1 /** @file exam_lsolve.cpp
3 * These exams test solving small linear systems of symbolic equations. */
6 * GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany
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25 static unsigned exam_lsolve1()
32 eq = (3*x+5 == numeric(8));
36 clog << "solution of 3*x+5==8 erroneously returned "
43 static unsigned exam_lsolve2a()
45 // An example from the Maple online help.
47 symbol a("a"), b("b"), x("x"), y("y");
51 // Create the linear system [a*x+b*y==3,x-y==b]...
52 eqns.append(a*x+b*y==3).append(x-y==b);
53 // ...to be solved for [x,y]...
54 vars.append(x).append(y);
56 sol = lsolve(eqns, vars);
57 ex sol_x = sol.op(0).rhs(); // rhs of solution for first variable (x)
58 ex sol_y = sol.op(1).rhs(); // rhs of solution for second variable (y)
60 // It should have returned [x==(3+b^2)/(a+b),y==(3-a*b)/(a+b)]
61 if (!normal(sol_x - (3+pow(b,2))/(a+b)).is_zero() ||
62 !normal(sol_y - (3-a*b)/(a+b)).is_zero()) {
64 clog << "solution of the system " << eqns << " for " << vars
65 << " erroneously returned " << sol << endl;
71 static unsigned exam_lsolve2b()
73 // A boring example from Mathematica's online help.
75 symbol x("x"), y("y");
79 // Create the linear system [3*x+y==7,2*x-5*y==8]...
80 eqns.append(3*x+y==7).append(2*x-5*y==8);
81 // ...to be solved for [x,y]...
82 vars.append(x).append(y);
84 sol = lsolve(eqns, vars);
85 ex sol_x = sol.op(0).rhs(); // rhs of solution for first variable (x)
86 ex sol_y = sol.op(1).rhs(); // rhs of solution for second variable (y)
88 // It should have returned [x==43/17,y==-10/17]
89 if ((sol_x != numeric(43,17)) ||
90 (sol_y != numeric(-10,17))) {
92 clog << "solution of the system " << eqns << " for " << vars
93 << " erroneously returned " << sol << endl;
99 static unsigned exam_lsolve2c()
101 // A more interesting example from the Maple online help.
103 symbol x("x"), y("y");
107 // Create the linear system [I*x+y==1,I*x-y==2]...
108 eqns.append(I*x+y==1).append(I*x-y==2);
109 // ...to be solved for [x,y]...
110 vars.append(x).append(y);
112 sol = lsolve(eqns, vars);
113 ex sol_x = sol.op(0).rhs(); // rhs of solution for first variable (x)
114 ex sol_y = sol.op(1).rhs(); // rhs of solution for second variable (y)
116 // It should have returned [x==-3/2*I,y==-1/2]
117 if ((sol_x != numeric(-3,2)*I) ||
118 (sol_y != numeric(-1,2))) {
120 clog << "solution of the system " << eqns << " for " << vars
121 << " erroneously returned " << sol << endl;
127 static unsigned exam_lsolve2S()
129 // A degenerate example that went wrong in GiNaC 0.6.2.
131 symbol x("x"), y("y"), t("t");
135 // Create the linear system [0*x+0*y==0,0*x+1*y==t]...
136 eqns.append(0*x+0*y==0).append(0*x+1*y==t);
137 // ...to be solved for [x,y]...
138 vars.append(x).append(y);
140 sol = lsolve(eqns, vars);
141 ex sol_x = sol.op(0).rhs(); // rhs of solution for first variable (x)
142 ex sol_y = sol.op(1).rhs(); // rhs of solution for second variable (y)
144 // It should have returned [x==x,y==t]
148 clog << "solution of the system " << eqns << " for " << vars
149 << " erroneously returned " << sol << endl;
155 static unsigned exam_lsolve3S()
157 // A degenerate example that went wrong while trying to improve elimination
159 symbol b("b"), c("c");
160 symbol x("x"), y("y"), z("z");
164 // Create the linear system [y+z==b,-y+z==c] with one additional row...
165 eqns.append(ex(0)==ex(0)).append(b==z+y).append(c==z-y);
166 // ...to be solved for [x,y,z]...
167 vars.append(x).append(y).append(z);
169 sol = lsolve(eqns, vars);
170 ex sol_x = sol.op(0).rhs(); // rhs of solution for first variable (x)
171 ex sol_y = sol.op(1).rhs(); // rhs of solution for second variable (y)
172 ex sol_z = sol.op(2).rhs(); // rhs of solution for third variable (z)
174 // It should have returned [x==x,y==t,]
176 (sol_y != (b-c)/2) ||
177 (sol_z != (b+c)/2)) {
179 clog << "solution of the system " << eqns << " for " << vars
180 << " erroneously returned " << sol << endl;
186 unsigned exam_lsolve()
190 cout << "examining linear solve" << flush;
191 clog << "----------linear solve:" << endl;
193 result += exam_lsolve1(); cout << '.' << flush;
194 result += exam_lsolve2a(); cout << '.' << flush;
195 result += exam_lsolve2b(); cout << '.' << flush;
196 result += exam_lsolve2c(); cout << '.' << flush;
197 result += exam_lsolve2S(); cout << '.' << flush;
198 result += exam_lsolve3S(); cout << '.' << flush;
201 cout << " passed " << endl;
202 clog << "(no output)" << endl;
204 cout << " failed " << endl;