The Macaulay2 script solving the Lagrange multiplier problem can be found here.
One can perform this computation in a Sage Notebook screen with macaulay2 enabled as I mentioned in an earlier blog post, or you can try installing Macaulay2 and emacs on your personal machine by following the installation instructions on the Macaulay2 Home Page.
If you have any problems setting it up, then I can try and help you via email.
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