I'm not very familiar with algebraic integers so I hope someone can
tell if the following is correct or not. It appears in the middle of
a calculation of Andrej's example of
ratsimp(diff(integrate(1/(x^5+1),x),x)).
(%i42) display2d:false;
(%o42) false
(%i43) algebraic:false;
(%o43) false
(%i44) gcd(x^5+1,2*x^2+(-sqrt(5)-1)*x+2,x);
(%o44) 1
(%i45) algebraic:true;
(%o45) true
(%i46) gcd(x^5+1,2*x^2+(-sqrt(5)-1)*x+2,x);
(%o46) 2*x^2+(-sqrt(5)-1)*x+2
The first gcd makes sense to me. But is the second gcd correct when
algebraic is true?
Ray