Chapter 18: Software

This picture of the pencil of conics was drawn by a package called "Quartics". It also can compute the Galois group of a quartic. First you must load the package:

<<  Quartics.m

A function CubicResolvent is defined which computes the cubic resolvent of a quartic, and then applies the criteria in the table above to determine the
Galois group (though it cannot distinguish between (Subscript[D, 4]) and (Subscript[C, 4])). For example, let

f = x^4 - 10x^2 + 1

CubicResolvent[f]

If the quartic has real roots, the function QuarticPlot will draw the
associated pencil of conics.

QuarticPlot[f]