I have the following system of equations, for which I expected Maxima's
solve() to be able to find a solution:
1) x^2 + y^2 = 1
2) (x - 0.5)^2 + (y - 0.5)^2 = 1
I obtain the following:
--
$ maxima
Maxima 5.24.0 http://maxima.sourceforge.net
using Lisp GNU Common Lisp (GCL) GCL 2.6.7 (a.k.a. GCL)
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) e1: x^2 + y^2 = 1;
2 2
(%o1) y + x = 1
(%i2) e2: (x - 0.5)^2 + (y - 0.5)^2 = 1;
2 2
(%o2) (y - 0.5) + (x - 0.5) = 1
(%i3) solve( [e1, e2], [x,y] );
rat: replaced -0.5 by -1/2 = -0.5
rat: replaced -0.5 by -1/2 = -0.5
(%o3) []
--
The last output line indicates no solution was found. A solution is
found for a simpler variant, however:
--
(%i4) e2: (x - 0.5)^2 + y^2 = 1;
2 2
(%o4) y + (x - 0.5) = 1
(%i5) solve( [e1, e2], [x, y] );
rat: replaced -0.5 by -1/2 = -0.5
1 sqrt(15) 1 sqrt(15)
(%o5) [[x = -, y = - --------], [x = -, y = --------]]
4 4 4 4
--
Are there some documented inherent limitations of Maxima's solve() which
prevent it from finding a solution to the first problem?
Thanks.
Krishna