Modelling Algebraic Structures in a Symbolic Computation Environment
|
Abstract:
Algebraic structures are a concept from mathematics to bring sets and their operations together. This process is well-known in computer science, too, say in the specification of abstract datatypes [4] or in module systems of some programming languages. Most languages used for symbolic computation and computer algebra are untyped, which means that algebraic structure can't be modelled adequately. Recently typed languages gained more attention in the computer algebra community in form of suitable type system. After giving two different definitions for algebraic structures, we show with a couple of examples how algebras and functions which create algebras are modelled in the symbolic computation system AlgBench which has been extended by a type system for computer algebra.
Citations
| 556 | Structure and interpretation of computer programs – Abelson, Sussman, et al. - 1996 |
| 422 | Mathematica : A system for doing mathematics by computer – WOLFRAM - 1991 |
| 160 | A course in universal algebra – Burris, Sankappanavar - 1981 |
| 126 | Basic category theory for computer scientists – Pierce - 1991 |
| 75 | AXIOM: the scientific computation system – Jenks, Sutor - 1992 |
| 71 | et al. Report on the programming language Haskell: a non-strict, purely functional language version 1.2 – Hudak - 1992 |
| 38 | Algebraische Spezifikation abstrakter Datentypen. Leitfäden und Monographien der Informatik – Ehrich, Gogolla, et al. - 1989 |
| 35 | The Definition of Standard ML (Version 2 – Harper, Milner, et al. - 1988 |
| 17 | Elliptic Curves: Diophantine Analysis – Lang - 1978 |
| 4 | AlgBench: An Object-Oriented Symbolic Core System – Maeder - 1992 |
| 2 | Klassenbasierte Umgebung fur algebraische Modellierungen in AlgBench – Missura - 1992 |
| 2 | Extending AlgBench with a type system – Missura - 1993 |
