- unsigned result = 0;
- ex det;
- matrix m1(1,1), m2(2,2), m3(3,3), m4(4,4);
- symbol a("a"), b("b"), c("c");
- symbol d("d"), e("e"), f("f");
- symbol g("g"), h("h"), i("i");
-
- // check symbolic trivial matrix determinant
- m1.set(0,0,a);
- det = m1.determinant();
- if (det != a) {
- clog << "determinant of 1x1 matrix " << m1
- << " erroneously returned " << det << endl;
- ++result;
- }
-
- // check generic dense symbolic 2x2 matrix determinant
- m2.set(0,0,a).set(0,1,b);
- m2.set(1,0,c).set(1,1,d);
- det = m2.determinant();
- if (det != (a*d-b*c)) {
- clog << "determinant of 2x2 matrix " << m2
- << " erroneously returned " << det << endl;
- ++result;
- }
-
- // check generic dense symbolic 3x3 matrix determinant
- m3.set(0,0,a).set(0,1,b).set(0,2,c);
- m3.set(1,0,d).set(1,1,e).set(1,2,f);
- m3.set(2,0,g).set(2,1,h).set(2,2,i);
- det = m3.determinant();
- if (det != (a*e*i - a*f*h - d*b*i + d*c*h + g*b*f - g*c*e)) {
- clog << "determinant of 3x3 matrix " << m3
- << " erroneously returned " << det << endl;
- ++result;
- }
-
- // check dense numeric 3x3 matrix determinant
- m3.set(0,0,numeric(0)).set(0,1,numeric(-1)).set(0,2,numeric(3));
- m3.set(1,0,numeric(3)).set(1,1,numeric(-2)).set(1,2,numeric(2));
- m3.set(2,0,numeric(3)).set(2,1,numeric(4)).set(2,2,numeric(-2));
- det = m3.determinant();
- if (det != 42) {
- clog << "determinant of 3x3 matrix " << m3
- << " erroneously returned " << det << endl;
- ++result;
- }
-
- // check dense symbolic 2x2 matrix determinant
- m2.set(0,0,a/(a-b)).set(0,1,1);
- m2.set(1,0,b/(a-b)).set(1,1,1);
- det = m2.determinant();
- if (det != 1) {
- if (det.normal() == 1) // only half wrong
- clog << "determinant of 2x2 matrix " << m2
- << " was returned unnormalized as " << det << endl;
- else // totally wrong
- clog << "determinant of 2x2 matrix " << m2
- << " erroneously returned " << det << endl;
- ++result;
- }
-
- // check sparse symbolic 4x4 matrix determinant
- m4.set(0,1,a).set(1,0,b).set(3,2,c).set(2,3,d);
- det = m4.determinant();
- if (det != a*b*c*d) {
- clog << "determinant of 4x4 matrix " << m4
- << " erroneously returned " << det << endl;
- ++result;
- }
-
- // check characteristic polynomial
- m3.set(0,0,a).set(0,1,-2).set(0,2,2);
- m3.set(1,0,3).set(1,1,a-1).set(1,2,2);
- m3.set(2,0,3).set(2,1,4).set(2,2,a-3);
- ex p = m3.charpoly(a);
- if (p != 0) {
- clog << "charpoly of 3x3 matrix " << m3
- << " erroneously returned " << p << endl;
- ++result;
- }
-
- return result;
+ unsigned result = 0;
+ ex det;
+ matrix m1(1,1), m2(2,2), m3(3,3), m4(4,4);
+ symbol a("a"), b("b"), c("c");
+ symbol d("d"), e("e"), f("f");
+ symbol g("g"), h("h"), i("i");
+
+ // check symbolic trivial matrix determinant
+ m1.set(0,0,a);
+ det = m1.determinant();
+ if (det != a) {
+ clog << "determinant of 1x1 matrix " << m1
+ << " erroneously returned " << det << endl;
+ ++result;
+ }
+
+ // check generic dense symbolic 2x2 matrix determinant
+ m2.set(0,0,a).set(0,1,b);
+ m2.set(1,0,c).set(1,1,d);
+ det = m2.determinant();
+ if (det != (a*d-b*c)) {
+ clog << "determinant of 2x2 matrix " << m2
+ << " erroneously returned " << det << endl;
+ ++result;
+ }
+
+ // check generic dense symbolic 3x3 matrix determinant
+ m3.set(0,0,a).set(0,1,b).set(0,2,c);
+ m3.set(1,0,d).set(1,1,e).set(1,2,f);
+ m3.set(2,0,g).set(2,1,h).set(2,2,i);
+ det = m3.determinant();
+ if (det != (a*e*i - a*f*h - d*b*i + d*c*h + g*b*f - g*c*e)) {
+ clog << "determinant of 3x3 matrix " << m3
+ << " erroneously returned " << det << endl;
+ ++result;
+ }
+
+ // check dense numeric 3x3 matrix determinant
+ m3.set(0,0,numeric(0)).set(0,1,numeric(-1)).set(0,2,numeric(3));
+ m3.set(1,0,numeric(3)).set(1,1,numeric(-2)).set(1,2,numeric(2));
+ m3.set(2,0,numeric(3)).set(2,1,numeric(4)).set(2,2,numeric(-2));
+ det = m3.determinant();
+ if (det != 42) {
+ clog << "determinant of 3x3 matrix " << m3
+ << " erroneously returned " << det << endl;
+ ++result;
+ }
+
+ // check dense symbolic 2x2 matrix determinant
+ m2.set(0,0,a/(a-b)).set(0,1,1);
+ m2.set(1,0,b/(a-b)).set(1,1,1);
+ det = m2.determinant();
+ if (det != 1) {
+ if (det.normal() == 1) // only half wrong
+ clog << "determinant of 2x2 matrix " << m2
+ << " was returned unnormalized as " << det << endl;
+ else // totally wrong
+ clog << "determinant of 2x2 matrix " << m2
+ << " erroneously returned " << det << endl;
+ ++result;
+ }
+
+ // check sparse symbolic 4x4 matrix determinant
+ m4.set(0,1,a).set(1,0,b).set(3,2,c).set(2,3,d);
+ det = m4.determinant();
+ if (det != a*b*c*d) {
+ clog << "determinant of 4x4 matrix " << m4
+ << " erroneously returned " << det << endl;
+ ++result;
+ }
+
+ // check characteristic polynomial
+ m3.set(0,0,a).set(0,1,-2).set(0,2,2);
+ m3.set(1,0,3).set(1,1,a-1).set(1,2,2);
+ m3.set(2,0,3).set(2,1,4).set(2,2,a-3);
+ ex p = m3.charpoly(a);
+ if (p != 0) {
+ clog << "charpoly of 3x3 matrix " << m3
+ << " erroneously returned " << p << endl;
+ ++result;
+ }
+
+ return result;