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. 
KASH: Recent Developments
TLDR
The computer algebra system KASH/KANT for number theory has evolved considerably and its new features are presented and the related components, QaoS (Querying Algebraic Objects System) and GiANT (Graphical Al algebraic Number Theory) are introduced.
Magma - A Tool for Number Theory
TLDR
Magma is a computer algebra system developed by the group of John Cannon at the University of Sydney to provide a framework for implementing algorithms at a much higher level of abstraction than CA systems such as Maple and Mathematica.
Exact p-adic computation in Magma
Abstract We describe a new arithmetic system for the Magma computer algebra system for working with p-adic numbers exactly, in the sense that numbers are represented lazily to infinite p-adic
Abstract Data Types in Computer Algebra
TLDR
The aim of this paper is to report on the practical applications of this theory of abstract data types within computer algebra, and to outline some of the theoretical issues raised by this practical application.
Current Challenges in Developing Open Source Computer Algebra Systems
TLDR
A number of current challenges in the development of Open Source computer algebra systems are discussed, with the main focus on algebraic geometry and the system Singular.
Computing in the Monster
  • S. Norton
  • Computer Science, Mathematics
    J. Symb. Comput.
  • 2001
We discuss the feasibility of a general technique for computing in the Fischer?Griess Monster, and provide information on some of its subgroups which illustrates the use of computational techniques
Testing isomorphism of modules
Abstract We present a new deterministic algorithm to test constructively for isomorphism between two given finite-dimensional modules of a finitely generated algebra. The algorithm uses only basic
Testing isomorphism of graded algebras
We present a new algorithm to decide isomorphism between finite graded algebras. For a broad class of nilpotent Lie algebras, we demonstrate that it runs in time polynomial in the order of the input
Equality in Computer Algebra and Beyond
  • J. Davenport
  • Computer Science, Mathematics
    J. Symb. Comput.
  • 2002
TLDR
The computerization of mathematical computation in computer algebra systems on the one hand, and mathematical reasoning in theorem provers on the other hand, forces us to explore the issue of equality in greater detail.
A Millennium Project: Constructing Small Groups
TLDR
Motivated by the millennium, these methods are used to construct the groups of order at most 2000; this calculation is reported on and the resulting group library is described.
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 17 REFERENCES
Programming with algebraic structures: design of the MAGMA language
TLDR
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
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
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
TLDR
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
TLDR
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
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
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
...
1
2
...