COMPUTATION OF THE GALOIS GROUP OF A POLYNOMIAL WITH DEGREE < 12
Copyright M. Olivier and Y. Eichenlaub (olivier@math.u-bordeaux.fr)
Version 1.5
Last released: 1996, April 01.
The directory contains 3 files and a lot of data :
galp is an executable file for SUN/SPARC station 1,2,4,5,10,20,...
galp.c is a source file ; the compilation requiests the installation of the PARI
library
makefile is an example of makefile to compile galp.c
All the others files are binary data files :
RESxxx are the invariant polynomials for degrees 8, 9, 10 and 11
COSxxx are the relative cosets of the transitive groups for degrees 8, 9, 10 and 11
(For degree <= 7, the method used is the one of PARI/GP package)
Example 1 : compute the Galois group of x^8-2
Invoke galp
Type x^8-2 or poly([1,0,0,0,0,0,0,0,-2],x)
The answer is T_8[8] which means the transitive group of degree 8 numbered 8 in
the paper : "The transitive groups of degree up to eleven" by G. Butler and J. McKay,
in Communications in Algebra, vol. 11, 1983, pages 863--911.
Example 2 : compute the Galois group of x^5-2
Type x^5-2 or poly([1,0,0,0,0,-1],x)
The answer is M_20 the metaplectic group of order 20
It is possible to invoke galp with at most two input parameters:
The first one is a flag (0 or 1) which indicates that you want
that galp verboses the execution of the program;
The second one is the precision of the initial computations, i.e.
an integer n which is the number of figures for the computations.
The syntax will be: galp flag precision
In case of a polynomial with large coefficients, it is better to invoke
galp with a given precision (and consequently also a flag value).
The defaults are flag=0 and precision=28 decimal digits.
Note that the polynomial has to be irreducible and with coefficients in Z.