Mathomatic

Mathomatic is a free, portable, general-purpose computer algebra system (CAS) that can symbolically solve, simplify, combine and compare algebraic equations, and can perform complex number, modular, and polynomial arithmetic, along with standard arithmetic. It can perform symbolic calculus (derivative, extrema, Taylor series, and polynomial integration and Laplace transforms), numerical integration, and can handle all elementary algebra except logarithms. Trigonometric functions can be entered and manipulated using complex exponentials, with the GNU m4 preprocessor. Not currently implemented are general functions such as ''f''(''x''), arbitrary-precision and interval arithmetic, as well as matrices.

Features

Mathomatic is capable of solving, differentiating, simplifying, calculating, and visualizing elementary algebra. It also can perform summations, products, and automated display of calculations of any length by plugging sequential or test values into any formula, then approximating and simplifying before display.

Intermediate results (showing the work) may be displayed by previously typing "set debug 1" (see the session example); this works for solving and almost every command in Mathomatic. "set debug 2" shows more details about the work done.

The software does not include a GUI except with the Mathomatic trademark authorized, versions for smartphones and tablets running iOS or Android. The Mathomatic software, available on the official Mathomatic website, is authorized for use in any other type of software, due to its permissive free software license (GNU LGPL). It is available as a free software library, and as a free console mode application that uses a color command-line interface with pretty-print output that runs in a terminal emulator under any operating system. The console interface is simple and requires learning the basic algebra notation to start. All input and output is line-at-a-time ASCII text. By default, input is standard input and output is standard output. Mathomatic is typically compiled with editline or GNU readline for easier input.

There is no programming capability; the interpreter works like an algebraic calculator. Expressions and equations are entered in standard algebraic infix notation. Operations are performed on them by entering simple English commands.

Because all numeric arithmetic is double precision floating point, and round-off error is not tracked, Mathomatic is not suitable for applications requiring high precision, such as astronomical calculations. It is useful for symbolic-numeric calculations of about 14 decimal digits accuracy, although many results will be exact, if possible.

Mathomatic can be used as a floating point or integer arithmetic code generating tool, simplifying and converting equations into optimized assignment statements in the Python, C, and Java programming languages. The output can be made compatible with most other mathematics programs, except TeX and MathML format input/output are currently not available. The ASCII characters that are allowed in Mathomatic variable names is configurable, allowing TeX format variable names.

The Mathomatic source code can be compiled as a symbolic math library with an API, which can be linked to C compatible programs that need to use the Mathomatic symbolic math engine.

Session examples

Solving and code generation example, where the work is shown:

1-> x = (a+1)*(b+2)
#1: x = (a + 1)*(b + 2)
1-> set debug 1
Success.
1-> solve for b
level 1: x = (a + 1)*(b + 2)
Subtracting "(a + 1)*(b + 2)" from both sides of the equation:
level 1: x - ((a + 1)*(b + 2)) = 0
Subtracting "x" from both sides of the equation:
level 1: -1*(a + 1)*(b + 2) = -1*x
Dividing both sides of the equation by "-1":
level 1: (a + 1)*(b + 2) = x
Dividing both sides of the equation by "a + 1":
level 1: b + 2 = x/(a + 1)
Subtracting "2" from both sides of the equation:
level 1: b = (x/(a + 1)) - 2
Solve completed:
level 1: b = (x/(a + 1)) - 2
Solve successful:
           x
#1: b = ------- - 2
        (a + 1)
1-> code C ; output C programming language code
b = ((x/(a + 1.0)) - 2.0);
1-> variables C ; define the variables for the C compiler
double x;
double a;
double b;
1->

History

Development of Mathomatic was started in the year 1986 by George Gesslein II, as an experiment in computerized mathematics. It was originally written in Microsoft C for MS-DOS. Versions 1 and 2 were published by Dynacomp of Rochester, New York in 1987The Software catalog: Microcomputer
sGoogle Books (6 February 2007). Retrieved 29 November 2011. and 1988 as a scientific software product for DOS. Afterwards it was released as shareware and then emailware, with a 2D equation graphing program. At the turn of the century, Mathomatic was ported to the GNU C Compiler under Linux and became free software. The graphing program was discontinued; 2D/ 3D graphing of equations is now accomplished with gnuplot.

The name "Mathomatic" is a portmanteau

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