to facilitate access to international expertise in the use of computer algebra in mathematics education; to promote the study of the use of computer algebra in mathematics education. CAME's principle activity is a two-yearly Symposium: the first was held in Israel, 1999 ; the second in The Netherlands, 2001 ; the third in France, 2003 ; the fourth in the USA, 2005 ; and the fifth in Hungary, 2007

10. Maxima - A GPL CAS Based On DOE-MACSYMA Maxima is a descendant of Macsyma, the legendary computer algebra system developed in the late 1960s at the Massachusetts Institute of Technology. http://maxima.sourceforge.net/

Maxima, a computer algebra system Home FAQ Docs Screen Shots ... Mail Lists About Maxima Maxima is a system for the manipulation of symbolic and numerical expressions, including differentiation, integration, Taylor series, Laplace transforms, ordinary differential equations, systems of linear equations, polynomials, and sets, lists, vectors, matrices, and tensors. Maxima yields high precision numeric results by using exact fractions, arbitrary precision integers, and arbitrarily precision floating point numbers. Maxima can plot functions and data in two and three dimensions. The Maxima source code can be compiled on many systems, including Windows, Linux, and MacOS X. The source code for all systems and precompiled binaries for Windows and Linux are available at the SourceForge file manager Maxima is a descendant of Macsyma, the legendary computer algebra system developed in the late 1960s at the Massachusetts Institute of Technology. It is the only system based on that effort still publicly available and with an active user community, thanks to its open source nature. Macsyma was revolutionary in its day, and many later systems, such as Maple and Mathematica, were inspired by it. The Maxima branch of Macsyma was maintained by William Schelter from 1982 until he passed away in 2001. In 1998 he obtained permission to release the source code under the GNU General Public License (GPL). It was his efforts and skill which have made the survival of Maxima possible, and we are very grateful to him for volunteering his time and expert knowledge to keep the original DOE Macsyma code alive and well. Since his passing a group of users and developers has formed to bring Maxima to a wider audience.

11. Fermat, Computer Algebra System computer algebra system that does arithmetic of arbitrarily long integers and fractions, symbolic calculations, graphics, and other numerical calculations. http://home.bway.net/lewis/

Above graphic created with the float version of Fermat. Fermat is a computer algebra system for Macintosh, Windows, Linux, and Unix by me, Robert H. Lewis of Fordham University, that does arithmetic of arbitrarily long integers and fractions, symbolic calculations, matrices over polynomial rings, graphics, and other numerical calculations. It is extremely fast and extremely economical of space. The main version that I care most about is oriented toward polynomial and matrix algebra over the rationals Q and finite fields. On the Mac side, there is a version for OS X and versions for OS 9. There is also a "float" version for graphics. All versions are available here. Fermat is a state-of-the-art research tool for real problems. See for example: Compare Your Computer Algebra System. Take the Fermat Tests! There are now four tests. One test involves evaluation of rational functions, the second involves Smith Normal Form, the third resultants, the fourth rational function arithmetic. Fermat is shareware, $US 50. The only exception is mathematicians earning less than $US 40000 per year. Institutions must pay $US 50 per machine.

12. Ontario Research Centre For Computer Algebra - ORCCA Researchers at ORCCA study algorithms and software systems for symbolic mathematical computation. At any given time a number of visitors and postdocs are http://www.orcca.on.ca/

13. The Yacas Computer Algebra System A general purpose easy program for It is built on top of its own programming language designed for symbolic manipulation of math symbols. http://yacas.sourceforge.net/

Your browser does not support Javascript, or Javascript is disabled. We highly recommend that you enable Javascript so that you can use the extended Yacas web site, with lots of tutorials and calculation examples. Alternatively, click here to go to the static part of the web site where you can also find a lot of information and download Yacas to run it locally. document.location.href ="homepage.html"; About Read the manual License (GPL) Download ... Email us

14. Computer Algebra Benchmarks Collated by computer algebra Fachgruppe, Mannheim. http://krum.rz.uni-mannheim.de/cafgbench.html

Computer Algebra Benchmarks Benchmark Initiative, Computer Algebra Fachgruppe of GI, DMV and GAMM Abstract: The initiative will discuss, develop, define, collect all facettes of this challenging problem. It should analyse and develop test suites but also define standard examples for the various topics of computer algebra where algorithm and system developer can test their newly developed and improved methods. Furthermore, all kinds of test examples should be collected and consolidated. Directory of Activities (new) Slides of the Meeting at ISSAC'98 Computer Algebra Benchmarks Collection from July 1998. The CASBENCH Computer Algebra Benchmarks , a proposal from 1995 for the beginning of some computer algebra benchmarking, discussed by the Computer Algebra Fachgruppe. More Links: Additional Computer Algebra WWW Pages CAIS der Computeralgebra Fachgruppe This servers homepage Heinz Kredel , e-mail: kredel@rz.uni-mannheim.de Last modified: Mon Jun 28 16:50:34 MEST 1999

15. Computer Algebra Systems A computer algebra system is a type of software package that is used in manipulation of mathematical formulae. The primary goal of a computer algebra system http://www.math.wpi.edu/IQP/BVCalcHist/calc5.html

Previous: Short Biographies Next Conclusions Home: Table of Contents 5. Computer Algebra Systems 5.1 Introduction - What is a Computer Algebra System? A Computer Algebra system is a type of software package that is used in manipulation of mathematical formulae. The primary goal of a Computer Algebra system is to automate tedious and sometimes difficult algebraic manipulation tasks. The principal difference between a Computer Algebra system and a traditional calculator is the ability to deal with equations symbolically rather than numerically. The specific uses and capabilities of these systems vary greatly from one system to another, yet the purpose remains the same: manipulation of symbolic equations. Computer Algebra systems often include facilities for graphing equations and provide a programming language for the user to define his/her own procedures. Computer Algebra systems have not only changed how mathematics is taught at many universities, but have provided a flexible tool for mathematicians worldwide. Examples of popular systems include Maple, Mathematica, and MathCAD. Computer Algebra systems can be used to simplify rational functions, factor polynomials, find the solutions to a system of equation, and various other manipulations. In Calculus, they can be used to find the limit of, symbolically integrate, and differentiate arbitrary equations. Attempting to expand the equation using the binomial theorem by hand would be a daunting task, nearly impossible to do without error. However, with the aid of Maple, this equation can be expanded in less than two seconds. Differentiating the result term-by-term can then be performed in milliseconds. The usefulness of such a system is obvious: not only does it act as a time saving device, but problems which simply were not reasonable to perform by hand can be performed in seconds.

16. ACM Communications In Computer Algebra computer algebra Home Page. Issues Online Editorial Board. Submissions of Material. Announcements, Timely Communications, and Unreviewed Articles http://www.sigsam.org/cca/

ACM Communications in Computer Algebra Home Page Issues Online Editorial Board Submissions of Material: Announcements, Timely Communications, and Unreviewed Articles Formally reviewed articles Advertising ... ACM Home Page

17. ZCA Home Page A scientific institution of the departments of Mathematics , Computer Science , and Electrical Engineering at the University of Kaiserslautern. http://www.mathematik.uni-kl.de/~zca/

Willkommen ZCA Kaiserslautern Centre for Computer Algebra Welcome Mathematics Computer Science , and Electrical Engineering at the University of Kaiserslautern . The goal of the centre is to advance and to support the use of Computer Algebra in industry, research, and teaching. Goals and activities Actively participating research groups and their projects Paper series Reports on Computer Algebra ... Links related to Computer Algebra c/o Prof. Dr. G.-M. Greuel FB Mathematik D-67663 Kaiserslautern Germany greuel@mathematik.uni-kl.de Last modified: Tue Nov 22 15:12:01 MEZ 2005

18. East Coast Computer Algebra Day 2003 East Coast computer algebra Day a series of annual one day conferences on symbolic and mathematical computation. Clemson University, South Carolina, USA; http://www.math.clemson.edu/~sgao/ECCAD03/

East Coast Computer Algebra Day Saturday, April 5, 2003 Madren Conference Center Clemson University Clemson South Carolina Sponsors Department of Mathematical Sciences Department of Computer Science National Science Foundation ECCAD, East Coast Computer Algebra Day, is an annual conference that provides opportunities to learn and share new developments and to present research results in the areas of symbolic and mathematical computation. Invited Speakers: Prof. Richard Brent Computing Lab, Oxford University Primitive and almost primitive trinomials over GF(2) Prof. Jeremy Johnson Computer Science, Drexel University Computer Algebra and Signal Processing Prof. Wolfgang Schreiner RISC-Linz, Johannes Kepler University Distributed Maple - lessons learned on parallel computer algebra distributed environments Program Registration and breakfast Opening remarks Invited talk Coffee break Invited talk Lunch Poster and demo session Invited talk Poster and demo session Closing remarks Important Dates: April 5, 2003 Deadline for room reservations February 19, 2003

19. REDUCE Home Page (archival Version) Version 3.8 of the REDUCE computer algebra System was released 15 April 2004. Information on this and future releases of REDUCE is now available from a http://www.uni-koeln.de/REDUCE/

The REDUCE Computer Algebra System Current Version: REDUCE 3.8 Version 3.8 of the REDUCE Computer Algebra System was released 15 April 2004. Information on this and future releases of REDUCE is now available from a dedicated website at reduce-algebra.com Information available from the current page (www.uni-koeln.de/REDUCE/) contains archival information on older versions of REDUCE, and is being offered to support those who may still be running older versions of REDUCE. Previous Versions Version 3.7 of REDUCE was released on April 30th, 1999. Please see the announcement by Tony Hearn and the documentation for the new version. The REDUCE Homepage of ZIB also includes much more information on the current version of REDUCE. There is also a Y2K compliance statement for REDUCE 3.7. REDUCE 3.6 Table of Contents Introduction General Information Ordering Information Demonstration Versions ... About the REDUCE Home Page Introduction REDUCE is an interactive program designed for general algebraic computations of interest to mathematicians, scientists and engineers. Its capabilities include: expansion and ordering of polynomials and rational functions;

20. SymbolicNet -- Information Center For Symbolic And Algebraic Computation The area of Symbolic and Algebraic Computation (SAC), also known as computer algebra (CA) in some circles, aims to automate mathematical computations of all http://www.symbolicnet.org/

The area of Symbolic and Algebraic Computation (SAC), also known as Computer Algebra (CA) in some circles, aims to automate mathematical computations of all sorts. The resulting computer systems, experimental and commercial, are powerful tools for scientists, engineers, and educators. SAC research usually combines mathematics with advanced computing techniques. SymbolicNet.org provides a convenient starting point for discovering information about SAC. While being maintained by ICM at Kent State University , SymbolicNet also links to information supplied and updated by individuals, and cooperating sites Use the SymbolicNet main site or a Mirror Site near you. SymbolicNet supported in-part by US NSF grant CCR-9423696 Website developed by webtong.com

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