Subject: Algebraic gcd and Rothstein-Trager algorithm
From: Raymond Toy
Date: Thu, 08 Jan 2009 11:16:15 -0500
I was reading over the Rothstein-Trager algorithm for integrating the
logarithmic part of rational functions in Symbolic Integration by
Bronstein. (Which is available on Google Books, by the way).
Maxima seems to have almost all of the necessary pieces to implement
this, but I don't know how to compute the gcd. In the example on page
48, we need to compute
gcd(x^6-5*x^4+x*x^2+4, x^4-3*x^2+6-a*(6*x^5-20*x^3+10*x))
where a is the algebraic number such that 4*a^2+1 = 0.
The book says the gcd is x^3+2*a*x^2-3*x-4*a.
Can I get maxima to do that?
Ray