Differences

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--- tutorial:caratheodory [2014/01/03 15:45] – external edit 127.0.0.1
+++ tutorial:caratheodory [2017/06/13 11:27] – added some formatting to enable automated tests oroehrig
@@ Line 8: / Line 8: @@
 The rows of this matrix describe a cone //C//:
 <code>
-polytope > $M=new
+polytope > $M = new Matrix<Rational>([[0,1,0,0,0,0],
-Matrix<Rational>([[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[1,0,2,1,1,2],[1,2,0,2,1,1],[1,1,2,0,2,1],[1,1,1,2,0,2],[1,2,1,1,2,0]]);
+polytope (2)> [0,0,1,0,0,0],
+polytope (3)> [0,0,0,1,0,0],
+polytope (4)> [0,0,0,0,1,0],
+polytope (5)> [0,0,0,0,0,1],
+polytope (6)> [1,0,2,1,1,2],
+polytope (7)> [1,2,0,2,1,1],
+polytope (8)> [1,1,2,0,2,1],
+polytope (9)> [1,1,1,2,0,2],
+polytope (10)> [1,2,1,1,2,0]]);
 polytope > $C=new Polytope<Rational>(POINTS=>$M);
 </code>
@@ Line 36: / Line 44: @@
 The following loop iterates over all invertible 6x6 submatrices of //M// and computes the unique representation of //x// as a linear combination of the rows of the submatrix.  The output (suppressed as it is too long) shows that each such linear combination requires at least one negative or one non-integral coefficient.
 <code>
-foreach (all_subsets_of_k(6,0..9)) {
+> foreach (all_subsets_of_k(6,0..9)) {
-  $B=$M->minor($_,All);
+>   $B = $M->minor($_,All);
-  if (det($B)) {
+>   if (det($B)) {
-    print lin_solve(transpose($B),$x), "\n";
+>     print lin_solve(transpose($B),$x), "\n";
-  }
+>   }
-}
+> }
 </code>
 This means that //x// cannot be represented as a non-negative linear combination of any six of the given generators of //C//.