(* use"../smltest/IsacKnowledge/rlang.sml";

   use"rlang.sml";

   *)

(******************************************************************

WN.060104 transfer marked (*E..*)examples to the exp-collection

 # exp_IsacCore_Equ_Uni_Poly.xml   from rlang.sml    (*EP*)   exp

 # exp_IsacCore_Equ_Uni_Rat.xml    from rlang.sml    (*ER*)   exp

 # exp_IsacCore_Equ_Uni_Root.xml   from rlang.sml    (*EO*)   exp

*******************************************************************)

(*WN.12.6.03: for TODOs search 'writeln', for simplification search MG*)

(* use"kbtest/rlang.sml";

   use"rlang.sml";

   (c) Richard Lang 2003

   tests over all equations implemented in his diploma thesis

   Elementare Gleichungen der Mittelschulmathematik in der ISAC Wissensbasis,

   Master's thesis, University of Technology, Graz, Austria, March 2003.

   created: 030228

   by: rlang

   last change: 030603

*)

(*@Book{bSchalk1,

  author =       {Schalk, Heinz-Christian and Binder, Christian and Fertl, Walter and 

                  Firneis, Friedrich and Gems, Werner and Lehner, Dieter and 

                  Plihal, Andreas and Würl,Manfred},

  title =        {Mathematik für höhere technische Lehranstalten Band I},

  publisher =    {Reniets Verlag},

  year =         {1986},

  note =         {Schulbuch-Nr. 942},

}

@Book{bSchalk2,

  author =       {Schalk, Heinz-Christian and Baumgartner, Gerhard and Binder, Christian and 

                  Eder, Hans Gerhard and Fertl, Walter and Firneis, Friedrich and 

                  Konstantiniuk, Peter and Plihal, Andreas and Rümmele, Goswin and 

                  Steinwender, Andreas and Zangerl, Nikolaus},

  title =        {Mathematik für höhere technische Lehranstalten Band II},

  publisher =    {Reniets Verlag},

  year =         {1987},

  note =         {Schulbuch-Nr. 1682},

}

*)

(* Compiler.Control.Print.printDepth:=5; (*4 default*) 

trace_rewrite:=true;

 trace_rewrite:=false;

 refine fmz ["univariate","equation"];

*)

"---- rlang.sml begin-----------------------------------";

(*-----------------  Schalk I s.86 Bsp 5 ------------------------*)

"Schalk I s.86 Bsp 5 (3*x - 1 - (5*x - (2 - 4*x)) = -11)";

"Schalk I s.86 Bsp 5 (3*x - 1 - (5*x - (2 - 4*x)) = -11)";

"Schalk I s.86 Bsp 5 (3*x - 1 - (5*x - (2 - 4*x)) = -11)";

(*EP*)

val fmz = ["equality (3*x - 1 - (5*x - (2 - 4*x)) = -11)",

	   "solveFor x","solutions L"];

val (dI',pI',mI') = ("PolyEq",["univariate","equation"],["no_met"]);

(*val p = e_pos'; 

val c = []; 

val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));

val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)

val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2]")) => ()

	 | _ => raise error "rlang.sml: diff.behav. in Schalk I s.86 Bsp 5 [x = 2]";

(*-----------------  Schalk I s.86 Bsp 19 ------------------------*)

"Schalk I s.86 Bsp 19 (x - 5)*(10 - x) = (3 - x)*(2 + x) + 2*(x + 20)";

"Schalk I s.86 Bsp 19 (x - 5)*(10 - x) = (3 - x)*(2 + x) + 2*(x + 20)";

"Schalk I s.86 Bsp 19 (x - 5)*(10 - x) = (3 - x)*(2 + x) + 2*(x + 20)";

(*EP*)

val fmz = ["equality ((x - 5)*(10 - x) = (3 - x)*(2 + x) + 2*(x + 20))",

	   "solveFor x","solutions L"];

val (dI',pI',mI') = ("PolyEq",["univariate","equation"],["no_met"]);

(*val p = e_pos'; 

val c = []; 

val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));

val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)

val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 8]")) => ()

	 | _ => raise error "rlang.sml: diff.behav. in Schalk I s.86 Bsp 19 [x = 8]";

(*-----------------  Schalk I s.86 Bsp 23 ------------------------*)

"Schalk I s.86 Bsp 19 ((2*x+5)^^^2+(3*x+4)^^^2=(13*x+2)*(x+1)+2*(15+14*x))";

"Schalk I s.86 Bsp 19 ((2*x+5)^^^2+(3*x+4)^^^2=(13*x+2)*(x+1)+2*(15+14*x))";

"Schalk I s.86 Bsp 19 ((2*x+5)^^^2+(3*x+4)^^^2=(13*x+2)*(x+1)+2*(15+14*x))";

(*EP*)

val fmz = ["equality ((2*x+5)^^^2+(3*x+4)^^^2=(13*x+2)*(x+1)+2*(15+14*x))",

	   "solveFor x","solutions L"];

val (dI',pI',mI') = ("PolyEq",["univariate","equation"],["no_met"]);

(*val p = e_pos'; 

val c = []; 

val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));

val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)

val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = -9]")) => ()

	 | _ => raise error "rlang.sml: diff.behav. in Schalk I s.86 Bsp 23 [x = -9]";

(*-----------------  Schalk I s.86 Bsp 25 ------------------------*)

"Schalk I s.86 Bsp 25 ((2*x+1)^^^3+(x+1)^^^3=(2*x+1)^^^2*2*x+(x+2)^^^3+x^^^2)";

"Schalk I s.86 Bsp 25 ((2*x+1)^^^3+(x+1)^^^3=(2*x+1)^^^2*2*x+(x+2)^^^3+x^^^2)";

"Schalk I s.86 Bsp 25 ((2*x+1)^^^3+(x+1)^^^3=(2*x+1)^^^2*2*x+(x+2)^^^3+x^^^2)";

(*EP*)

val fmz = ["equality ((2*x+1)^^^3+(x+1)^^^3=(2*x+1)^^^2*2*x+(x+2)^^^3+x^^^2)",

	   "solveFor x","solutions L"];

val (dI',pI',mI') = ("PolyEq",["univariate","equation"],["no_met"]);

(*val p = e_pos'; 

val c = []; 

val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));

val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)

val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = -6 / 5]")) => ()

	 | _ => raise error "rlang.sml: diff.behav. in Schalk I s.86 Bsp 25 [x = -6 / 5]";

(*-----------------  Schalk I s.86 Bsp 28b ------------------------*)

"Schalk I s.86 Bsp 28b ((3*x+5)/18 - x/2 = -((3*x - 2)/9))";

"Schalk I s.86 Bsp 28b ((3*x+5)/18 - x/2 = -((3*x - 2)/9))";

"Schalk I s.86 Bsp 28b ((3*x+5)/18 - x/2 = -((3*x - 2)/9))";

(*ER-2*)

val fmz = ["equality ((3*x+5)/18 - x/2 = -((3*x - 2)/9))",

	   "solveFor x","solutions L"];

val (dI',pI',mI') = ("PolyEq",["univariate","equation"],["no_met"]);

(*val p = e_pos'; val c = []; 

val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));

val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)

val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt; f2str f;

case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[]")) => ()

	 | _ => raise error "rlang.sml: diff.behav. in Schalk I s.86 Bsp 28b []";

(*WN---v *)

val bdv= (term_of o the o (parse thy)) "bdv";

val v = (term_of o the o (parse thy)) "x";

val t = (term_of o the o (parse thy)) "3 * x / 5";

val SOME (t',_) = rewrite_set_inst_ PolyEq.thy true 

				    [(bdv, v)] make_ratpoly_in t;

if term2str t' = "3 / 5 * x" then () else raise error "rlang.sml: 1";

val t = str2term "(3*x+5)/18 - x/2  - -(3*x - 2)/9 = 0";

val subst = [(str2term "bdv", str2term "x")];

val SOME (t',_) = rewrite_set_inst_ thy false subst make_ratpoly_in t;

if term2str t' = "1 / 18 = 0" then () else raise error "rlang.sml: 2";

(*WN---^ *)

(*-----------------  Schalk I s.87 Bsp 36b ------------------------*)

"Schalk I s.87 Bsp 36b ((17*x - 51)/9 - (-(13*x - 3)/6) + 11 -(9*x- 7)/4 = 0)";

"Schalk I s.87 Bsp 36b ((17*x - 51)/9 - (-(13*x - 3)/6) + 11 -(9*x- 7)/4 = 0)";

"Schalk I s.87 Bsp 36b ((17*x - 51)/9 - (-(13*x - 3)/6) + 11 -(9*x- 7)/4 = 0)";

(*ER-1*)

val fmz = ["equality ((17*x - 51)/9 - (-(13*x - 3)/6) + 11 - (9*x - 7)/4 = 0)",

	   "solveFor x","solutions L"];

val (dI',pI',mI') = ("PolyEq",["univariate","equation"],["no_met"]);

(*val p = e_pos'; 

val c = []; 

val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));

val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)

val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = -237 / 65]")) => ()

	 | _ => raise error "rlang.sml: diff.behav. in Schalk I s.86 Bsp 36b [x = -237 / 65]";

(*WN---v *)

val t = str2term "(17*x - 51)/9 - (-(13*x - 3)/6) + 11 - (9*x - 7)/4 = 0";

val subst = [(str2term "bdv", str2term "x")];

val SOME (t',_) = rewrite_set_inst_ thy false subst make_ratpoly_in t;

term2str t';

if term2str t' = "79 / 12 + 65 / 36 * x = 0" then () 

else raise error "rlang.sml: 3";

(*WN---^ *)

(*-----------------  Schalk I s.87 Bsp 38b ------------------------*)

"Schalk I s.87 Bsp 38b (-(2/x) + 3/(2*x) - 4/(3*x) + 5/(4*x) + 6/(5*x) =65/8)";

"Schalk I s.87 Bsp 38b (-(2/x) + 3/(2*x) - 4/(3*x) + 5/(4*x) + 6/(5*x) =65/8)";

"Schalk I s.87 Bsp 38b (-(2/x) + 3/(2*x) - 4/(3*x) + 5/(4*x) + 6/(5*x) =65/8)";

(*ER-3*)

val fmz = ["equality (-2/x + 3/(2*x) - 4/(3*x) + 5/(4*x) + 6/(5*x) = 65/8)",

	   "solveFor x","solutions L"];

val (dI',pI',mI') = ("RatEq",["univariate","equation"],["no_met"]);

(*val p = e_pos'; 

val c = []; 

val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));

val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)

val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

if f = Form' (FormKF (~1, EdUndef, 0, Nundef, "296 + -3900 * x = 0")) then ()

else raise error "rlang.sml: diff.behav. in Schalk I s.87 Bsp 38b";

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 74 / 975]")) => ()

	 | _ => raise error "rlang.sml: diff.behav. in Schalk I s.86 Bsp 38b [x = 74 / 975]";

(*-----------------  Schalk I s.87 Bsp 40b ------------------------*)

"Schalk I s.87 Bsp 40b ((x+3)/(2*x - 4)=3)";

"Schalk I s.87 Bsp 40b ((x+3)/(2*x - 4)=3)";

"Schalk I s.87 Bsp 40b ((x+3)/(2*x - 4)=3)";

(*ER-4*)

val fmz = ["equality ((x+3)/(2*x - 4)=3)",

	   "solveFor x","solutions L"];

val (dI',pI',mI') = ("RatEq",["univariate","equation"],["no_met"]);

(*val p = e_pos'; 

val c = []; 

val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));

val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)

val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt; f2str f;

(*val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;*)

if f = Form' (FormKF (~1, EdUndef, 0, Nundef, "15 + -5 * x = 0")) then ()

else raise error "rlang.sml: diff.behav. in Schalk I s.87 Bsp 40b";

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 3]")) => ()

	 | _ => raise error "rlang.sml: diff.behav. in Schalk I s.87 Bsp 40b [x = 3]";

(*-----------------  Schalk I s.87 Bsp 44a ------------------------*)

"Schalk I s.87 Bsp 44a ((1/2+(5*x)/2)^^^2 -((13*x)/2- 5/2)^^^2 -(6*x)^^^2+29)";

"Schalk I s.87 Bsp 44a ((1/2+(5*x)/2)^^^2 -((13*x)/2- 5/2)^^^2 -(6*x)^^^2+29)";

"Schalk I s.87 Bsp 44a ((1/2+(5*x)/2)^^^2 -((13*x)/2- 5/2)^^^2 -(6*x)^^^2+29)";

(*ER-5*)

val fmz = ["equality ((1/2 + (5*x)/2)^^^2 - ((13*x)/2 - 5/2)^^^2 = -1*(6*x)^^^2 + 29)",

	   "solveFor x","solutions L"];

val (dI',pI',mI') = ("PolyEq",["univariate","equation"],["no_met"]);

(*val p = e_pos'; 

val c = []; 

val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));

val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)

val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];

(*trace_rewrite:=true;

*)

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 1]")) => ()

	 | _ => raise error "rlang.sml: diff.behav. in Schalk I s.87 Bsp 44a [x = 1]";

(*WN---v *)

val t = str2term "(1/2 + (5*x)/2)^^^2 - ((13*x)/2 - 5/2)^^^2 - (6*x)^^^2 + 29";

val subst = [(str2term "bdv", str2term "x")];

val SOME (t',_) = rewrite_set_inst_ thy false subst make_ratpoly_in t;

if term2str t' = "23 + 35 * x + -72 * x ^^^ 2" then () 

else raise error "rlang.sml: 4";

val t = str2term "(1/2 + (5*x)/2)^^^2 - ((13*x)/2 - 5/2)^^^2 + (6*x)^^^2 - 29";

val subst = [(str2term "bdv", str2term "x")];

val SOME (t',_) = rewrite_set_inst_ thy false subst make_ratpoly_in t;

if term2str t' = "-35 + 35 * x" then () 

else raise error "rlang.sml: 4.1";

(*WN---^ *)

(*-----------------  Schalk I s.87 Bsp 52a ------------------------*)

"Schalk I s.87 Bsp 52a ((5*x)/(x - 2) - x/(x+2)=4)";

"Schalk I s.87 Bsp 52a ((5*x)/(x - 2) - x/(x+2)=4)";

"Schalk I s.87 Bsp 52a ((5*x)/(x - 2) - x/(x+2)=4)";

(*ER-6*)

val fmz = ["equality ((5*x)/(x - 2) - x/(x+2)=4)",

	   "solveFor x","solutions L"];

val (dI',pI',mI') = ("RatEq",["univariate","equation"],["no_met"]);

val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

 (*"12 * x + 4 * x ^^^ 2 = 4 * (-4 + x ^^^ 2)",Subproblem["normalize", "poly*)

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

if f = Form' (FormKF (~1, EdUndef, 0, Nundef, "16 + 12 * x = 0")) then ()

else raise error "rlang.sml: diff.behav. in Schalk I s.87 Bsp 52a";

            (*Subproblem["degree_1", "polynomial", "univariate", "equation"]*)

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = -4 / 3]")) => ()

	 | _ => raise error "rlang.sml: diff.behav. in  Schalk I s.87 Bsp 52a [x = -4 / 3]";

(*-----------------  Schalk I s.87 Bsp 55b ------------------------*)

"Schalk I s.87 Bsp 55b (x/(x^^^2 - 6*x+9) - 1/(x^^^2 - 3*x) =1/x)";

"Schalk I s.87 Bsp 55b (x/(x^^^2 - 6*x+9) - 1/(x^^^2 - 3*x) =1/x)";

"Schalk I s.87 Bsp 55b (x/(x^^^2 - 6*x+9) - 1/(x^^^2 - 3*x) =1/x)";

(*ER-7*)

val fmz = ["equality (x/(x^^^2 - 6*x+9) - 1/(x^^^2 - 3*x) =1/x)",

	   "solveFor x","solutions L"];

val (dI',pI',mI') = ("RatEq",["univariate","equation"],["no_met"]);

val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];

(*val nxt = ("Model_Problem",Model_Problem["rational","univariate","equation"*)

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

(*//me's dropped !val it = ["9 * x + -6 * x ^^^ 2 + 1 * x ^^^ 3 ~= 0","x ~= 0"]

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

WN: Grad hoeher      ~~~~~~~~~~~~  als notwendig                   ~~~~~~~~*)

(* nxt =Model_Problem ["normalize","polynomial","univariate","equation"])*)

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

(*val (p,_,f,nxt,_,pt) = me nxt p [1] pt; 040209 MGs norm_Rational*)

(* val nxt = Subproblem ("PolyEq",["polynomial","univariate","equation"])*)

if f= Form' (FormKF (~1, EdUndef, 0, Nundef, "-6 * x + 5 * x ^^^ 2 = 0"))then()

else raise error "rlang.sml: diff.behav. in Schalk I s.87 Bsp 55b";

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

(*nxt=Model_Problem["bdv_only","degree_2","polynomial","univariate","equation*)

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

(*val f = Form' (FormKF (~1,EdUndef,3,Nundef,"x = 0 | x = 6 / 5")) : mout

val nxt = ("Or_to_List",Or_to_List) *)

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

(*val f = Form' (FormKF (~1,EdUndef,3,Nundef,"[x = 0, x = 6 / 5]")) : mout

val nxt = ("Check_elementwise",Check_elementwise "Assumptions")

get_assumptions pt (fst p);

val it = [] : string list ... correct for this subproblem !*)

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

(*val p = ([6,5,5],Res) : pos'

val f = Form' (FormKF (~1,EdUndef,3,Nundef,"[x = 0, x = 6 / 5]")) : mout

nxt=Check_Postcond ["bdv_only","degree_2","polynomial","univariate","equation*)

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

(*val p = ([6,5],Res) : pos'

val f = Form' (FormKF (~1,EdUndef,2,Nundef,"[x = 0, x = 6 / 5]")) : mout

val nxt =Check_Postcond ["normalize","polynomial","univariate","equation"])*)

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

(*val p = ([6],Res) : pos'

val f = Form' (FormKF (~1,EdUndef,1,Nundef,"[x = 0, x = 6 / 5]")) : mout

val nxt = ("Check_elementwise",Check_elementwise "Assumptions")*)

val [(aaa,ppp)] = get_assumptions_ pt p;

if term2str aaa = "9 * x + -6 * x ^^^ 2 + x ^^^ 3 ~= 0" then ()

else raise error "rlang.sml: diff.behav. in I s.87 Bsp 55b [x = 6 / 5], asms";

(*WN060717 unintentionally changed some rls/ord while 

     completing knowl. for thes2file...

if term2str aaa = "9 * x + (x ^^^ 3 + -6 * x ^^^ 2) ~= 0" then ()

else raise error "rlang.sml: diff.behav. in I s.87 Bsp 55b [x = 6 / 5], asms";

.... but it became even better*)

(*22.10.03:

val it = "9 * x + (x ^^^ 3 + -6 * x ^^^ 2) ~= 0" : string;

  before 22.10.03:

val it = ["9 * x + -6 * x ^^^ 2 + 1 * x ^^^ 3 ~= 0","x ~= 0"]

> val subs = [(str2term "x", str2term "0")];

> val pred = str2term "9 * x + -6 * x ^^^ 2 + 1 * x ^^^ 3 ~= 0 & x ~= 0";

> eval_true thy [subst_atomic subs pred] rateq_erls;

val it = false : bool 

> val subs = [(str2term "x", str2term "6 / 5")];

> val pred = str2term "9 * x + -6 * x ^^^ 2 + 1 * x ^^^ 3 ~= 0 & x ~= 0";

> eval_true thy [subst_atomic subs pred] rateq_erls;

val it = true : bool*)

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

(*val p = ([7],Res) : pos'

val f = Form' (FormKF (~1,EdUndef,1,Nundef,"[x = 6 / 5]")) : mout

val nxt =Check_Postcond ["rational","univariate","equation"])        *)

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 6 / 5]")) => ()

	| _ => raise error "rlang.sml: diff.behav. in  Schalk I s.87 Bsp 55b [x = 6 / 5]";

(*-----------------  Schalk I s.88 Bsp 64c ------------------------*)

"Schalk I s.88 Bsp 64c (((x - 1)/(x+1)+1)/((x - 1)/(x+1) - (x+1)/(x - 1))=2)";

"Schalk I s.88 Bsp 64c (((x - 1)/(x+1)+1)/((x - 1)/(x+1) - (x+1)/(x - 1))=2)";

"Schalk I s.88 Bsp 64c (((x - 1)/(x+1)+1)/((x - 1)/(x+1) - (x+1)/(x - 1))=2)";

(*ER-8*)

val fmz = ["equality (((x - 1)/(x+1)+1)/((x - 1)/(x+1) - (x+1)/(x - 1))=2)",

	   "solveFor x","solutions L"];

val (dI',pI',mI') = ("RatEq",["univariate","equation"],["no_met"]);

(*val p = e_pos'; val c = []; 

val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));

val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)

val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt; f2str f;

if f = Form' (FormKF (~1, EdUndef, 0, Nundef, "-3 + -1 * x = 0")) then ()

else raise error "rlangsml: diff.behav. in Schalk I s.88 Bsp 64c";

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

case f of Form' (FormKF (_,_,0,_,"[x = -3]")) => ()

	 | _ => raise error "rlang.sml: diff.behav. in  Schalk I s.88 Bsp 64c [x = -3]";

(*-----------------  Schalk I s.88 Bsp 79a (2) ------------------------*)

"Schalk I s.88 Bsp 79a (2) (m1*v1+m2*v2=0)";

"Schalk I s.88 Bsp 79a (2) (m1*v1+m2*v2=0)";

"Schalk I s.88 Bsp 79a (2) (m1*v1+m2*v2=0)";

(*ER-10*)

val fmz = ["equality (m1*v1+m2*v2=0)",

	   "solveFor m1","solutions L"];

val (dI',pI',mI') = ("PolyEq",["univariate","equation"],["no_met"]);

(*val p = e_pos'; val c = []; 

val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));

val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)

val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[m1 = -1 * m2 * v2 / v1]")) => ()

	 | _ => raise error "rlang.sml: diff.behav. in  Schalk I s.88 Bsp 79a (2) [m1 = -1 * m2 * v2 / v1]";

(*-----------------  Schalk I s.89 Bsp 90a(1) ------------------------*)

"Schalk I s.89 Bsp 90a (1) (f=((w+u)/(w+v))*v0)";

"Schalk I s.89 Bsp 90a (1) (f=((w+u)/(w+v))*v0)";

"Schalk I s.89 Bsp 90a (1) (f=((w+u)/(w+v))*v0)";

(*ER-11*)

val fmz = ["equality (f=((w+u)/(w+v))*v0)",

	   "solveFor v","solutions L"];

val (dI',pI',mI') = ("RatEq",["univariate","equation"],["no_met"]);

(*val p = e_pos'; val c = []; 

val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));

val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)

val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

(*val nxt = Specify_Problem ["rational","univariate","equation"])      *)

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

(*val nxt = Specify_Method ["RatEq","solve_rat_equation"])      *)

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

(*nxt = Subproblem ("RatEq",["univariate","equation"]))      *)

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

(*val nxt =Model_Problem ["normalize","polynomial","univariate","equation"])*)

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

(*val nxt = ("Apply_Method",Apply_Method ["PolyEq","normalize_poly"])*)

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

(*val nxt =Subproblem ("PolyEq",["polynomial","univariate","equation"]))*)

if f = Form'

      (FormKF

         (~1,

            EdUndef,

            0,

            Nundef,

            "f * w + -1 * u * v0 + -1 * v0 * w + f * v = 0")) then ()

else raise error "rlang.sml: diff.behav. in Schalk I s.89 Bsp 90a";

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

(*val nxt = Model_Problem ["degree_1","polynomial","univariate","equation"])*)

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

(*val nxt = ("Apply_Method",Apply_Method ["PolyEq","solve_d1_poly_equation"])*)

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

(*val f = "v = -1 * (f * w + -1 * u * v0 + -1 * v0 * w) / f")) : mout

val nxt = ("Or_to_List",Or_to_List) : string * tac *)

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

(*val f = "[v = -1 * (f * w + -1 * u * v0 + -1 * v0 * w) / f]")) : mout

val nxt = ("Check_elementwise",Check_elementwise "Assumptions") *)

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

(*val f = "[v = -1 * (f * w + -1 * u * v0 + -1 * v0 * w) / f]")) : mout

val nxt = Check_Postcond ["degree_1","polynomial","univariate","equation"])*)

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

(*val f = "[v = -1 * (f * w + -1 * u * v0 + -1 * v0 * w) / f]")) : mout

val nxt = Check_Postcond ["normalize","polynomial","univariate","equation"])*)

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

(*val f = "[v = -1 * (f * w + -1 * u * v0 + -1 * v0 * w) / f]")) : mout

val nxt = ("Check_elementwise",Check_elementwise "Assumptions")*)

get_assumptions_ pt p;

(*it = ["v + w ~= 0"]    ... goes to the solution as an assumption*)

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

(*val f = Form' (FormKF (~1,EdUndef,1,Nundef,"[]")) : mout

val nxt = Check_Postcond ["rational","univariate","equation"])        *)

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

case f of Form'  (FormKF (~1,EdUndef,0,Nundef,

        "[v = (u * v0 + v0 * w + -1 * f * w) / f]")) => ()

	 | _ => raise error "rlang.sml: diff.behav. in  Schalk I s.89 Bsp 90a (1) [v=...]";

if get_assumptions_ pt p = 

   [(str2term"(u * v0 + v0 * w + -1 * f * w) / f + w ~= 0",[])] then () 

else raise error "rlang.sml: diff.behav. in I s.89 Bsp 90a (1) [v=...] asm";

(*-----------------  Schalk I s.89 Bsp 90a(2) ------------------------*)

"Schalk I s.89 Bsp 90a (2) (f=((w+u)/(w+v))*v0)";

"Schalk I s.89 Bsp 90a (2) (f=((w+u)/(w+v))*v0)";

"Schalk I s.89 Bsp 90a (2) (f=((w+u)/(w+v))*v0)";

(*ER-12*)

val fmz = ["equality (f=((w+u)/(w+v))*v0)",

	   "solveFor w","solutions L"];

val (dI',pI',mI') = ("RatEq",["univariate","equation"],["no_met"]);

(*val p = e_pos';val c = []; 

val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));

val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)

val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

if f = Form'

      (FormKF

         (~1,

            EdUndef,

            0,

            Nundef,

            "f * v + -1 * u * v0 + (f + -1 * v0) * w = 0")) then ()

else raise error "rlang.sml: diff.behav. in Schalk I s.89 Bsp 90a (2)";

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[w = (u * v0 + -1 * f * v) / (f + -1 * v0)]")) => ()

	 | _ => raise error "rlang.sml: diff.behav. in Schalk I Bsp 90a(2)";

if get_assumptions_ pt p = 

[(str2term"v + (u * v0 + -1 * f * v) / (f + -1 * v0) ~= 0",[]),

 (str2term"f + -1 * v0 ~= 0",[])]

then writeln "asm should be simplified ???" 

else raise error "rlang.sml: diff.behav. in Schalk I Bsp 90a(2) asm";

(*-----------------  Schalk I s.89 Bsp 98a(1) ------------------------*)

"Schalk I s.89 Bsp 98a (1) (1/R=1/R1+1/R2)";

"Schalk I s.89 Bsp 98a (1) (1/R=1/R1+1/R2)";

"Schalk I s.89 Bsp 98a (1) (1/R=1/R1+1/R2)";

(*ER-9*)

val fmz = ["equality (1/R=1/R1+1/R2)",

	   "solveFor R1","solutions L"];

val (dI',pI',mI') = ("RatEq",["univariate","equation"],["no_met"]);

(*val p = e_pos'; val c = []; 

val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));

val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)

val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

if f = Form'

      (FormKF

        (~1, EdUndef, 0, Nundef, "-1 * R * R2 + (R2 + -1 * R) * R1 = 0"))then()

else raise error "rlang.sml: diff.behav. in Schalk I s.89 Bsp 98a (1)";

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[R1 = R * R2 / (R2 + -1 * R)]")) => ()

	 | _ => raise error "rlang.sml: diff.behav. in 98a(1) [R1 = ...]";

if get_assumptions_ pt p = [(str2term"R * R2 * R2 ~= (R2 + -1 * R) * 0",[]),

			    (str2term"R2 + -1 * R ~= 0",[]),

			    (str2term"R2 + -1 * R ~= 0",[])] 

    then writeln "asm should be simplified"

else raise error "rlang.sml: diff.behav. in 98a(1) asm";

(*-----------------  Schalk I s.89 Bsp 104a(1) ------------------------*)

"Schalk I s.89 Bsp 104a (1) (y^^^2=2*p*x)";

"Schalk I s.89 Bsp 104a (1) (y^^^2=2*p*x)";

"Schalk I s.89 Bsp 104a (1) (y^^^2=2*p*x)";

(*ER-13 + EO-11 ?!?*)

val fmz = ["equality (y^^^2=2*p*x)",

	   "solveFor p","solutions L"];

val (dI',pI',mI') = ("PolyEq",["univariate","equation"],["no_met"]);

(*val p = e_pos'; val c = []; 

val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));

val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)

val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt; 

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

case f of Form' (FormKF (_,_,0,_,"[p = y ^^^ 2 / (2 * x)]")) => ()

	 | _ => raise error "rlang.sml: diff.behav. in  Schalk I s.89 Bsp 104a (1) [p = y^2/(2*x)]";

if get_assumptions_ pt p = [(str2term"-2 * x ~= 0",[])] 

then writeln"should be x ~= 0\nshould be x ~= 0\nshould be x ~= 0\n" 

else raise error "rlang.sml: diff.behav. in  I s.89 Bsp 104a(1) asm";

(*-----------------  Schalk I s.89 Bsp 104a(2) ------------------------*)

"Schalk I s.89 Bsp 104a (2) (y^^^2=2*p*x)";

"Schalk I s.89 Bsp 104a (2) (y^^^2=2*p*x)";

"Schalk I s.89 Bsp 104a (2) (y^^^2=2*p*x)";

(*EO ??*)

val fmz = ["equality (y^^^2=2*p*x)",

	   "solveFor y","solutions L"];

val (dI',pI',mI') = ("PolyEq",["univariate","equation"],["no_met"]);

(*val p = e_pos'; 

val c = []; 

val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));

val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)

val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

case f of Form' (FormKF (_,_,0,_,"[y = sqrt (2 * p * x), y = -1 * sqrt (2 * p * x)]")) => ()

| _ => raise error "rlang.sml: diff.behav. Schalk I s.89 Bsp 104a(2) [x = ]";

if get_assumptions_ pt p = [(str2term"0 <= -1 * (-2 * p * x)",[]),(str2term"0 <= -1 * (-2 * p * x)",[])] then writeln "asm should be simplified\nshould be simplified"

else raise error "rlang.sml: diff.behav. in I s.89 Bsp 104a(2) asm";

(*-----------------  Schalk I s.90 Bsp 118a (1) ------------------------*)

"Schalk I s.90 Bsp 118a (1) (b^^^2*x^^^2 + a^^^2*y^^^2 = a^^^2*b^^^2)";

"Schalk I s.90 Bsp 118a (1) (b^^^2*x^^^2 + a^^^2*y^^^2 = a^^^2*b^^^2)";

"Schalk I s.90 Bsp 118a (1) (b^^^2*x^^^2 + a^^^2*y^^^2 = a^^^2*b^^^2)";

(*EO-8*)

val fmz = ["equality (b^^^2*x^^^2 + a^^^2*y^^^2 = a^^^2*b^^^2)",

	   "solveFor x","solutions L"];

val (dI',pI',mI') = ("PolyEq",["univariate","equation"],["no_met"]);

(*val p = e_pos'; 

val c = []; 

val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));

val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)

val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;f2str f;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;f2str f;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;f2str f;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;f2str f;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;f2str f;get_asm (fst p, fst p) pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;f2str f;get_asm (fst p, fst p) pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;f2str f;get_asm (fst p, fst p) pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;f2str f;get_asm (fst p, fst p) pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;f2str f;asms2str (get_asm (fst p, fst p) pt);

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;f2str f;asms2str (get_asm (fst p, fst p) pt);

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;f2str f;get_asm (fst p, fst p) pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;f2str f;get_asm (fst p, fst p) pt;

case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = sqrt ((a ^^^ 2 * b ^^^ 2 + -1 * a ^^^ 2 * y ^^^ 2) / b ^^^ 2),\n x = -1 * sqrt ((a ^^^ 2 * b ^^^ 2 + -1 * a ^^^ 2 * y ^^^ 2) / b ^^^ 2)]")) => writeln"should be simplified MG"

| _ => raise error "rlang.sml: diff.behav. in  Schalk I s.89 Bsp 118a(2) [x = ]";

val asms = get_assumptions_ pt p;

if asms = [(str2term"0 * b ^^^ 2 <= -1 * (a ^^^ 2 * y ^^^ 2 + -1 * a ^^^ 2 * b ^^^ 2)", []),

	   (str2term"b ^^^ 2 ~= 0", []),

	   (str2term"0 * b ^^^ 2 <= -1 * (a ^^^ 2 * y ^^^ 2 + -1 * a ^^^ 2 * b ^^^ 2)", []),

	   (str2term"b ^^^ 2 ~= 0", [])

	   ] then writeln"should be simplified MG"

else raise error "rlang.sml: diff.behav. in Schalk I s.89 Bsp 118a(2) asms";

(*-----------------  Schalk I s.102 Bsp 268(1) ------------------------*)

"Schalk I s.102 Bsp 268(1) (A = (1/2)*(x1*(y2-y3)+x2*(y3 - y1)+x3*(y1 - y2)))";

"Schalk I s.102 Bsp 268(1) (A = (1/2)*(x1*(y2-y3)+x2*(y3 - y1)+x3*(y1 - y2)))";

"Schalk I s.102 Bsp 268(1) (A = (1/2)*(x1*(y2-y3)+x2*(y3 - y1)+x3*(y1 - y2)))";

(*ER-14*)

val fmz = ["equality (A = (1/2)*(x1*(y2 - y3)+x2*(y3 - y1)+x3*(y1 - y2)))",

	   "solveFor x2","solutions L"];

val (dI',pI',mI') = ("PolyEq",["univariate","equation"],["no_met"]);

(*val p = e_pos'; 

val c = []; 

val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));

val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)

val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x2 =\n (-2 * A + x1 * y2 + x3 * y1 + -1 * x1 * y3 + -1 * x3 * y2) /\n (y1 + -1 * y3)]")) => ()

| _ => raise error "rlang.sml: diff.behav. Schalk I s.102 Bsp 268(1) [x2=...]";

if get_assumptions_ pt p = [(str2term"y1 / 2 + -1 * y3 / 2 ~= 0",[])] then ()

else raise error "rlang.sml: diff.behav. in I s.102 Bsp 268(1) asm";

(*--------------------  Schalk II ----------------------------*)

(*--------------------  Schalk II ----------------------------*)

(*--------------------  Schalk II ----------------------------*)

(*--------------------  Schalk II ----------------------------*)

(*--------------------  Schalk II ----------------------------*)

(*-----------------  Schalk II s.56 Bsp 67b ------------------------*)

"Schalk II s.56 Bsp 67b (4*sqrt(4*x+1)=3*sqrt(7*x+2))";

"Schalk II s.56 Bsp 67b (4*sqrt(4*x+1)=3*sqrt(7*x+2))";

"Schalk II s.56 Bsp 67b (4*sqrt(4*x+1)=3*sqrt(7*x+2))";

(*EO*)

val fmz = ["equality (4*sqrt(4*x+1)=3*sqrt(7*x+2))",

	   "solveFor x","solutions L"];

val (dI',pI',mI') = ("RootEq",["univariate","equation"],["no_met"]);

(*val p = e_pos'; 

val c = []; 

val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));

val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)

val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt; f2str f;

if f = Form' (FormKF (~1, EdUndef, 0, Nundef, "-2 + x = 0")) then ()

else raise error "rlang.sml: diff.behav. in Schalk II s.56 Bsp 67b";

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2]")) => ()

	 | _ => raise error "rlang.sml: diff.behav. in  Schalk II s.56 Bsp 67b [x=2]";

(*-----------------  Schalk II s.56 Bsp 68a ------------------------*)

"Schalk II s.56 Bsp 68a (5*sqrt(x) - 1 = 7*sqrt(x) - 5)";

"Schalk II s.56 Bsp 68a (5*sqrt(x) - 1 = 7*sqrt(x) - 5)";

"Schalk II s.56 Bsp 68a (5*sqrt(x) - 1 = 7*sqrt(x) - 5)";

val fmz = ["equality (5*sqrt(x) - 1 = 7*sqrt(x) - 5)",

	   "solveFor x","solutions L"];

val (dI',pI',mI') = ("RootEq",["univariate","equation"],["no_met"]);

(*val p = e_pos'; 

val c = []; 

val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));

val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)

val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];

(* val nxt = ("Model_Problem",Model_Problem ["normalize","root'","univariate","equation"])*)

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

(* val nxt = ("Model_Problem",Model_Problem ["sq","root'","univariate","equation"]) *)

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

(* val nxt = ("Model_Problem",Model_Problem ["sq","root'","univariate","equation"]) *)

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

get_assumptions_ pt p;

(* val nxt = ("Model_Problem",  Model_Problem ["normalize","polynomial","univariate","equation"])*)

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

if f = Form'

      (FormKF

         (~1, EdUndef, 0, Nundef, "256 + -2368 * x + 576 * x ^^^ 2 = 0"))then()

else raise error "rlang.sml: diff.behav. in Schalk II s.56 Bsp 68a";

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

get_assumptions_ pt p;

(* val nxt = ("Model_Problem",  Model_Problem

     ["abcFormula","degree_2","polynomial","univariate","equation"])*)

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;