diff -r 7f3760f39bdc -r f8845fc8f38d doc-isac/jrocnik/Test_Complex.thy
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/doc-isac/jrocnik/Test_Complex.thy	Tue Sep 17 09:50:52 2013 +0200
@@ -0,0 +1,113 @@
+theory Test_Complex imports Isac begin
+
+section {*terms and operations*}
+ML {*
+  print_depth 999; @{term "Complex 1 (2::real)"};
+*}
+ML {*
+@{term "Complex 1 2 + Complex 3 4"};
+print_depth 999; str2term "Complex 1 2 + Complex 3 4"; print_depth 999;
+*}
+ML {*
+@{term "Complex 1 2 * Complex 3 4"};
+@{term "Complex 1 2 - Complex 3 4"};
+@{term "Complex 1 2 / Complex 3 4"};
+(*@{term "Complex 1 2 ^ Complex 3 4"};
+  Type unification failed: Clash of types "complex" and "nat"
+  Operator:  op ^ (Complex 1 2) :: nat \<Rightarrow> complex
+  Operand:   Complex 3 4 :: complex*)
+*}
+ML {*
+term2str @{term "Complex 1 2 + Complex 3 4"};
+term2str @{term "Complex 1 2 / Complex 3 4"};
+*}
+
+ML {*
+val a = @{term "Complex 1 2"};
+atomty a;
+val a = str2term "Complex 1 2";
+atomty a;
+*}
+ML {*
+val b = @{term "Complex 3 4"};
+val b = str2term "Complex 3 4";
+(*a + (b::complex); ERROR: term + term*)
+*}
+
+section {*use the operations for simplification*}
+
+
+
+subsection {*example 1 -- ADD*}
+ML {*
+  print_depth 1;
+  val (thy, ro, er) = (@{theory}, tless_true, eval_rls);
+*}
+ML {*
+  val thm = @{thm "complex_add"};
+  val t = str2term "Complex 1 2 + Complex 3 4";
+  val SOME _ = rewrite_ thy ro er true thm t;
+  val SOME (t', _) = rewrite_ thy ro er true thm t;
+  "Complex (1 + 3) (2 + 4)" = term2str t';
+*}
+
+
+
+
+subsection {*example 2 -- ADD, MULT*}
+ML {*
+
+val Simplify_complex = append_rls "Simplify_complex" e_rls
+  [ Thm  ("complex_add",num_str @{thm complex_add}),
+		    Thm  ("complex_mult",num_str @{thm complex_mult}),
+		    Rls_ norm_Poly
+		  ];
+
+*}
+ML {*
+
+val t = str2term "(Complex 1 2 * (Complex 3 4 + Complex 5 (6::real)))";
+term2str t = "Complex 1 2 * (Complex 3 4 + Complex 5 6)";
+atomty t;
+
+*}
+ML {*
+
+
+val SOME (t, _) = rewrite_set_ thy true Simplify_complex t;
+
+term2str t = "Complex -12 26";
+atomty t;
+
+*}
+
+subsection {*example 3*}
+ML {*
+val Simplify_complex = append_rls "Simplify_complex" e_rls
+  [ Thm  ("complex_mult",num_str @{thm complex_mult}),
+    Thm  ("complex_inverse",num_str @{thm complex_inverse}),
+		    Rls_ norm_Poly
+		  ];
+*}
+ML {*
+val t = str2term "inverse (Complex (2::real) (4::real))";
+term2str t = "inverse Complex (2) (4)";
+atomty t;
+*}
+ML {*
+trace_rewrite := true;
+val SOME (t, _) = rewrite_set_ thy true Simplify_complex t;
+trace_rewrite := false;
+term2str t = "Complex -12 26";
+atomty t;
+*}
+
+
+
+ML {*
+trace_rewrite := true;
+trace_rewrite := false;
+*}
+
+end
+