This exercise asks you to get access to a computer algebra system. I suggest to use SINGULAR, but if you prefer to use one that you already know (e.g. Macaulay2 or MAGMA), you can use that instead.

The homepage for SINGULAR is here. You should get access to it in one of the following ways:

• Use the one I have installed on the leland system: Log in to bramble.stanford.edu. At the command line type ~galatius/Singular/Singular (to run it in a terminal) or ~galatius/Singular/ESingular (to run it inside Emacs).
• Install it on your own computer. It is explained on the SINGULAR home page how to do that. On a computer running Microsoft Windows, you have to install Cygwin (which is also explained on the home page, and is really easy).
• Use an online calculator.

• ring r = 0,(x,y,z),dp;

• poly f = x^3 + y^3 + z^3;

• poly g = (x+y+z)*(x^2 + y^2 + z^2);

• f; f+g; f*g;

• ideal I = f,g;

• groebner(I);