ex sol_y = sol.op(1).rhs(); // rhs of solution for second variable (y)
// It should have returned [x==43/17,y==-10/17]
- if (!(sol_x - numeric(43,17)).is_zero() ||
- !(sol_y - numeric(-10,17)).is_zero()) {
+ if ((sol_x != numeric(43,17)) ||
+ (sol_y != numeric(-10,17))) {
++result;
clog << "solution of the system " << eqns << " for " << vars
<< " erroneously returned " << sol << endl;
ex sol_y = sol.op(1).rhs(); // rhs of solution for second variable (y)
// It should have returned [x==-3/2*I,y==-1/2]
- if (!(sol_x - numeric(-3,2)*I).is_zero() ||
- !(sol_y - numeric(-1,2)).is_zero()) {
+ if ((sol_x != numeric(-3,2)*I) ||
+ (sol_y != numeric(-1,2))) {
++result;
clog << "solution of the system " << eqns << " for " << vars
<< " erroneously returned " << sol << endl;
ex sol_y = sol.op(1).rhs(); // rhs of solution for second variable (y)
// It should have returned [x==x,y==t]
- if (!(sol_x - x).is_zero() ||
- !(sol_y - t).is_zero()) {
+ if ((sol_x != x) ||
+ (sol_y != t)) {
+ ++result;
+ clog << "solution of the system " << eqns << " for " << vars
+ << " erroneously returned " << sol << endl;
+ }
+
+ return result;
+}
+
+static unsigned exam_lsolve3S(void)
+{
+ // A degenerate example that went wrong while trying to improve elimination
+ unsigned result = 0;
+ symbol b("b"), c("c");
+ symbol x("x"), y("y"), z("z");
+ lst eqns, vars;
+ ex sol;
+
+ // Create the linear system [y+z==b,-y+z==c] with one additional row...
+ eqns.append(ex(0)==ex(0)).append(b==z+y).append(c==z-y);
+ // ...to be solved for [x,y,z]...
+ vars.append(x).append(y).append(z);
+ // ...and solve it:
+ sol = lsolve(eqns, vars);
+ ex sol_x = sol.op(0).rhs(); // rhs of solution for first variable (x)
+ ex sol_y = sol.op(1).rhs(); // rhs of solution for second variable (y)
+ ex sol_z = sol.op(2).rhs(); // rhs of solution for third variable (z)
+
+ // It should have returned [x==x,y==t,]
+ if ((sol_x != x) ||
+ (sol_y != (b-c)/2) ||
+ (sol_z != (b+c)/2)) {
++result;
clog << "solution of the system " << eqns << " for " << vars
<< " erroneously returned " << sol << endl;
result += exam_lsolve2b(); cout << '.' << flush;
result += exam_lsolve2c(); cout << '.' << flush;
result += exam_lsolve2S(); cout << '.' << flush;
+ result += exam_lsolve3S(); cout << '.' << flush;
if (!result) {
cout << " passed " << endl;