Database of Galois Group Polynomials

This library contains, for each transitive group G with degree between 2 and 11, a univariate polynomial over the integers which has G as its Galois group.

The polynomials are accessed by the following function.

PolynomialWithGaloisGroup(d, n)

Returns a polynomial p whose Galois group is the n-th transitive group of degree d, where the numbering is that of Butler and McKay.

Example

> load galpols;
Loading "galpols"
> P<x> := PolynomialRing(IntegerRing());
> print PolynomialWithGaloisGroup(8, 2); 
x^8 - x^7 - 19*x^6 - 2*x^5 + 46*x^4 - 2*x^3 - 19*x^2 - x + 1