computer science

Mathomatic

Mathomatic is a computer science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Mathomatic rather than just read about it. In short: 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 a…

Key takeaways

Mathomatic belongs to computer science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Mathomatic to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Mathomatic from memory before moving on to harder problems.

Reference excerpt

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 1987 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 of "math" and "automatic", and was inspired by the naming and automation of Rog-O-Matic, which was an early experiment in artificial intelligence. Development has ceased as a result of the death of the author on February 24, 2013.

Available platforms Mathomatic is available for almost all platforms, including Microsoft Windows using MinGW. It is available for Mac OS X, for iOS, for Android, and for the Nintendo DS under DSLinux and stand-alone. Fedora Linux, Slackware, Debian, Ubuntu, Gentoo Linux, and all of the main BSD Unix distributions include Mathomatic as an automatically installable package. There is a port to JavaScript using Emscripten, allowing Mathomatic to run in a web browser. The ports are all maintained by separate individuals.

… excerpt ends here. Continue reading the full article.

Illustrations

Worked examples

Example 1 — a first encounter with Mathomatic

Start with the simplest possible case. Write down what Mathomatic claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In computer science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Mathomatic before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Mathomatic ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Mathomatic

In research: Mathomatic appears in computer science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Mathomatic in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Mathomatic is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1987 software, Android (operating system) software, C (programming language) libraries, so understanding it makes those chapters shorter.
In everyday life: Look for Mathomatic outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Mathomatic in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Mathomatic means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Mathomatic out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Mathomatic in simple terms?

Why does Mathomatic matter?

Because it connects several computer science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Mathomatic?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Mathomatic.