A Course on Solving Algebraic Equations

Risa/Asir [10] is a general computer algebra system which can be used for Gröbner basis computations for zero dimensional ideal with ${\bf Q}$ coefficients. However, it is not good at graphical presentations and numerical methods. We integrated Risa/Asir, ox_phc (based on PHC pack by Verschelde [20] for the polyhedral homotopy method) and ox_gnuplot (GNUPLOT) servers to teach a course on solving algebraic equations. This course was presented with the text book [2], which discusses on the Gröbner basis method and the polyhedral homotopy method to solve systems of algebraic equations. We taught the course with a unified environment controlled by the Asir user language, which is similar to C. The following is an Asir session to solve algebraic equations by calling the PHC pack (Figure 2 is the output of [292]):

[287] phc(katsura(7));
The detailed output is in the file tmp.output.*
The answer is in the variable Phc.
0
[290] B=map(first,Phc)$
[291] gnuplot_plotDots([],0)$
[292] gnuplot_plotDots(B,0)$

Figure 2: The first components of the solutions to the system of algebraic equations Katsura 7.