ABSTRACT
In order to apply Galois theory to a specific polynomial it is necessary to compute the corresponding Galois group. This was the weak point in a memoir that Galois submitted to the French Academy of Sciences. However, the computation is possible — at least in principle. It becomes practical only with modern computers. This chapter discusses the problem for cubic and quartic polynomials. It also provides a general algorithm for equations of any degree, which is of theoretical importance but is too cumbersome to use in practice. More practical methods exist, but they go beyond the scope of this book. The packages Maple and GAP can compute Galois groups for relatively small degrees.
