- if (abs(det.evalf()-numeric(".10097939769690107E-3789"))>numeric("1.E-3800")) {
- clog << "determinant of 80x80 erroneously returned " << det << endl;
+ /*
+ The closed form of the determinant of n x n Hilbert matrices is:
+
+ n-1 / n-1 \
+ ----- | ----- |
+ | | | pow(factorial(r),2) | | hilbert(r,c) |
+ | | | | | |
+ r = 0 \ c = 0 /
+ */
+
+ ex hilbdet = 1;
+ for (unsigned r=0; r<n; ++r) {
+ hilbdet *= pow(factorial(numeric(r)),2);
+ for (unsigned c=0; c<n; ++c)
+ hilbdet *= hilbert(r,c);
+ }
+
+ if (det != hilbdet) {
+ clog << "determinant of " << n << "x" << n << " erroneously returned " << det << endl;