Subject: Bug in solve? do not give me wanted effect.
From: maxio at sohu
Date: Tue, 26 Apr 2005 11:03:51 +0800 (CST)
I have met such a geometry problem:
Suppose a line l: x+y-m=0 intersects an ellipse 2*x^2+4*y^2=3 with A(x0,y0),B(x1,y1), and x0*x1+y0*y1=0, .i.e OA is vertical to OB, Solve the x0,x1,y0,y1.
solve([x0+y0-x1-y1,2*x0^2+4*y0^2-3,2*x1^2+4*y1^2-3,x0*x1+y0*y1]);
[[Y1 = - -------, y0 = - -------, x1 = ----------, x0 = ------------],
SQRT(2) SQRT(2) SQRT(2) 2 SQRT(3)
SQRT(3) SQRT(3) SQRT(3) %I 3 SQRT(2) %I
[Y1 = - -------, y0 = - -------, x1 = - ----------, x0 = - ------------],
SQRT(2) SQRT(2) SQRT(2) 2 SQRT(3)
SQRT(3) SQRT(3) SQRT(3) %I 3 SQRT(2) %I
[Y1 = -------, y0 = -------, x1 = ----------, x0 = ------------],
SQRT(2) SQRT(2) SQRT(2) 2 SQRT(3)
SQRT(3) SQRT(3) SQRT(3) %I 3 SQRT(2) %I
[Y1 = -------, y0 = -------, x1 = - ----------, x0 = - ------------]]
SQRT(2) SQRT(2) SQRT(2) 2 SQRT(3)
Intuitionisticly, it should exists real x0,y0,x1,y1, but Maxima do not give the real solution. It should be pointed out that the real solution does exits.