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Magma

Language type:

M - Mathematical or Simulation

Description:

Magma is an environment and high-level language for number theory, algebra, and general mathematical programming.
The fundamental features of Magma are its procedural syntax and statement structure, coupled with very sophisticated built-in data types and operations. In general, Magma is dynamically typed and performs automatic conversions rather than enforcing type checking. Some of the built-in types are: unlimited-precision integers, rational numbers, real and complex numbers, sets, atoms, arrays of various sorts, groups and fields of various sorts, and various kinds of functional types. Newer versions of Magma support closures and higher-order functions.
Magma has simple I/O facilities used mainly for reading and writing mathematical objects to and from files.
There is only one implementation of the Magma language. It is an interpreter written in C.
Magma runs on PCs and Unix systems. Magma was developed at the University of Sydney, and used to be downloadable free. Since about 1996, users have had to pay for subscriptions to Magma. Documentation is available with the distributions.

Origin:

J. Cannon, et al, 1993.

See Also:

Mathematica    Matlab    SETL    Pari   

Remarks:

Magma evolved from an earlier system called Cayley. Both systems were intended for use by serious mathematicians using computers to model and study mathematical concepts in detail. It borrows basic ideas from OO programming languages, particularly abstract types and type composition. In Magma, the fundamental classes based on modern notions of algebra and category theory.

Links:

Magma Examples at U. of Sydney

Date:

Last updated 1/10/98

Sample code:

A Magma program to produce random selections of strings from a simple grammar, by D. Taylor.

produce := procedure();
    seq := ["S"];
    rhs := ["(", "S", ")", "S"];
    i := 1;
    repeat
        if Random(1, 10) gt 7 then
            Insert(~seq, i, i, rhs);
        else
            Remove(~seq, i);
        end if;
        print #seq gt 0 select &*seq else "eps";
        i := Position(seq, "S");
    until i eq 0;
    print "Length:", #seq;
end procedure

Descriptions in this dictionary are ©1997-99 Neal Ziring. Some examples copyright of their respective authors. Some technologies and languages are trademarked. Permission to copy descriptions is granted as long as authorship credit is preserved.

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