+using namespace std;
+
+static unsigned matrix_determinants()
+{
+ 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 = matrix{{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 = matrix{{a, b},
+ {c, 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 = matrix{{a, b, c},
+ {d, e, f},
+ {g, h, 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 = matrix{{0, -1, 3},
+ {3, -2, 2},
+ {3, 4, -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 = matrix{{a/(a-b), 1},
+ {b/(a-b), 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 = matrix{{a, -2, 2},
+ {3, a-1, 2},
+ {3, 4, a-3}};
+ ex p = m3.charpoly(a);
+ if (p != 0) {
+ clog << "charpoly of 3x3 matrix " << m3
+ << " erroneously returned " << p << endl;
+ ++result;
+ }
+
+ return result;
+}
+
+static unsigned matrix_invert1()
+{
+ unsigned result = 0;
+ matrix m(1,1);
+ symbol a("a");
+
+ m.set(0,0,a);
+ matrix m_i = m.inverse();
+
+ if (m_i(0,0) != pow(a,-1)) {
+ clog << "inversion of 1x1 matrix " << m
+ << " erroneously returned " << m_i << endl;
+ ++result;
+ }
+
+ return result;
+}
+
+static unsigned matrix_invert2()
+{
+ unsigned result = 0;
+ symbol a("a"), b("b"), c("c"), d("d");
+ matrix m = {{a, b},
+ {c, d}};
+ matrix m_i = m.inverse();
+ ex det = m.determinant();
+
+ if ((normal(m_i(0,0)*det) != d) ||
+ (normal(m_i(0,1)*det) != -b) ||
+ (normal(m_i(1,0)*det) != -c) ||
+ (normal(m_i(1,1)*det) != a)) {
+ clog << "inversion of 2x2 matrix " << m
+ << " erroneously returned " << m_i << endl;
+ ++result;
+ }
+
+ return result;
+}
+
+static unsigned matrix_invert3()
+{
+ unsigned result = 0;
+ symbol a("a"), b("b"), c("c");
+ symbol d("d"), e("e"), f("f");
+ symbol g("g"), h("h"), i("i");
+ matrix m = {{a, b, c},
+ {d, e, f},
+ {g, h, i}};
+ matrix m_i = m.inverse();
+ ex det = m.determinant();
+
+ if ((normal(m_i(0,0)*det) != (e*i-f*h)) ||
+ (normal(m_i(0,1)*det) != (c*h-b*i)) ||
+ (normal(m_i(0,2)*det) != (b*f-c*e)) ||
+ (normal(m_i(1,0)*det) != (f*g-d*i)) ||
+ (normal(m_i(1,1)*det) != (a*i-c*g)) ||
+ (normal(m_i(1,2)*det) != (c*d-a*f)) ||
+ (normal(m_i(2,0)*det) != (d*h-e*g)) ||
+ (normal(m_i(2,1)*det) != (b*g-a*h)) ||
+ (normal(m_i(2,2)*det) != (a*e-b*d))) {
+ clog << "inversion of 3x3 matrix " << m
+ << " erroneously returned " << m_i << endl;
+ ++result;
+ }
+
+ return result;
+}