#1266 solve() problem

[Anonymous]

Trying to solve two polynomial equations in two unknowns fails, but when I add a third trivial equation with a third unknown it works.

Maxima 5.13.0 http://maxima.sourceforge.net
Using Lisp GNU Common Lisp (GCL) GCL 2.6.7 (aka GCL)
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
This is a development version of Maxima. The function bug_report()
provides bug reporting information.
(%i1) solve([x^2+x+1=0,x^2*y+1=0]);
(%o1) []
(%i2) solve([x^2+x+1=0,x^2*y+1=0,z=0]);
sqrt(3) %i + 1 sqrt(3) %i + 1
(%o2) [[z = 0, y = --------------, x = - --------------],
2 2
sqrt(3) %i - 1 sqrt(3) %i - 1
[z = 0, y = - --------------, x = --------------]]
2 2
(%i3) bug_report();

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Please include the following build information with your bug report:
-------------------------------------------------------------

Maxima version: 5.13.0
Maxima build date: 14:20 8/31/2007
host type: i686-pc-linux-gnu
lisp-implementation-type: GNU Common Lisp (GCL)
lisp-implementation-version: GCL 2.6.7

-------------------------------------------------------------
The above information is also available from the Maxima function build_info().

[Robert Dodier]

Logged In: YES
user_id=501686
Originator: NO

It appears that Maxima obtains the same result if you solve the first equation for x and then substitute into the second and solve for y.

(%i1) display2d:false;
(%o1) false
(%i2) solve (x^2 + x + 1 = 0, x);
(%o2) [x = -(sqrt(3)*%i+1)/2,x = (sqrt(3)*%i-1)/2]
(%i3) solve (x^2*y + 1 = 0, y), first (%o2);
(%o3) [y = -2/(sqrt(3)*%i-1)]
(%i4) solve (x^2*y + 1 = 0, y), second (%o2);
(%o4) [y = 2/(sqrt(3)*%i+1)]

I don't know why Maxima can solve at least two different versions of this problem, but not the original formulation. I think some other reported bugs in solve have the same flavor.

[David Billinghurst]

Commit [2986fc], which fixed a number of algsys bugs - see [bugs:#3208] - has made this worse. I think this is due to heap overflow in radcan called from function EBAKSUBST1. My changes didn't cause this, but they did allow the solution to procede to the point of failure.

(%i1) solve([x^2+x+1=0,x^2*y+1=0]);
Heap exhausted during garbage collection: 0 bytes available, 16 requested.

Probably same as [bugs:#1106]

[David Billinghurst]

Fixed by commit [640ca7]. Test case is now in maxima testsuite.

(%i6) solve([x^2+x+1=0,x^2*y+1=0]);

(%o6) [[y = -(sqrt(3)*%i-1)/2,x = (sqrt(3)*%i-1)/2],
       [y = (sqrt(3)*%i+1)/2,x = -(sqrt(3)*%i+1)/2]]