1 /** @file exam_lsolve.cpp
3 * These exams test solving small linear systems of symbolic equations. */
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24 using namespace GiNaC;
29 static unsigned exam_lsolve1()
36 eq = (3*x+5 == numeric(8));
40 clog << "solution of 3*x+5==8 erroneously returned "
47 static unsigned exam_lsolve2a()
49 // An example from the Maple online help.
51 symbol a("a"), b("b"), x("x"), y("y");
55 // Create the linear system [a*x+b*y==3,x-y==b]...
56 eqns.append(a*x+b*y==3).append(x-y==b);
57 // ...to be solved for [x,y]...
58 vars.append(x).append(y);
60 sol = lsolve(eqns, vars);
61 ex sol_x = sol.op(0).rhs(); // rhs of solution for first variable (x)
62 ex sol_y = sol.op(1).rhs(); // rhs of solution for second variable (y)
64 // It should have returned [x==(3+b^2)/(a+b),y==(3-a*b)/(a+b)]
65 if (!normal(sol_x - (3+pow(b,2))/(a+b)).is_zero() ||
66 !normal(sol_y - (3-a*b)/(a+b)).is_zero()) {
68 clog << "solution of the system " << eqns << " for " << vars
69 << " erroneously returned " << sol << endl;
75 static unsigned exam_lsolve2b()
77 // A boring example from Mathematica's online help.
79 symbol x("x"), y("y");
83 // Create the linear system [3*x+y==7,2*x-5*y==8]...
84 eqns.append(3*x+y==7).append(2*x-5*y==8);
85 // ...to be solved for [x,y]...
86 vars.append(x).append(y);
88 sol = lsolve(eqns, vars);
89 ex sol_x = sol.op(0).rhs(); // rhs of solution for first variable (x)
90 ex sol_y = sol.op(1).rhs(); // rhs of solution for second variable (y)
92 // It should have returned [x==43/17,y==-10/17]
93 if ((sol_x != numeric(43,17)) ||
94 (sol_y != numeric(-10,17))) {
96 clog << "solution of the system " << eqns << " for " << vars
97 << " erroneously returned " << sol << endl;
103 static unsigned exam_lsolve2c()
105 // A more interesting example from the Maple online help.
107 symbol x("x"), y("y");
111 // Create the linear system [I*x+y==1,I*x-y==2]...
112 eqns.append(I*x+y==1).append(I*x-y==2);
113 // ...to be solved for [x,y]...
114 vars.append(x).append(y);
116 sol = lsolve(eqns, vars);
117 ex sol_x = sol.op(0).rhs(); // rhs of solution for first variable (x)
118 ex sol_y = sol.op(1).rhs(); // rhs of solution for second variable (y)
120 // It should have returned [x==-3/2*I,y==-1/2]
121 if ((sol_x != numeric(-3,2)*I) ||
122 (sol_y != numeric(-1,2))) {
124 clog << "solution of the system " << eqns << " for " << vars
125 << " erroneously returned " << sol << endl;
131 static unsigned exam_lsolve2S()
133 // A degenerate example that went wrong in GiNaC 0.6.2.
135 symbol x("x"), y("y"), t("t");
139 // Create the linear system [0*x+0*y==0,0*x+1*y==t]...
140 eqns.append(0*x+0*y==0).append(0*x+1*y==t);
141 // ...to be solved for [x,y]...
142 vars.append(x).append(y);
144 sol = lsolve(eqns, vars);
145 ex sol_x = sol.op(0).rhs(); // rhs of solution for first variable (x)
146 ex sol_y = sol.op(1).rhs(); // rhs of solution for second variable (y)
148 // It should have returned [x==x,y==t]
152 clog << "solution of the system " << eqns << " for " << vars
153 << " erroneously returned " << sol << endl;
159 static unsigned exam_lsolve3S()
161 // A degenerate example that went wrong while trying to improve elimination
163 symbol b("b"), c("c");
164 symbol x("x"), y("y"), z("z");
168 // Create the linear system [y+z==b,-y+z==c] with one additional row...
169 eqns.append(ex(0)==ex(0)).append(b==z+y).append(c==z-y);
170 // ...to be solved for [x,y,z]...
171 vars.append(x).append(y).append(z);
173 sol = lsolve(eqns, vars);
174 ex sol_x = sol.op(0).rhs(); // rhs of solution for first variable (x)
175 ex sol_y = sol.op(1).rhs(); // rhs of solution for second variable (y)
176 ex sol_z = sol.op(2).rhs(); // rhs of solution for third variable (z)
178 // It should have returned [x==x,y==t,]
180 (sol_y != (b-c)/2) ||
181 (sol_z != (b+c)/2)) {
183 clog << "solution of the system " << eqns << " for " << vars
184 << " erroneously returned " << sol << endl;
190 unsigned exam_lsolve()
194 cout << "examining linear solve" << flush;
196 result += exam_lsolve1(); cout << '.' << flush;
197 result += exam_lsolve2a(); cout << '.' << flush;
198 result += exam_lsolve2b(); cout << '.' << flush;
199 result += exam_lsolve2c(); cout << '.' << flush;
200 result += exam_lsolve2S(); cout << '.' << flush;
201 result += exam_lsolve3S(); cout << '.' << flush;
206 int main(int argc, char** argv)
208 return exam_lsolve();