diff -r 41caee260bd4 -r 43a3d06e0ee0 src/work/athos/lp_old/magic_square.cc
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/work/athos/lp_old/magic_square.cc	Wed Mar 23 09:49:41 2005 +0000
@@ -0,0 +1,99 @@
+// -*- c++ -*-
+#include <iostream>
+#include <fstream>
+
+#include <lemon/time_measure.h>
+#include <lp_solver_glpk.h>
+
+using std::cout;
+using std::endl;
+using namespace lemon;
+
+/*
+  On an 1537Mhz PC, the run times with 
+  glpk are the following.
+  for n=3,4, some secondes
+  for n=5, 25 hours
+ */
+
+int main(int, char **) {
+  const int n=3;
+  const double row_sum=(1.0+n*n)*n/2;
+  Timer ts;
+  ts.reset();
+  typedef LpGlpk LPSolver;
+  typedef LPSolver::Col Col;
+  LPSolver lp;
+  typedef std::map<std::pair<int, int>, Col> Coords;
+  Coords x;
+  // we create a new variable for each entry 
+  // of the magic square
+  for (int i=1; i<=n; ++i) {
+    for (int j=1; j<=n; ++j) { 
+      Col col=lp.addCol();
+      x[std::make_pair(i,j)]=col;
+      lp.setColLowerBound(col, 1.0);
+      lp.setColUpperBound(col, double(n*n));
+    }
+  }
+  LPSolver::Expression expr3, expr4;
+  for (int i=1; i<=n; ++i) {
+    LPSolver::Expression expr1, expr2;
+    for (int j=1; j<=n; ++j) {
+      expr1+=x[std::make_pair(i, j)];
+      expr2+=x[std::make_pair(j, i)];
+    }
+
+    // sum of rows and columns
+    lp.addRow(expr1==row_sum);
+    lp.addRow(expr2==row_sum);
+      cout <<"Expr1: "<<expr1<<endl;
+      cout <<"Expr2: "<<expr2<<endl;
+
+    expr3+=x[std::make_pair(i, i)];
+    expr4+=x[std::make_pair(i, (n+1)-i)];
+  }
+  cout <<"Expr3: "<<expr3<<endl;
+  cout <<"Expr4: "<<expr4<<endl;
+  // sum of the diagonal entries
+  lp.addRow(expr3==row_sum);
+  lp.addRow(expr4==row_sum);
+  lp.solveSimplex();
+  cout << "elapsed time: " << ts << endl;
+  for (int i=1; i<=n; ++i) {
+    for (int j=1; j<=n; ++j) { 
+      cout << "x("<<i<<","<<j<<")="<<lp.getPrimal(x[std::make_pair(i,j)]) 
+	   << endl;
+    }
+  }
+
+
+
+//   // we make new binary variables for each pair of 
+//   // entries of the square to achieve that 
+//   // the values of different entries are different
+//   lp.setMIP();
+//   for (Coords::const_iterator it=x.begin(); it!=x.end(); ++it) {
+//     Coords::const_iterator jt=it; ++jt;
+//     for(; jt!=x.end(); ++jt) {
+//       Col col1=(*it).second;
+//       Col col2=(*jt).second;
+//       Col col=lp.addCol();
+//       lp.setColLowerBound(col, 0.0);
+//       lp.setColUpperBound(col, 1.0);
+//       lp.addRow(double(-n*n+1.0)<=1.0*col2-1.0*col1-double(n*n)*col<=-1.0);
+//       lp.setColInt(col);
+//     }
+//   }
+//   cout << "elapsed time: " << ts << endl;
+//   lp.solveSimplex();
+//   // let's solve the integer problem
+//   lp.solveBandB();
+//   cout << "elapsed time: " << ts << endl;
+//   for (int i=1; i<=n; ++i) {
+//     for (int j=1; j<=n; ++j) { 
+//       cout << "x("<<i<<","<<j<<")="<<lp.getMIPPrimal(x[std::make_pair(i,j)]) 
+// 	   << endl;
+//     }
+//   }
+}