# The Magma Algebra System I: The User Language

@article{Bosma1997TheMA, title={The Magma Algebra System I: The User Language}, author={Wieb Bosma and John J. Cannon and Catherine Playoust}, journal={J. Symb. Comput.}, year={1997}, volume={24}, pages={235-265} }

Abstract In the first of two papers on MAGMA , a new system for computational algebra, we present the MAGMA language, outline the design principles and theoretical background, and indicate its scope and use. Particular attention is given to the constructors for structures, maps, and sets.

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## References

SHOWING 1-10 OF 17 REFERENCES

Programming with algebraic structures: design of the MAGMA language

- Mathematics, Computer ScienceISSAC '94
- 1994

The use of algebraic structure as a design paradigm provides a natural strong typing mechanism and the result is a powerful, clean language which deals with objects in a mathematically rigorous manner.

A Computer Algebra System Based on Ordersorted Algebra

- Computer Science, MathematicsJ. Symb. Comput.
- 1995

This paper presents the prototype design of an algebraic computation system that manipulates algebraic quantities as generic objects using order-sorted algebra as the underlying model. The resulting…

Cayley, Version 4: The User Language

- Mathematics, Computer ScienceISSAC
- 1988

Cayley, version 4, is a proposed knowledge-based system for modern algebra. The proposal integrates the existing powerful algorithm base of Cayley with modest deductive facilities and large…

The Design of Cayley - a Language for Modern Algebra

- Mathematics, Computer ScienceDISCO
- 1990

The design of Cayley's user language has been responsive to the needs of its users and influenced by established practice in the domain of modern algebra.

AXIOM: the scientific computation system

- Computer Science
- 1992

This book gives the reader a technical introduction to AXIOM, interacts with the system's tutorial, accesses algorithms newly developed by the symbolic computation community, and presents advanced programming and problem solving techniques.

Universal Algebra

- 1982

I was brought to Universal Algebra against my will, as it were by Hermann Grassmann, and the main point of this paper is to describe a piece of Grass-mann's work and to ask those who know the subject…

The Correctness Problem in Computer Science

- Computer Science
- 1982

A container formed in articulated sections pivotally hinged about fold lines to provide ready access to end panels of retained packages for price-marking purposes. The container itself and a center…

An informal introduction to specifications using CLEAR

- 1981

Algebraic Programming with Magma: The Categories

- Algebraic Programming with Magma: The Categories
- 1996

Algebraic Programming with Magma: The Language

- Algebraic Programming with Magma: The Language
- 1996