Computational Physics/Chapter 2
Computer algebra systems began to appear in the 1960s, and evolved out of two quite different sources - the requirements of theoretical physicists and research into artificial intelligence.
A prime example for the first development was the pioneering work conducted by the later Nobel Prize laureate in physics Martin Veltman, who designed a program for symbolic mathematics, especially High Energy Physics, called Schoonschip (Dutch for "clean ship") in 1963.
Using LISP as the programming basis, Carl Engelman created MATHLAB in 1964 at MITRE within an artificial intelligence research environment. Later MATHLAB was made available to users on PDP-6 and PDP-10 Systems running TOPS-10 or TENEX in universities. Today it can still be used on SIMH-Emulations of the PDP-10. MATHLAB ("mathematical laboratory") should not be confused with MATLAB ("matrix laboratory") which is a system for numerical computation built 15 years later at the University of New Mexico, accidentally named rather similarly.
The first popular computer algebra systems were muMATH, Reduce, Derive (based on muMATH), and Macsyma; a popular copyleft version of Macsyma called Maxima is actively being maintained. As of today, the most popular commercial systems are Mathematica and Maple, which are commonly used by research mathematicians, scientists, and engineers. Freely available alternatives include Sage (which can act as a front-end to several other free and nonfree CAS).
In 1987 Hewlett-Packard introduced the first hand held calculator CAS with the HP-28 series, and it was possible, for the first time in a calculator, to arrange algebraic expressions, differentiation, limited symbolic integration, Taylor series construction and a solver for algebraic equations.
The Texas Instruments company in 1995 released the TI-92 calculator with an advanced CAS based on the software Derive. This, along with its successors (including the TI-89 series and the newer TI-Nspire CAS released in 2007) featured a reasonably capable and inexpensive hand-held computer algebra system.
CAS-equipped calculators are not permitted on the ACT, the PLAN, and in some classrooms because they may affect the integrity of the test/class, though it may be permitted on all of College Board's calculator-permitted tests, including the SAT, some SAT Subject Tests and the AP Calculus, Chemistry, Physics, and Statistics exams.
muMATH is a computer algebra system, which was developed in the late 1970s and early eighties by Albert D. Rich and David Stoutemyer of the Soft Warehouse in Honolulu, Hawaii. It was implemented in the muSIMP programming language which was built on top of a LISP dialect called muLISP. Platforms supported were CP/M and TRS-DOS (since muMATH-79), Apple II (since muMATH-80) and MS-DOS (in muMATH-83, the last version, which was published by Microsoft). The Soft Warehouse later developed Derive, another computer algebra system. The company was purchased by Texas Instruments in 1999, and development of Derive ended in 2006.
MuPAD is a computer algebra system (CAS). Originally developed by the MuPAD research group at the University of Paderborn, Germany, development was taken over by the company SciFace Software GmbH & Co. KG in cooperation with the MuPAD research group and partners from some other universities starting in 1997.
Until autumn 2005, the version "MuPAD Light" was offered for free for research and education, but as a result of the closure of the home institute of the MuPAD research group, only the version "MuPAD Pro" became available for purchase. The MuPAD kernel is bundled with Scientific Notebook and Scientific Workplace. Former versions of MuPAD Pro were bundled with SciLab. Its version 14 release was adopted as the CAS engine for the MathCAD software package. In September 2008, SciFace was purchased by MathWorks and the MuPAD code was included in the Symbolic Math Toolbox add-on for MATLAB. On 28 September 2008, MuPAD was withdrawn from the market as a software product in its own right. However, it is still available in the Symbolic Math Toolbox in MATLAB and can also be used as a stand-alone program.