Summary: Galois: A Theory Development Project \Lambda
Departments of Computer Science and Mathematics
Manchester University, Manchester M13 9PL, U.K.
June 12, 1995
A report on work in progress, for the Turin meeting on the Representation of Math
ematics in Logical frameworks, January 2023, 1993
1 The aims of the project
This is intended to be a large scale, ambitious and perhaps collaborative project to
develop a significant body of machine checked mathematics. The primary aim of the
project is to produce enough algebra to cover Galois Theory and some of its applications,
such as the unsolvability of the general polynomial of any degree greater than four.
In order to develop Galois Theory it will be necessary to define and develop, to some
extent, several algebraic theories and then use combinations of the theories to create
Galois Theory itself. In particular there will need to be chapters on Group Theory,
Linear Algebra, Polynomial Rings, Field Extensions, etc.
One advantage in choosing Galois Theory is that there is a significant amount of
algorithmic work to be done in applications of the theory, and it would be interesting to
explore the possibilities of combining this theory and proof development work with the
use of computer algebra systems. 1