[GiNaC-list] lsolve problem

[Diego Conti]

Hi,
I think I have found a bug in lsolve. I have tested the following 
program under ginac 1.3.9 and 1.4.1, and I obtain an incorrect result in 
both cases: the linear system contains the equation lambda28=0, but I 
obtain lambda28==lambda28 in the solution.

code:

#include "ginac/ginac.h"
#include <iostream>
using namespace std;
using namespace GiNaC;

int main()
{
symbol 
lambda1("lambda1"),lambda2("lambda2"),lambda3("lambda3"),lambda4("lambda4"),lambda5("lambda5"), 
lambda6("lambda6"),lambda7("lambda7"),    
lambda8("lambda8"),lambda9("lambda9"),lambda10("lambda10"),lambda11("lambda11"),lambda12("lambda12"),lambda13("lambda13"), 
lambda14("lambda14"),    
lambda15("lambda15"),lambda16("lambda16"),lambda17("lambda17"),lambda18("lambda18"),lambda19("lambda19"),lambda20("lambda20"),lambda21("lambda21"),    
lambda22("lambda22"),lambda23("lambda23"),lambda24("lambda24"),lambda25("lambda25"),lambda26("lambda26"), 
lambda27("lambda27"),lambda28("lambda28"),lambda29("lambda29");
ex sqrt3=sqrt(ex(3));
lst syms;
syms=lambda1,lambda2,lambda3,lambda4,lambda5,lambda6,lambda7,lambda8,lambda9,lambda10,lambda11,
lambda12,lambda13,lambda14,lambda15,lambda16,lambda17,lambda18,lambda19,lambda20,lambda21,lambda22,lambda23,lambda24,
lambda25,lambda26,lambda27,lambda28,lambda29;   

    lst eqns;
    eqns.append(-lambda20+lambda24-lambda2-lambda25*sqrt3==0);
    eqns.append(-sqrt3*lambda23-lambda22==0);
    eqns.append(lambda15-lambda9-sqrt3*lambda7-lambda6==0);
    eqns.append(lambda23+lambda1-2*lambda21==0);
    eqns.append(lambda15-lambda9-lambda6==0);
    eqns.append(-2*lambda28==0);
    eqns.append(sqrt3*lambda12-lambda13==0);
    eqns.append(lambda26-sqrt3*lambda27+lambda19+lambda8==0);
    eqns.append(-lambda28==0);
    eqns.append(-sqrt3*lambda19+lambda27+sqrt3*lambda8==0);
    eqns.append(sqrt3*lambda17+lambda18==0);
    eqns.append(lambda4-2*lambda17-lambda11==0);
    eqns.append(lambda20+2*lambda24+lambda2==0);
    eqns.append(-lambda16+lambda3+2*lambda12==0);
    eqns.append(-sqrt3*lambda22-lambda23-lambda1-lambda21==0);
    eqns.append(lambda9*sqrt3-lambda7+lambda15*sqrt3==0);
    eqns.append(-sqrt3*lambda3-lambda13==0);
    eqns.append(-lambda15+lambda9-sqrt3*lambda7+lambda6==0);
    eqns.append(lambda25-sqrt3*lambda24==0);
    eqns.append(-lambda5-lambda10-lambda14==0);
    eqns.append(2*lambda20+lambda24-lambda2==0);
    cout<<GiNaC::lsolve(eqns,syms)<<endl;
}

output:
{lambda1==lambda23,lambda2==-1/3*sqrt(3)*lambda25,lambda3==-lambda16,lambda4==-2/3*sqrt(3)*lambda18+lambda11,lambda5==-lambda14-lambda10,lambda6==2*lambda15,lambda7==0,lambda8==-1/2*lambda26+1/3*sqrt(3)*lambda27,lambda9==-lambda15,lambda10==lambda10,lambda11==lambda11,lambda12==lambda16,lambda13==sqrt(3)*lambda16,lambda14==lambda14,lambda15==lambda15,lambda16==lambda16,lambda17==-1/3*sqrt(3)*lambda18,lambda18==lambda18,lambda19==-1/6*(sqrt(3)*lambda26-4*lambda27)*sqrt(3),lambda20==-1/3*sqrt(3)*lambda25,lambda21==lambda23,lambda22==-lambda23*sqrt(3),lambda23==lambda23,lambda24==1/3*sqrt(3)*lambda25,lambda25==lambda25,lambda26==lambda26,lambda27==lambda27,lambda28==lambda28,lambda29==lambda29}

I suspect the problem is the sqrt(3), since replacing it with an integer 
the result appears to be correct. Or am I doing something wrong?
Diego