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# 1 Introduction

The main functionality of this package is to solve a rational polynomial by radicals and display the solution. That is possible iff the Galois group of the polynomial -- a permutation group on its roots -- is solvable. This fact has first been discovered by Évariste Galois (1811 -- 1832), on whose ideas this implementation is based. The implemented algorithm is discribed in Distler05.

For example, a radical expression for the roots of the polynomial x4 − x3 − x2 + x + 1 is

1

4

+

1

4

√

−3

+

1

2


√

7

2

+

1

2

√

−3

·

The package creates a LaTex file for the radical expression. Therefore you need a Latex compiler and the dvi viewer xdvi, to use the main functionality.

In addition to the readout you get several results in GAP. Some of them can be computed on their own. This are the splitting field of a rational polynomial and its Galois group as a permutation group on the roots.

This package uses the interface to KANT KANT in the package Alnuth to factorize polynomials over algebraic numberfields. This functionality must be available to use the functions in Radiroot.

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