Author: Stefan Karnel

    Author: Walther Neuper

    Copyright (c) Stefan Karnel 2002

 "-------- fun factout_p_ -----------------------------------------------------";

 "-------- integration lev.1 fun factout_p_ -----------------------------------";

 "-------- fun cancel_p_ ------------------------------------------------------";

 "-------- integration lev.1 fun cancel_p_ ------------------------------------";

 "-------- fun common_nominator_p_ --------------------------------------------";

 "-------- integration lev.1 fun common_nominator_p_ --------------------------";

 "-------- fun add_fraction_p_ ------------------------------------------------";

 "-------- integration lev.1 fun add_fraction_p_ ------------------------------";

 "-------- TODO ---------------------------------------------------------------";

 "-------- and app_rev ...traced down from rewrite_set_ until prepats ---------";

 "-------- and app_rev --------------------------------------------------------";

 "-------- fun rewrite_set_ cancel_p downto fun gcd_poly ----------------------";

 "-------- external calculating functions test -----------";

 "-------- rewrite_set_ cancel_p from: Mathematik 1 Schalk Reniets Verlag -----";

 "-------- cancel from: Mathematik 1 Schalk Reniets Verlag";

 "-------- rewrite_set_ common_nominator_p from: Mathematik 1 Schalk ----------";

 "-------- common_nominator_p ----------------------------";

 "-------- reverse rewrite -------------------------------";

 "-------- reverse rewrite ----------------------------------------------------";

 "-------- 'reverse-ruleset' cancel_p --------------------";

 "-------- 'reverse-ruleset' cancel_p -----------------------------------------";

 "-------- norm_Rational ---------------------------------";

 "-------- investigate rls norm_Rational --------------------------------------";

 "-------- examples: rls norm_Rational ----------------------------------------";

 "-------- fun factout_p_ -----------------------------------------------------";

 "-------- integration lev.1 fun factout_p_ -----------------------------------";

 "-------- fun factout_p_ -----------------------------------------------------";

 "-------- integration lev.1 fun factout_p_ -----------------------------------";

 "-------- fun factout_p_ -----------------------------------------------------";

 "-------- integration lev.1 fun factout_p_ -----------------------------------";

 "-------- fun cancel_p_ ------------------------------------------------------";

 "-------- integration lev.1 fun cancel_p_ ------------------------------------";

 "-------- fun cancel_p_ ------------------------------------------------------";

 "-------- integration lev.1 fun cancel_p_ ------------------------------------";

 "-------- fun cancel_p_ ------------------------------------------------------";

 "-------- integration lev.1 fun cancel_p_ ------------------------------------";

 "-------- fun common_nominator_p_ --------------------------------------------";

 "-------- integration lev.1 fun common_nominator_p_ --------------------------";

 "-------- fun common_nominator_p_ --------------------------------------------";

 "-------- integration lev.1 fun common_nominator_p_ --------------------------";

 "-------- fun common_nominator_p_ --------------------------------------------";

 "-------- integration lev.1 fun common_nominator_p_ --------------------------";

   "(x + -1) * (-1 + x) / (1 * ((1 + x) * (-1 + x))) +\n(x + 1) * (1 + x) / (1 * ((1 + x) * (-1 + x)))"

    "(x + -1) * (-1 + x) / ((1 + x) * (-1 + x)) +\n(x + 1) * (1 + x) / ((1 + x) * (-1 + x))"

 "-------- fun add_fraction_p_ ------------------------------------------------";

 "-------- integration lev.1 fun add_fraction_p_ ------------------------------";

 "-------- fun add_fraction_p_ ------------------------------------------------";

 "-------- integration lev.1 fun add_fraction_p_ ------------------------------";

 "-------- fun add_fraction_p_ ------------------------------------------------";

 "-------- integration lev.1 fun add_fraction_p_ ------------------------------";

 "-------- TODO ---------------------------------------------------------------";

 "-------- and app_rev ...traced down from rewrite_set_ until prepats ---------";

 "-------- TODO ---------------------------------------------------------------";

 "-------- and app_rev ...traced down from rewrite_set_ until prepats ---------";

 "-------- TODO ---------------------------------------------------------------";

 "-------- and app_rev ...traced down from rewrite_set_ until prepats ---------";

 "-------- and app_rev --------------------------------------------------------";

 "-------- and app_rev --------------------------------------------------------";

 "-------- and app_rev --------------------------------------------------------";

 (*========== inhibit exn WN130824 TODO =======================================================

 "-------- fun rewrite_set_ cancel_p downto fun gcd_poly ----------------------";

 "-------- external calculating functions test -----------";

 "-------- fun rewrite_set_ cancel_p downto fun gcd_poly ----------------------";

 "-------- external calculating functions test -----------";

 "-------- fun rewrite_set_ cancel_p downto fun gcd_poly ----------------------";

 "-------- external calculating functions test -----------";

 val t = str2term "(12 * x * y) / (8 * y^^^2 )";

 val t = str2term "((3 * x^^^2 + 6 *x + 3) / (2*x + 2))";

 (* "-------- example 187a": exception Div raised...

 val SOME (t', asm) = factout_p_ thy t;

 val SOME (t', asm) = rewrite_set_ thy false cancel_p t;*)

 if term2str t' = "(3 + 3 * x) * (1 + x) / (2 * (1 + x))" andalso terms2str asm = "[]"

 val t = str2term "(8 * x^^^2 * y * z ) / (18 * x * y^^^2 * z )";

 then () else error "factout_p_ 1 changed";

 (* "-------- example 187b": doesn't terminate...

 val SOME (t', asm) = cancel_p_ thy t;

 val SOME (t', asm) = rewrite_set_ thy false cancel_p t;*)

 if term2str t' = "(3 + 3 * x) / 2" andalso terms2str asm = "[\"1 + x ~= 0\"]"

 val t = str2term "(9 * x^^^5 * y^^^2 * z^^^4) / (15 * x^^^6 * y^^^3 * z )";

 then () else error "cancel_p_ 1 changed";

 (* "-------- example 187c": doesn't terminate...

 val SOME (t', asm) = rewrite_set_ thy false cancel_p t;*)

 val t = str2term "((-3 * x^^^2 + 6 *x - 3) / (2*x - 2))";

 "~~~~~ fun rewrite_set_, args:"; val (thy, bool, rls, term) = (@{theory Isac}, false, cancel_p, t);

 val SOME (t', asm) = factout_(*p_*) thy t;

 (* WN130827: exception Div raised...

 if term2str t' = "(3 - 3 * x) * (-1 + x) / (2 * (-1 + x))" andalso terms2str asm = "[]"

 rewrite__set_ thy 1 bool [] rls term

 then () else error "factout_ 2 changed";

 *)

 val SOME (t', asm) = cancel_(*p_*) thy t;

 "~~~~~ and rewrite__set_, args:"; val (thy, i, _, _, (rrls as Rrls _), t) =

 if term2str t' = "(3 - 3 * x) / 2" andalso terms2str asm = "[\"-1 + x ~= 0\"]"

   (thy, 1, bool, [], rls, term);

 then () else error "cancel_ 2 changed";

 (* WN130827: exception Div raised...

 	val (t', asm, rew) = app_rev thy (i+1) rrls t

 val t = str2term "((x + (-1)) / (x + 1)) + ((x + 1) / (x + (-1)))";

 *)

 val SOME (t', asm) = add_fraction_p_ thy t;

 "~~~~~ fun app_rev, args:"; val (thy, i, rrls, t) = (thy, (i+1), rrls, t);

 if term2str t' = "(2 + 2 * x ^^^ 2) / (-1 + x ^^^ 2)" andalso terms2str asm = "[]"

 (* WN130827: exception Div raised...

 then () else error "add_fraction_p_ 3 changed";

     val opt = app_rev' thy rrls t

 val SOME (t', asm) = common_nominator_p_ thy t;

 *)

 if term2str t' = 

 "~~~~~ fun app_rev', args:"; val (thy, (Rrls{erls,prepat,scr=Rfuns{normal_form,...},...}), t) =

   "(-1 + x) * (-1 + x) / ((1 + x) * (-1 + x)) +\n(1 + x) * (1 + x) / ((1 + x) * (-1 + x))"

   (thy, rrls, t);

   andalso terms2str asm = "[]"

 chk_prepat thy erls prepat t    = true;

 then () else error "common_nominator_p_ 3 changed";

 (* WN130827: exception Div raised...

 normal_form t

 val t = str2term "((x - 1) / (x + 1)) + ((x + 1) / (x - 1))";

 *)

 val SOME (t', asm) = add_fraction_ thy t;

 (* lookup Rational.thy, cancel_p: normal_form = cancel_p_ thy*)

 if term2str t' = "(2 + 2 * x ^^^ 2) / (-1 + x ^^^ 2)" andalso terms2str asm = "[]"

 "~~~~~ fun cancel_p_, args:"; val (t) = (t);

 then () else error "factout_ 4 changed";

 val opt = check_fraction t;

 val SOME (t', asm) = common_nominator_ thy t;

 val SOME (numerator, denominator) = opt

 if term2str t' = 

         val vs = t |> vars |> map free2str |> sort string_ord

   "(-1 + x) * (-1 + x) / ((1 + x) * (-1 + x)) +\n(1 + x) * (1 + x) / ((1 + x) * (-1 + x))" 

         val baseT = type_of numerator

   andalso terms2str asm = "[]"

         val expT = HOLogic.realT

 then () else error "cancel_ 4 changed";

 val (SOME a, SOME b) = (poly_of_term vs numerator, poly_of_term vs denominator);

 (*"-------- example 187a": exception Div raised...

 val t = str2term 

 val a = [(12, [1, 1])]: poly

   "((1) / (2*x + 2)) + ((1) / (2*x + (-2))) + ((1) / ( x^^^2 + (-1)))+((1) / (x^^^2 + (-2)*x + 1))";

 val b = [(8, [0, 2])]: poly

 val SOME (t', asm) = add_fraction_p_ thy t;

               val ((a', b'), c) = gcd_poly a b

 if term2str t' = "x / (1 + -2 * x + x ^^^ 2)" andalso terms2str asm = "[\"1 + x ~= 0\"]"

 *)

 then () else error "add_fraction_p_ 5 changed";

 (* "-------- example 187b": doesn't terminate...

 val SOME (t', asm) = norm_rational_ thy t;

 val a = [(8, [2, 1, 1])]: poly

 if term2str t' = "x / (1 + -2 * x + x ^^^ 2)" andalso terms2str asm = "[\"1 + x ~= 0\"]"

 val b = [(18, [1, 2, 1])]: poly

 then () else error "norm_rational_ 5 changed";

               val ((a', b'), c) = gcd_poly a b

 ============ inhibit exn WN130826 TODO ========================================================*)

 *)

 (* "-------- example 187c": doesn't terminate...

 val a = [(9, [5, 2, 4])]: poly

 "-------- cancel_p from: Mathematik 1 Schalk Reniets Verlag ------------------";

 val b = [(15, [6, 3, 1])]: poly

 "-------- cancel_p from: Mathematik 1 Schalk Reniets Verlag ------------------";

               val ((a', b'), c) = gcd_poly a b

 "-------- cancel_p from: Mathematik 1 Schalk Reniets Verlag ------------------";

 *)

 "-------- rewrite_set_ cancel_p from: Mathematik 1 Schalk Reniets Verlag -----";

 "-------- rewrite_set_ cancel_p from: Mathematik 1 Schalk Reniets Verlag -----";

 "-------- rewrite_set_ cancel_p from: Mathematik 1 Schalk Reniets Verlag -----";

 (*========== inhibit exn WN130826 TODO =========================================================

 "-------- example heuberger";

 "-------- some old tests REVISE ! --------------------------------------------";

 val t = str2term ("(x^^^4 + x * y + x^^^3 * y + y^^^2) / " ^

 "-------- some old tests REVISE ! --------------------------------------------";

   "(x + 5 * x^^^2 + y + 5 * x * y + x^^^2 * y^^^3 + x * y^^^4)");

 "-------- some old tests REVISE ! --------------------------------------------";

 val SOME (t', asm) = rewrite_set_ thy false cancel_p t;

 (*WAS --- external calculating functions test ---*)

 if (term2str t', terms2str asm) = 

 val t = str2term "((3 * x^^^2 + 6 *x + 3) / (2*x + 2))";

   ("(x ^^^ 3 + y) / (1 + 5 * x + x * y ^^^ 3)", "[\"1 + 5 * x + x * y ^^^ 3 ~= 0\"]")

 val SOME (t', asm) = factout_p_ thy t;

 then () else error "rational.sml cancel_p heuberger";

 if term2str t' = "(3 + 3 * x) * (1 + x) / (2 * (1 + x))" andalso terms2str asm = "[]"

 then () else error "factout_p_ 1 changed";

 "-------- rewrite_set_ common_nominator_p from: Mathematik 1 Schalk ----------";

 val SOME (t', asm) = cancel_p_ thy t;

 "-------- rewrite_set_ common_nominator_p from: Mathematik 1 Schalk ----------";

 if term2str t' = "(3 + 3 * x) / 2" andalso terms2str asm = "[\"1 + x ~= 0\"]"

 "-------- rewrite_set_ common_nominator_p from: Mathematik 1 Schalk ----------";

 then () else error "cancel_p_ 1 changed";

 (*deleted example 204 ... 236b at update Isabelle2012-->2013*)

 val t = str2term "((-3 * x^^^2 + 6 *x - 3) / (2*x - 2))";

 val SOME (t', asm) = factout_(*p_*) thy t;

 if term2str t' = "(3 - 3 * x) * (-1 + x) / (2 * (-1 + x))" andalso terms2str asm = "[]"

 then () else error "factout_ 2 changed";

 val SOME (t', asm) = cancel_(*p_*) thy t;

 if term2str t' = "(3 - 3 * x) / 2" andalso terms2str asm = "[\"-1 + x ~= 0\"]"

 then () else error "cancel_ 2 changed";

 val t = str2term "((x + (-1)) / (x + 1)) + ((x + 1) / (x + (-1)))";

 val SOME (t', asm) = add_fraction_p_ thy t;

 if term2str t' = "(2 + 2 * x ^^^ 2) / (-1 + x ^^^ 2)" andalso terms2str asm = "[]"

 then () else error "add_fraction_p_ 3 changed";

 val SOME (t', asm) = common_nominator_p_ thy t;

 if term2str t' = 

   "(-1 + x) * (-1 + x) / ((1 + x) * (-1 + x)) +\n(1 + x) * (1 + x) / ((1 + x) * (-1 + x))"

   andalso terms2str asm = "[]"

 then () else error "common_nominator_p_ 3 changed";

 val t = str2term "((x - 1) / (x + 1)) + ((x + 1) / (x - 1))";

 val SOME (t', asm) = add_fraction_ thy t;

 if term2str t' = "(2 + 2 * x ^^^ 2) / (-1 + x ^^^ 2)" andalso terms2str asm = "[]"

 then () else error "factout_ 4 changed";

 val SOME (t', asm) = common_nominator_ thy t;

 if term2str t' = 

   "(-1 + x) * (-1 + x) / ((1 + x) * (-1 + x)) +\n(1 + x) * (1 + x) / ((1 + x) * (-1 + x))" 

   andalso terms2str asm = "[]"

 then () else error "cancel_ 4 changed";

 val t = str2term 

   "((1) / (2*x + 2)) + ((1) / (2*x + (-2))) + ((1) / ( x^^^2 + (-1)))+((1) / (x^^^2 + (-2)*x + 1))";

 val SOME (t', asm) = add_fraction_p_ thy t;

 if term2str t' = "x / (1 + -2 * x + x ^^^ 2)" andalso terms2str asm = "[\"1 + x ~= 0\"]"

 then () else error "add_fraction_p_ 5 changed";

 val SOME (t', asm) = norm_rational_ thy t;

 if term2str t' = "x / (1 + -2 * x + x ^^^ 2)" andalso terms2str asm = "[\"1 + x ~= 0\"]"

 then () else error "norm_rational_ 5 changed";

 val t3 = (term_of o the o (parse thy)) "((1) / (2*x + 2)) + ((1) / (2*x - 2)) + ((1) / ( x^^^2 - 1))+((1) / (x^^^2 - 2 * x + 1))";

 val SOME (t3',_) = common_nominator_ thy t3; 

 val SOME (t3'',_) = add_fraction_ thy t3; 

 (term2str t3'); 

 (term2str t3''); 

 val SOME(t4,t5) = norm_expanded_rat_ thy t3;

 term2str t4;

 term2str (hd(t5));

   val t=(term_of o the o (parse thy)) "(9 - x^^^2)/(9 - 6*x + x^^^2)";

   val SOME (t',_) = factout_ thy t;

   val SOME (t'',_) = cancel_ thy t;

   term2str t';

   term2str t'';

   "(3 + x) * (3 - x) / ((3 - x) * (3 - x))";

   "(3 + x) / (3 - x)";

   val t=(term_of o the o (parse thy))

 	    "(9 - x^^^2) / (9 - 6*x + x^^^2) + 1 / (3 - x)";

   val SOME (t',_) = common_nominator_ thy t;

   val SOME (t'',_) = add_fraction_ thy t;

   term2str t';

   term2str t'';

   "(9 - x ^^^ 2) / ((3 - x) * (3 - x)) + 1 * (3 - x) / ((3 - x) * (3 - x))";

   "(4 + x) / (3 - x)";

 (*WN021016 added -----vv---*)

 val t = str2term "(9 - x^^^2) / (9 - 6*x + x^^^2) + 1";

 val SOME (t',_) = common_nominator_ thy t;

 val SOME (t'',_) = add_fraction_ thy t;

 term2str t' = "(9 - x ^^^ 2) / (9 - 6 * x + x ^^^ 2) +\n1" ^

 		" * (9 - 6 * x + x ^^^ 2) / (9 - 6 * x + x ^^^ 2)" (*true*);

 term2str t'' = "6 / (3 - x)" (*true*);

 val t = str2term "1 + (9 - x^^^2) / (9 - 6*x + x^^^2)";

 val SOME (t',_) = common_nominator_ thy t;

 val SOME (t'',_) = add_fraction_ thy t;

 term2str t' = "1 * (9 - 6 * x + x ^^^ 2) / (9 - 6 * x + x ^^^ 2) +\n" ^

 		"(9 - x ^^^ 2) / (9 - 6 * x + x ^^^ 2)" (*true*);

 term2str t'' = "6 / (3 - x)" (*true*);

 (*WN021016 added -----^^---*)

 (*WN030602 added -----vv--- no rewrite -> NONE !*)

 val t = str2term "1 / a";

 val NONE =  cancel_p_ thy t;

 val NONE = rewrite_set_ thy false cancel_p t;

 (*WN.2.6.03 added -------^^---*)

 val t = str2term "(y^^^2 - x^^^2)/(y^^^2 - 2*y*x + x^^^2)";

 val SOME (t',_) = factout_ thy t;

 val SOME (t'',_) = cancel_ thy t;

 term2str t' = "(y + x) * (y - x) / ((y - x) * (y - x))"(*true*);

 term2str t'' = "(y + x) / (y - x)";

 val t = str2term "(y^^^2 - x^^^2)/(y^^^2 - 2*y*x + x^^^2) + 1 / (y - x)";

 val SOME (t',_) = common_nominator_ thy t;

 val SOME (t'',_) = add_fraction_ thy t;

 term2str t' =

 "(-1 * x ^^^ 2 + y ^^^ 2) / ((-1 * x + y) * (-1 * x + y)) +\n1" ^

 " * (-1 * x + y) / ((-1 * x + y) * (-1 * x + y))" (*true*);

 term2str t'' = "(-1 - x - y) / (x - y)" (*true*);

 val t = str2term "(x^^^2 - y^^^2)/(x^^^2 - 2*x*y + y^^^2) + 1 / (x - y)";

 val SOME (t',_) = common_nominator_ thy t;

 val SOME (t'',_) = add_fraction_ thy t;

 if term2str t' = "(-1 * y ^^^ 2 + x ^^^ 2) / ((-1 * y + x) * (-1 * y + x))" ^

 " +\n1 * (-1 * y + x) / ((-1 * y + x) * (-1 * y + x))" then ()

 else error "rational.sml lex-ord 1";

 if term2str t'' = "(-1 - y - x) / (y - x)" then ()

 else error "rational.sml lex-ord 2";

 (*WN.16.10.02 WN070905 lexicographische Ordnung erhalten *)

 val t = str2term "(x^^^2 - y^^^2)/(x^^^2 - 2*x*y + y^^^2)";

 val SOME (t',_) = norm_expanded_rat_ thy t; 

 if term2str t' = "(x + y) / (x - y)" then ()

 else error "rational.sml term2poly: invalid x ^^^ 2 - y ^^^ 2 No.1";

 (*val SOME (t'',_) = norm_rational_ thy t;

  *** RATIONALS_TERM2POLY_EXCEPTION: Invalid Polynomial 

 WN.16.10.02 ?! + WN060831???SK4 

 WN070905 *** term2poly: invalid = x ^^^ 2 - y ^^^ 2*)

 val t = str2term "(9 - x^^^2)/(9 - 6*x + x^^^2) + (1)/(3 + x)";

 val SOME (t',_) = norm_expanded_rat_ thy t;

 if term2str t' = "(12 + 5 * x + x ^^^ 2) / (9 - x ^^^ 2)" then ()

 else error "rational.sml (9 - x^^^2)/(9 - 6*x + x^^^2) +...";

 (*val SOME (t'',_) = norm_rational_ thy t;

   *** RATIONALS_TERM2POLY_EXCEPTION: Invalid Polynomial WN.16.10.02 ?!

 WN070906 *** term2poly: invalid = 9 - x ^^^ 2 SK.term2poly*)

   val t=(term_of o the o (parse thy)) 

 	    "(9 + (-1)* x^^^2)/(9 + (-1)* 6*x + x^^^2) + (1)/(3 + x)";

   val SOME (t',_) = norm_expanded_rat_ thy t;

   val SOME (t'',_) = norm_rational_ thy t;

   term2str t';

   term2str t'';

   "(12 + 5 * x + x ^^^ 2) / (9 - x ^^^ 2)";

   "(12 + 5 * x + x ^^^ 2) / (9 + (-1) * x ^^^ 2)";

 "-------- cancel from: Mathematik 1 Schalk Reniets Verlag";

 "-------- cancel from: Mathematik 1 Schalk Reniets Verlag";

 "-------- cancel from: Mathematik 1 Schalk Reniets Verlag";

 val thy  = @{theory "Rational"};

 val thy' = "Rational";

 val rls' = "cancel";

 val mp = "make_polynomial";

 writeln ("example 186:");

 writeln("a)");

 val e186a'="(14 * x * y) / ( x * y )";(*SRC*)

 rewrite_set_ thy false cancel (str2term e186a');

 "@@@@@@@@@@@@@@";

 val e186a = the (rewrite_set thy' false "cancel" e186a');

   is_expanded (parse_rat "14 * x * y");

   is_expanded (parse_rat "x * y");

 if e186a = ("14 / 1", "[\"y * x ~= 0\"]") then ()

 else error "rational.sml cancel Schalk e186a";

 writeln("b)");

 val e186b'="(60 * a * b) / ( 15 * a  * b )";

 val e186b = the (rewrite_set thy' false "cancel" e186b');

 writeln("c)");

 val e186c'="(144 * a^^^2 * b * c) / (12 * a * b * c )";

 val e186c = (the (rewrite_set thy' false "cancel" e186c'))

     handle e => print_exn_G e;

 val t = (term_of o the o (parse thy)) e186c';

 if e186c = ("12 * a / 1", "[\"12 * (c * (b * a)) ~= 0\"]") then ()

 else error "rational.sml cancel Schalk e186c";

 writeln ("example 187:");

 writeln("a)");

 val e187a'="(12 * x * y) / (8 * y^^^2 )";(*SRC*)

 val e187a = the (rewrite_set thy' false "cancel" e187a');

 writeln("b)");

 val e187b'="(8 * x^^^2 * y * z ) / (18 * x * y^^^2 * z )";

 val e187b = the (rewrite_set thy' false "cancel" e187b');

 writeln("c)");

 val e187d'="(9 * x^^^5 * y^^^2 * z^^^4) / (15 * x^^^6 * y^^^3 * z )";(*SRC*)

 val e187d = the (rewrite_set thy' false "cancel" e187d');

 if e187d = ("3 * z ^^^ 3 / (5 * (y * x))",

             "[\"3 * (z * (y ^^^ 2 * x ^^^ 5)) ~= 0\"]") then ()

 else error "rational.sml cancel Schalk e186d";

 writeln "example 188:";

 val e188a'="(-8 + 8 * x) / (-9 + 9 * x)";(*SRC*)

 val e188a = the (rewrite_set thy' false "cancel" e188a');

   is_expanded (parse_rat "8 * x + -8");

 (* e188a = ("8 / 9",["not ((-1) + x = 0)"]) then () 13.3.03*)

 if e188a = ("8 / 9", "[\"-1 + x ~= 0\"]") then ()

 else error "rational.sml: e188a new behaviour";

 val SOME (t,_) = rewrite_set thy' false mp "(8*((-1) + x))/(9*((-1) + x))";

 writeln("b)");

 val e188b'="(-15 + 5 * x) / (-18 + 6 * x)";(*SRC*)

 val SOME (t, asm) = rewrite_set thy' false "cancel" e188b';

 t = "5 / 6" (*true*);

 writeln("c)");

 val e188c'="( a + -1 * b ) / ( b + -1 * a )";

 val e188c = the (rewrite_set thy' false "cancel_p" e188c');

 (*is_expanded (parse_rat "a + -1 * b");*)

 val SOME (t,_) = 

     rewrite_set thy' false mp "((-1)*(b + (-1) * a))/(1*(b + (-1) * a))";

 if t= "(a + -1 * b) / (-1 * a + b)"  then()

 else error "rational.sml: e188c new behaviour";

 writeln ("example 190:");

 writeln("c)");

 val e190c'="( 27 * a^^^3 + 9 * a^^^2 + 3 * a + 1 ) / ( 27 * a^^^3 + 18 * a^^^2 + 3 * a )";

 val e190c = the (rewrite_set thy' false "cancel" e190c');

 val SOME (t,_) = rewrite_set thy' false mp "((1 + 9 * a ^^^ 2)*(1 + 3 * a))/((3 * a + 9 * a ^^^ 2)*(1 + 3 * a))";

 if t = "(1 + 3 * a + 9 * a ^^^ 2 + 27 * a ^^^ 3) /\n(3 * a + 18 * a ^^^ 2 + 27 * a ^^^ 3)" then ()

 else error "rational.sml: e190c new behaviour";

 writeln ("example 191:");

 writeln("a)");

 val e191a'="( x^^^2 + -1 * y^^^2 ) / ( x + y )";

 (*WN.23.10.02-------

 val e191a = the (rewrite_set thy' false "cancel" e191a'); 

   is_expanded (parse_rat "x^^^2 + -1 * y^^^2");

   false;

   is_expanded (parse_rat "x + y");

   true; -----------*)

 val SOME (t,_) = rewrite_set thy' false mp "((x + (-1) * y)*(x + y))/((1)*(x + y))";

 (* t="(x ^^^ 2 + -1 * y ^^^ 2) / (x + y)" then() WN.13.3.03*)

 if t="(x ^^^ 2 + -1 * y ^^^ 2) / (x + y)" then()

 else error "rational.sml: e191a new behaviour";

 writeln("c)");

 val e191c'="( 9 * x^^^2 + -30 * x + 25 ) / ( 9 * x^^^2 + -25 )";

 (*WN.23.10.02-------

 val e191c = the (rewrite_set thy' false "cancel" e191c');

   is_expanded (parse_rat "9 * x^^^2 + -30 * x + 25");

   false;

   is_expanded (parse_rat "25 + -30*x + 9*x^^^2");

   false;

   is_expanded (parse_rat "-25 + 9*x^^^2");

   true;------------*)

 val SOME (t,_) = rewrite_set thy' false mp "(((-5) + 3 * x)*((-5) + 3 * x))/((5 + 3 * x)*((-5) + 3 * x))";

 (* t="(25 + ((-30) * x + 9 * x ^^^ 2)) / ((-25) + 9 * x ^^^ 2)"then() 13.3.03*)

 if t= "(25 + -30 * x + 9 * x ^^^ 2) / (-25 + 9 * x ^^^ 2)" then()

 else error "rational.sml: 'e191c' new behaviour";

 writeln ("example 192:");

 writeln("b)");

 val e192b'="( 7 * x^^^3 + -1 * x^^^2 * y ) / ( 7 * x * y^^^2 + -1 *  y^^^3 )";

 (*WN.23.10.02-------

 val e192b = the (rewrite_set thy' false "cancel" e192b');

 -------------------*)

 val SOME (t',_) = rewrite_set thy' false mp "((x ^^^ 2)*(7 * x + (-1) * y))/((y ^^^ 2)*(7 * x + (-1) * y))";

 (*========== inhibit exn 110317 ================================================

 if t' = "(7 * x ^^^ 3 + -1 * x ^^^ 2 * y) / (7 * x * y ^^^ 2 + -1 * y ^^^ 3)"

 (*"(-1 * y * x ^^^ 2 + 7 * x ^^^ 3) / (-1 * y ^^^ 3 + 7 * x * y ^^^ 2)"WN050929*)

 then () else error "rational.sml: 'e192b' new behaviour";

 (*^^^ works with MG's simplifier vvv*)

 val t =str2term"((x ^^^ 2)*(7 * x + (-1) * y))/((y ^^^ 2)*(7 * x + (-1) * y))";

 val SOME (t',_) = rewrite_set_ thy false make_polynomial t;

 if term2str t' = "(7 * x ^^^ 3 + -1 * x ^^^ 2 * y) / (7 * x * y ^^^ 2 + -1 * y ^^^ 3)" then () else error "rational.sml: 'e192b'MG new behaviour";

 ============ inhibit exn 110317 ==============================================*)

 writeln ("example 193:");

 writeln("a)");

 val e193a'="( x^^^2 + -6 * x + 9 ) / ( x^^^2 + -9 )";

 (*WN.23.10.02-------

 val e193a = the (rewrite_set thy' false "cancel" e193a');

 -------------------*)

 writeln("b)");

 val e193b'="( x^^^2 + -8 * x + 16 ) / ( 2 * x^^^2 + -32 )";

 (*WN.23.10.02-------

 val e193b = the (rewrite_set thy' false "cancel" e193b');

 writeln("c)");

 val e193c'="( 2 * x + -50 * x^^^3 ) / ( 25 * x^^^2 + -10 * x + 1 )";

 val SOME(t,_) = rewrite_set thy' false "cancel" e193c';

 -------------------*)

 val wn01 = "(-25 + 9*x^^^2)/(5 + 3*x)";

 val SOME (t, asm) = rewrite_set thy' false "cancel" wn01;

 (* t = "((-5) + 3 * x) / 1" then () WN.13.3.03*)

 if t = "(-5 + 3 * x) / 1" andalso asm = "[\"5 + 3 * x ~= 0\"]" then ()

 else error "rational.sml: new behav. in cancel wn01";

 "-------- common_nominator_p ----------------------------";

 "-------- common_nominator_p ----------------------------";

 "-------- common_nominator_p ----------------------------";

 val rls' = "common_nominator_p";

 writeln ("example 204:");

 writeln("a)");

 val e204a'="((5 * x) / 9) + ((3 * x) / 9) + (x / 9)";

 val e204a = the (rewrite_set thy' false "common_nominator_p" e204a');

 writeln("b)");

 val e204b'="5 / x + -3 / x + -1 / x";

 val e204b = the (rewrite_set thy' false "common_nominator_p" e204b');

 if e204b = ("1 / x", "[]") then ()

 else error "rational.sml common_nominator_p example e204b";

 writeln ("example 205:");

 writeln("a)");

 val e205a'="((4 * x + 7) / 8) + ((4 * x + 3) / 8)";

 val e205a = the (rewrite_set thy' false "common_nominator_p" e205a');

 writeln("b)");

 val e205b'="((5 * x + 2) / 3) + ((-2 * x + 1) / 3)";

 val e205b = the (rewrite_set thy' false "common_nominator_p" e205b');

 if e205b = ("(1 + x) / 1", "[]") then ()

 else error "rational.sml common_nominator_p example e204b";

 writeln ("example 206:");

 writeln("a)");

 val e206a'="((5 * x + 4) / (2 * x + -1)) + ((9 * x + 5) / (2 * x + -1))";

 val e206a = the (rewrite_set thy' false "common_nominator_p" e206a'); 

 writeln("b)");

 val e206b'="((17 * x + -23) / (5 * x + 4)) + ((-25 + -17 * x) / (5 * x + 4))";

 val e206b = the (rewrite_set thy' false "common_nominator_p" e206b');

 writeln ("example 207:");

 val e207'="((3 * x * y + 3 * y) / (x * y)) + ((5 * x * y + 7 * y) / (x * y)) + ((9 * x * y + -2 * y) / (x * y)) + ((x * y + 4 * y) / (x * y)) ";

 val e207 = the (rewrite_set thy' false "common_nominator_p" e207'); 

 writeln ("example 208:");

 val e208'="((3 * x + 2) / (x + 2)) + ((5 * x + -1) / (x + 2)) + ((-7 * x + -3) / (x + 2)) + ((-1 * x + -3) / (x + 2)) ";

 val e208 = the (rewrite_set thy' false "common_nominator_p" e208'); 

 writeln ("example 209:");

 val e209'="((3 * x + -7 * y + 3 * z) / (4)) + ((2 * x + 17 * y + 10 * z) / (4)) + ((-1 * x + 2 * y + z) / (4)) ";

 val e209 = the (rewrite_set thy' false "common_nominator_p" e209'); 

 writeln ("example 210:");

 val e210'="((2 * x + 3 +  -1 * x^^^2) / (5 * x)) + ((5 * x^^^2 + -2 * x + 1) / (5 * x)) + ((-3 * x^^^2 + -2 * x + 1) / (5 * x)) + ((-1 * x^^^2 + -3 * x + -5) / (5 * x)) ";

 val e210 = the (rewrite_set thy' false "common_nominator_p" e210'); 

 writeln ("example 211:");

 writeln("a)"); 

 val e211a'="((b) / (a + -1 * b)) + ((-1 * a) / (a + -1 * b))"; 

 val e211a = the (rewrite_set thy' false "common_nominator_p" e211a'); 

 writeln("b)");

 val e211b'="((b) / (b^^^2 + -1 * a^^^2)) + ((-1 * a) / (b^^^2 + -1 * a^^^2))";

 val e211b = the (rewrite_set thy' false "common_nominator_p" e211b');

 writeln ("example 212:");

 writeln("a)");

 val e212a'="((4) / (x)) + ((-3) / (y)) + -1";

 val e212a = the (rewrite_set thy' false "common_nominator_p" e212a'); 

 writeln("b)");

 val e212b'="((4) / (x)) + ((-5) / (y)) + ((6) / (x*y))";

 val e212b = the (rewrite_set thy' false "common_nominator_p" e212b');

 writeln ("example 213:");

 writeln("a)"); 

 val e213a'="((5 * x) / (3 * y^^^2)) + ((19 * z) / (6 * x * y)) +  ((-2 * x) / (3 * y^^^2)) + ((7 * y^^^2) / (6 * x^^^2)) ";

 val e213a = the (rewrite_set thy' false "common_nominator_p" e213a'); 

 writeln("b)"); 

 val e213b'="((2 * b) / (3 * a^^^2)) + ((3 * c) / (7 * a * b)) +  ((4 * b) / (3 * a^^^2)) + ((3 * a) / (7 * b^^^2))";

 val e213b = the (rewrite_set thy' false "common_nominator_p" e213b');

 writeln ("example 214:");

 writeln("a)");

 val e214a'="((3 * x + 2 * y + 2 * z) / (4)) + ((-5 * x + -3 * y) / (3)) + ((x + y + -2 * z) / (2))";

 val e214a = the (rewrite_set thy' false "common_nominator_p" e214a'); 

 writeln("b)");

 val e214b'="((5 * x + 2 * y + z) / (2)) + ((-7 * x + -3 * y) / (3)) + ((3 * x + 6 * y + -1 * z) / (12))";

 val e214b = the (rewrite_set thy' false "common_nominator_p" e214b');

 writeln ("example 216:");

 writeln("a)"); 

 val e216a'="((2 * b + 3 * c) / (a * c)) + ((3 * a + b) / (a * b)) + ((-2 * b^^^2 + -3 * a * c) / (a * b * c))";

 val e216a = the (rewrite_set thy' false "common_nominator_p" e216a');  

 writeln("b)");

 val e216b'="((2 * a + 3 * b) / (b * c)) + ((3 * c + a) / (a * c)) + ((-2 * a^^^2 + -3 * b * c) / (a * b * c))";

 val e216b = the (rewrite_set thy' false "common_nominator_p" e216b');

 writeln ("example 217:");

 val e217'="((z + -1) / (z)) + ((3 * z ^^^2 + -6 * z + 5) / (z^^^2)) + ((-4 * z^^^3 + 7 * z^^^2 + -5 * z + 5) / (z^^^3))";

 val e217 = the (rewrite_set thy' false "common_nominator_p" e217'); 

 val rls' = "common_nominator";

 writeln ("example 218:"); 

 val e218'="((9 * a^^^3 - 5 * a^^^2 + 2 * a + 8) / (108 * a^^^4)) + ((-5 * a + 3 * a^^^2 + 4) / (8 * a^^^3)) + ((-261 * a^^^3 + 19 * a^^^2 + -112 * a + 16) / (216 * a^^^4))";

 val e218 = the (rewrite_set thy' false "common_nominator" e218'); 

 if e218 = ("(16 - 63 * a ^^^ 2 - 81 * a ^^^ 3) / (108 * a ^^^ 4)", "[]") then ()

 else error "rationa.sml common_nominator example e218";

 writeln ("example 219:");

 writeln("a)");

 val e219a'="((1) / (y + 1)) + ((1) / (y + 2)) + ((1) / (y + 3))";

 val e219a = the (rewrite_set thy' false "common_nominator" e219a');

 writeln("b)");

 val e219b'="((1) / (x + 1)) + ((1) / (x + 2)) + ((-2) / (x + 3))";

 val e219b = the (rewrite_set thy' false "common_nominator" e219b'); 

 if e219b = ("(5 + 3 * x) / (6 + 11 * x + 6 * x ^^^ 2 + x ^^^ 3)", "[]") then ()

 else error "rationa.sml common_nominator example e219b";

 writeln ("example 220:");

 writeln("a)");

 val e220a'="((17) / (5 * r + -2)) + ((-13) / (2 * r + 3)) + ((4) / (3 * r + -5))";

 val e220a = the (rewrite_set thy' false "common_nominator" e220a');

 writeln("b)");

 val e220b'="((20 * a) / (a + -3)) + ((-19 * a) / (a + -4)) + ((a) / (a + -5))";

 val e220b = the (rewrite_set thy' false "common_nominator" e220b'); 

 writeln ("example 221:");

 writeln("a)");

 val e221a'="((a + b) / (a + -1 * b)) + ((a + -1 * b) / (a + b))";

 val e221a = the (rewrite_set thy' false "common_nominator" e221a');

 writeln("b)");

 val e221b'="((x + -1 * y) / (x + y)) + ((x + y) / (x + -1 * y)) ";

 val e221b = the (rewrite_set thy' false "common_nominator" e221b');

 writeln ("example 222:");

 writeln("a)");

 val e222a'="((1 + -1 * x) / (1 + x)) + ((-1 + -1 * x) / (1 + -1 * x)) + ((4 * x) / (1 + -1 * x^^^2))";

 val e222a = the (rewrite_set thy' false "common_nominator" e222a');

 writeln("b)");

 val e222b'="((1 + x ) / (1 + -1 * x)) + ((-1 + x) / (1 + x)) + ((2 * x) / (1 + -1 * x^^^2))";

 val e222b = the (rewrite_set thy' false "common_nominator" e222b'); 

 writeln ("example 225:");

 writeln("a)");

 val e225a'="((6 * a) / (a^^^2 + -64)) + ((a + 2) / (2 * a + 16)) + ((-1) / (2))";

 val e225a = the (rewrite_set thy' false "common_nominator" e225a');

 writeln("b)");

 val e225b'="((a + 2 ) / (2 * a + 12)) + ((4 * a) / (a^^^2 + -36)) + ((-1) / (2))";

 val e225b = the (rewrite_set thy' false "common_nominator" e225b'); 

 writeln ("example 226:");

 writeln("a)");

 val e226a'="((35 * z) / (49 * z^^^2 + -4)) + -1 + ((14 * z + -1) / (14 * z + 4)) ";

 val e226a = the (rewrite_set thy' false "common_nominator" e226a');

 writeln("b)"); 

 val e226b'="((45 * a * b) / (25 * a^^^2 + -9 * b^^^2)) + ((20 * a + 3 * b) / (10 * a + 6 * b))  + -2";

 val e226b = the (rewrite_set thy' false "common_nominator" e226b');  

 writeln ("example 227:");

 writeln("a)");

 val e227a'="((6 * z + 11) / (6 * z + 14)) + ((9 * z ) / (9 * z^^^2 + -49)) + -1 ";

 val e227a = the (rewrite_set thy' false "common_nominator" e227a');

 writeln("b)");

 val e227b'="((16 * a + 37 * b) / (4 * a + 10 * b)) + ((6 * a * b) / (4 * a^^^2 + -25 * b^^^2)) + -4 ";

 val e227b = the (rewrite_set thy' false "common_nominator" e227b'); 

 writeln ("example 228:");

 writeln("a)");

 val e228a'="((7 * a + 11) / (3 * a^^^2 + -3)) + ((-2 * a + -1) / (a^^^2 + -1 * a)) + ((-1) / (3 * a + 3))";

 val e228a = the (rewrite_set thy' false "common_nominator" e228a'); 

 writeln("b)");

 val e228b'="((11 * z + 2 * b) / (4 * b * z + -8 * b^^^2)) + ((-8 * z) / (z^^^2 + -4 * b^^^2)) + ((-9 * z + -2 * b) / (4 * b * z + 8 * b^^^2))";

 val e228b = the (rewrite_set thy' false "common_nominator" e228b');  

 writeln ("example 229:");

 writeln("a)");

 val e229a'="((5 * x^^^2 + y) / (x + 2 * y)) + ((-8 * x^^^3 + 4 * x^^^2 * y + 3 * x * y) / (x^^^2 + -4 * y^^^2)) + ((3 * x^^^2 + -4 * y) / (x + -2 * y))";

 val e229a = the (rewrite_set thy' false "common_nominator" e229a'); 

 writeln("b)");

 val e229b'="((7 * x^^^2 + y) / (x + 3 * y)) + ((-24 * x^^^2 * y + 5 * x * y + 21 * y^^^2) / (x^^^2 + -9 * y^^^2)) + ((4 * x^^^2 + -6 * y) / (x + -3 * y))"; 

 val e229b = the (rewrite_set thy' false "common_nominator" e229b'); 

 writeln ("example 230:");

 writeln("a)"); 

 val e230a'="((5 * x^^^2 + y) / (2 * x + y)) + ((-16 * x^^^3 + 2 * x^^^2 * y + 6 * x * y) / (4 * x^^^2 + -1 * y^^^2)) + ((3 * x^^^2 + -4 * y) / (2 * x + -1 * y))";

 val e230a = the (rewrite_set thy' false "common_nominator" e230a');

 writeln("b)");

 val e230b'="((7 * x^^^2 + y) / (3 * x + y)) + ((-3 * x^^^3  + 15 * x * y + -7 * x^^^2 * y + 7 * y^^^2) / (9 * x^^^2 + -1 * y^^^2)) + ((4 * x^^^2 + -6 * y) / (3 * x + -1 * y))";

 val e230b = the (rewrite_set thy' false "common_nominator" e230b');

 writeln ("example 231:");

 writeln("a)");

 val e231a'="((2 * x + 5 * y) / (x)) + ((2 * x^^^3 + -5 * y^^^3 + 3 * x * y^^^2) / (x^^^3 + -2 * x^^^2 * y + x * y^^^2)) + ((-3 * x + -6 * y) / (x + -1 * y))";

 val e231a = the (rewrite_set thy' false "common_nominator" e231a'); 

 writeln("b)");

 val e231b'="((6 * x + 2 * y) / (x)) + ((6 * x^^^2 * y + -4 * x * y^^^2 + -2 * y^^^3) / (x^^^3 + -2 * x^^^2 * y + x * y^^^2)) + ((-5 * x + -3 * y) / (x + -1 * y))";

 val e231b = the (rewrite_set thy' false "common_nominator" e231b');

 writeln ("example 232:");

 writeln("a)");

 val e232a'="((2 * x + 3 * y) / (x)) + ((4 * x^^^3 + -1 * x * y^^^2 + -3 * y^^^3) / (x^^^3 + -2 * x^^^2 * y + x * y^^^2)) + ((-5 * x + -6 * y) / (x + -1 * y))";

 val e232a = the (rewrite_set thy' false "common_nominator" e232a'); 

 writeln("b)");

 val e232b'="((5 * x + 2 * y) / (x)) + ((2 * x^^^3 + -3 * x * y^^^2 + 3 * x^^^2 * y + -2 * y^^^3) / (x^^^3 + -2 * x^^^2 * y + x * y^^^2)) + ((-6 * x + -3 * y) / (x + -1 * y))";

 val e232b = the (rewrite_set thy' false "common_nominator" e232b');

 writeln ("example 233:");

 writeln("a)");

 val e233a'="((5 * x + 6 * y) / (x)) + ((5 * x * y^^^2 + -6 * y^^^3 + -2 * x^^^3 + 3 * x^^^2 * y) / (x^^^3 + -2 * x^^^2 * y + x * y^^^2)) + ((-2 * x + -3 * y) / (x + -1 * y))";

 val e233a = the (rewrite_set thy' false "common_nominator" e233a'); 

 writeln("b)");

 val e233b'="((6 * x + 5 * y) / (x)) + ((4 * x^^^2 * y + 3 * x * y^^^2 + -5 * y^^^3 + -2 * x^^^3) / (x^^^3 + -2 * x^^^2 * y + x * y^^^2)) + ((-3 * x + -2 * y) / (x + -1 * y))";

 val e233b = the (rewrite_set thy' false "common_nominator" e233b');

 writeln ("example 234:");

 writeln("a)");

 val e234a'="((5 * a + b) / (2 * a * b + -2 * b^^^2)) + ((-3 * a + -1 * b) / (2 * a * b + 2 * b^^^2)) + ((-2 * a) / (a^^^2 + -1 * b^^^2))";

 val e234a = the (rewrite_set thy' false "common_nominator" e234a'); 

 writeln("b)"); 

 val e234b'="((5 * a + 3 * b) / (6 * a * b + -18 * b^^^2)) + ((-3 * a + -3 * b) / (6 * a * b + 18 * b^^^2)) + ((-2 * a) / (a^^^2 + -9 * b^^^2)) ";

 val e234b = the (rewrite_set thy' false "common_nominator" e234b');  

 writeln ("example 235:");

 writeln("a)");

 val e235a'="((10 * x + 3 * y) / (12 * x * y + -18 * y^^^2)) + ((-6 * x + -3 * y) / (12 * x * y + 18 * y^^^2)) + ((-4 * x) / (4 * x^^^2 + -9 * y^^^2))";

 val e235a = the (rewrite_set thy' false "common_nominator" e235a'); 

 writeln("b)"); 

 val e235b'="((8 * a + b) / (4 * a * b + -2 * b^^^2)) + ((-4 * a + -1 * b) / (4 * a * b + 2 * b^^^2)) + ((-2 * a) / (4 * a^^^2 + -1 * b^^^2)) ";

 val e235b = the (rewrite_set thy' false "common_nominator" e235b');  

 writeln ("example 236:");

 writeln("a)"); 

 val e236a'="((8 * a + 5 * b) / (20 * a * b + -50 * b^^^2)) + ((-4 * a + -5 * b) / (20 * a * b + 50 * b^^^2)) + ((-2 * a) / (4 * a^^^2 + -25 * b^^^2))";

 val e236a = the (rewrite_set thy' false "common_nominator" e236a');  

 writeln("b)");   

 val e236b'="((24 * x + y) / (6 * x * y + -2 * y^^^2)) + ((-18 * x + -1 * y) / (6 * x * y + 2 * y^^^2)) + ((-15 * x) / (9 * x^^^2 + -1 * y^^^2)) ";

 val e236b = the (rewrite_set thy' false "common_nominator" e236b');  

 val rls' = "cancel";

 writeln ("example heuberger:");

 val eheu'="(x^^^4 + x * y + x^^^3 * y + y^^^2) / (x + 5 * x^^^2 + y + 5 * x * y + x^^^2 * y^^^3 + x * y^^^4)";

 val eheu = the (rewrite_set thy' false "cancel" eheu');

 val rls' = "common_nominator_p";

 writeln ("example stiefel:");

 val est1'="(7) / (-14) + (-2) / (4)";

 val est1 = the (rewrite_set thy' false "common_nominator_p" est1');

 if est1 = ("-1 / 1", "[]") then ()

 else error "new behaviour in rational.sml: est1'";

 val t = (term_of o the o (parse thy))

 "(9 - x ^^^ 2) / (9 - 6 * x + x ^^^ 2)";

 val SOME (t',_) = factout_ thy t;

 if term2str t' = "(3 + x) * (3 - x) / ((3 - x) * (3 - x))" then ()

 else error "rational.sml factout_ (9 - x ^^^ 2) / (9 - 6 * x + x ^^^ 2)";

 "-------- reverse rewrite -------------------------------";

 "-------- reverse rewrite ----------------------------------------------------";

 "-------- reverse rewrite -------------------------------";

 "-------- reverse rewrite ----------------------------------------------------";

 "-------- reverse rewrite -------------------------------";

 "-------- reverse rewrite ----------------------------------------------------";

 (*WN.28.8.02: tests for the 'reverse-rewrite' functions:

 (** the term for which reverse rewriting is demonstrated **)

   these are defined in Rationals.ML and stored in 

 val t = str2term "(9 + -1 * x ^^^ 2) / (9 + 6 * x + x ^^^ 2)";

   the 'reverse-ruleset' cancel*)

 val Rrls {scr = Rfuns {init_state = ini, locate_rule = loc,

   next_rule = nex, normal_form = nor, ...},...} = cancel_p;

 (*the term for which reverse rewriting is demonstrated*)

   val t = (term_of o the o (parse thy))

 (** normal_form produces the result in ONE step **)

 	      "(9 - x ^^^ 2) / (9 + 6 * x + x ^^^ 2)";

   val Rrls {scr=Rfuns {init_state=ini,locate_rule=loc,

   		       next_rule=nex,normal_form=nor,...},...} = cancel;

 (*normal_form produces the result in ONE step*)

 if term2str t' = "(3 - x) / (3 + x)" then ()

 if term2str t' = "(3 + -1 * x) / (3 + x)" then ()

 (*initialize the interpreter state used by the 'me'*)

 (** initialize the interpreter state used by the 'me' **)

   val (t,_,revsets,_) = ini t;

   val (t, _, revsets, _) = ini t;

 (*find the rule 'r' to apply to term 't'*)

 if length (hd revsets) = 11 then () else error "length of revset changed";

 if (revsets |> nth 1 |> nth 1 |> id_of_thm) = 

   (@{thm realpow_twoI} |> string_of_thm |> thmID_of_derivation_name)

 then () else error "first element of revset changed";

 if

 (revsets |> nth 1 |> nth 1 |> rule2str) = "Thm (\"realpow_twoI\",??.unknown)" andalso

 (revsets |> nth 1 |> nth 2 |> rule2str) = 

   "Thm (\"sym_#power_Float ((3,0), (0,0)) __ ((2,0), (0,0))\",??.unknown)" andalso

 (revsets |> nth 1 |> nth 3 |> rule2str) = 

   "Thm (\"sym_#mult_Float ((2,0), (0,0)) __ ((3,0), (0,0))\",??.unknown)" andalso

 (revsets |> nth 1 |> nth 4 |> rule2str) = 

   "Thm (\"sym_#mult_Float ((~1,0), (0,0)) __ ((3,0), (0,0))\",??.unknown)" andalso

 (revsets |> nth 1 |> nth 5 |> rule2str) = 

   "Thm (\"sym_#mult_Float ((3,0), (0,0)) __ ((3,0), (0,0))\",??.unknown)" andalso

 (revsets |> nth 1 |> nth 6 |> rule2str) = "Rls_ (\"sym_order_mult_rls_\")" andalso

 (revsets |> nth 1 |> nth 7 |> rule2str) = 

   "Thm (\"sym_mult_assoc\",Groups.semigroup_mult_class.mult_assoc)"

 then () else error "first 7 elements in revset changed"

 (** find the rule 'r' to apply to term 't' **)

 (*/------- since cancel_ (accepted "-" between monomials) has been replaced by cancel_p_ 

   for Isabelle2013, we don't get a working revset, but non-termination:

 (* before Isa02->09-2 was not checked automatically, ?was different?:

 \---------------------------------------------------------------------------------------/*)

 val SOME r = nex revsets t;

 val r = Thm ("sym_#mult_2_3","6 = 2 * 3") : rule*)

 (** check, if the rule 'r' applied by the user to 't' belongs to the ruleset;

 (* check, if the rule 'r' applied by the user to 't' belongs to the ruleset;

   which are listed after the head in reverse order *)

   which are listed after the head in reverse order **)

 (*/-------------------------------------------- Isabelle2013: this gives "error id_of_thm";

   we don't repair this, because interaction within "reverse rewriting" never worked properly:

 then () 

 then () else error "rational.sml locate_rule (9 - x ^^^ 2) / (9 - 6 * x + x ^^^ 2)";

 else error "rational.sml locate_rule (9 - x ^^^ 2) / (9 - 6 * x + x ^^^ 2)";

 \--------------------------------------------------------------------------------------/*)

 "-------- 'reverse-ruleset' cancel_p --------------------";

 "-------- 'reverse-ruleset' cancel_p --------------------";

 "-------- 'reverse-ruleset' cancel_p -----------------------------------------";

 "-------- 'reverse-ruleset' cancel_p --------------------";

 "-------- 'reverse-ruleset' cancel_p -----------------------------------------";

 (*WN.11.9.02: the 'reverse-ruleset' cancel_p*)

 "-------- 'reverse-ruleset' cancel_p -----------------------------------------";

 (*Isabelle2013: the example below shows, why "reverse rewriting" only worked for

   special cases.*)

 *)

 *)                    

 writeln "******************  all tests successfull  *************************";

 (*========== inhibit exn WN130824 TODO =======================================================

 "-------- examples: rls norm_Rational ----------------------------------------";

 "-------- examples: rls norm_Rational ----------------------------------------";

 "-------- examples: rls norm_Rational ----------------------------------------";

 (*WN.17.3.03 =========================================================vvv---*)

 "-------- norm_Rational ---------------------------------";

 "-------- norm_Rational ---------------------------------";

 "-------- norm_Rational ---------------------------------";

 (* nonterm.SK

 (* nonterm.SK = WN130830

 trace_rewrite := true;

 trace_rewrite := false;

 "--- 1 ---: non-terminating with ### add_fract: done t22 ";

 "--- 1 ---: non-terminating with ### add_fract: done t22 "; = WN130830

 trace_rewrite:= true;

 trace_rewrite := false;