(* tests for various kinds of univariate equations.

  Author: Richard Lang 2003

  (c) due to copyright terms

These tests have not been updated with the transition Isabelle2002 --> 2011

# because there are many other tests on equations in other test-files

# some of these equations are twice, e.g. x / (x ^ 2 - 6 * x + 9) - 1 / (x ^ 2 - 3 * x) = 1 / x, x

# this file needs specifically much cleaning.

*)

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

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},

}

*)

(*

 Rewrite.trace_on:=false; (*true false*)

 Refine.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,_,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' (Test_Out.FormKF (~1,EdUndef,0,Nundef,"[x = 2]")) => ()

	 | _ => 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,_,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' (Test_Out.FormKF (~1,EdUndef,0,Nundef,"[x = 8]")) => ()

	 | _ => 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) \<up> 2+(3*x+4) \<up> 2=(13*x+2)*(x+1)+2*(15+14*x))";

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

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

(*EP*)

val fmz = ["equality ((2*x+5) \<up> 2+(3*x+4) \<up> 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,_,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' (Test_Out.FormKF (~1,EdUndef,0,Nundef,"[x = -9]")) => ()

	 | _ => 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) \<up> 3+(x+1) \<up> 3=(2*x+1) \<up> 2*2*x+(x+2) \<up> 3+x \<up> 2)";

"Schalk I s.86 Bsp 25 ((2*x+1) \<up> 3+(x+1) \<up> 3=(2*x+1) \<up> 2*2*x+(x+2) \<up> 3+x \<up> 2)";

"Schalk I s.86 Bsp 25 ((2*x+1) \<up> 3+(x+1) \<up> 3=(2*x+1) \<up> 2*2*x+(x+2) \<up> 3+x \<up> 2)";

(*EP*)

val fmz = ["equality ((2*x+1) \<up> 3+(x+1) \<up> 3=(2*x+1) \<up> 2*2*x+(x+2) \<up> 3+x \<up> 2)",

	   "solveFor x", "solutions L"];

val (dI',pI',mI') = ("PolyEq",["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;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

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

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

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

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

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

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

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me 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' (Test_Out.FormKF (~1,EdUndef,0,Nundef,"[x = -6 / 5]")) => ()

	 | _ => 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,_,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' (Test_Out.FormKF (~1,EdUndef,0,Nundef,"[]")) => ()

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

(*WN---v *)

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

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

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

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

				    [ (bdv, v) ] make_ratpoly_in t;

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

val t = TermC.parse_test @{context} "(3*x+5)/18 - x/2  - -(3*x - 2)/9 = 0";

val subst = [(TermC.parse_test @{context} "bdv", TermC.parse_test @{context} "x")];

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

if UnparseC.term t' = "1 / 18 = 0" then () else 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,_,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' (Test_Out.FormKF (~1,EdUndef,0,Nundef,"[x = - 237 / 65]")) => ()

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

(*WN---v *)

val t = TermC.parse_test @{context} "(17*x - 51)/9 - (-(13*x - 3)/6) + 11 - (9*x - 7)/4 = 0";

val subst = [(TermC.parse_test @{context} "bdv", TermC.parse_test @{context} "x")];

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

UnparseC.term t';

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

else 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,_,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' (Test_Out.FormKF (~1, EdUndef, 0, Nundef, "296 + -3900 * x = 0")) then ()

else 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' (Test_Out.FormKF (~1,EdUndef,0,Nundef,"[x = 74 / 975]")) => ()

	 | _ => 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,_,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' (Test_Out.FormKF (~1, EdUndef, 0, Nundef, "15 + -5 * x = 0")) then ()

else 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' (Test_Out.FormKF (~1,EdUndef,0,Nundef,"[x = 3]")) => ()

	 | _ => 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) \<up> 2 -((13*x)/2- 5/2) \<up> 2 -(6*x) \<up> 2+29)";

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

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

(*ER-5*)

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

	   "solveFor x", "solutions L"];

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

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

Rewrite.trace_on:=true; (*true false*)

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

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

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

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

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

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

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

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

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

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

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

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

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me 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' (Test_Out.FormKF (~1,EdUndef,0,Nundef,"[x = 1]")) => ()

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

(*WN---v *)

val t = TermC.parse_test @{context} "(1/2 + (5*x)/2) \<up> 2 - ((13*x)/2 - 5/2) \<up> 2 - (6*x) \<up> 2 + 29";

val subst = [(TermC.parse_test @{context} "bdv", TermC.parse_test @{context} "x")];

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

if UnparseC.term t' = "23 + 35 * x + -72 * x \<up> 2" then () 

else error "rlang.sml: 4";

val t = TermC.parse_test @{context} "(1/2 + (5*x)/2) \<up> 2 - ((13*x)/2 - 5/2) \<up> 2 + (6*x) \<up> 2 - 29";

val subst = [(TermC.parse_test @{context} "bdv", TermC.parse_test @{context} "x")];

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

if UnparseC.term t' = "-35 + 35 * x" then () 

else error "rlang.sml: 4.1";

(*WN---^ *)

(*-----------------  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,_,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' (Test_Out.FormKF (~1, EdUndef, 0, Nundef, "-3 + - 1 * x = 0")) then ()

else 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' (Test_Out.FormKF (_,_,0,_,"[x = -3]")) => ()

	 | _ => 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,_,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' (Test_Out.FormKF (~1,EdUndef,0,Nundef,"[m1 = - 1 * m2 * v2 / v1]")) => ()

	 | _ => 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,_,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 ["normalise", "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", "normalise_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'

      (Test_Out.FormKF

         (~1,

            EdUndef,

            0,

            Nundef,

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

else 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 ["normalise", "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")*)

Ctree.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' (Test_Out.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'  (Test_Out.FormKF (~1,EdUndef,0,Nundef,

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

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

if Ctree.get_assumptions pt p = 

   [TermC.parse_test @{context}"(u * v0 + v0 * w + - 1 * f * w) / f + w ~= 0"] then () 

else 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,_,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'

      (Test_Out.FormKF

         (~1,

            EdUndef,

            0,

            Nundef,

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

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

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

if Ctree.get_assumptions pt p = 

[TermC.parse_test @{context}"v + (u * v0 + - 1 * f * v) / (f + - 1 * v0) ~= 0",

 TermC.parse_test @{context}"f + - 1 * v0 ~= 0"]

then writeln "asm should be simplified ???" 

else 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,_,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'

      (Test_Out.FormKF

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

else 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' (Test_Out.FormKF (~1,EdUndef,0,Nundef,"[R1 = R * R2 / (R2 + - 1 * R)]")) => ()

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

if Ctree.get_assumptions pt p = [TermC.parse_test @{context}"R * R2 * R2 ~= (R2 + - 1 * R) * 0",

			    TermC.parse_test @{context}"R2 + - 1 * R ~= 0",

			    TermC.parse_test @{context}"R2 + - 1 * R ~= 0"] 

    then writeln "asm should be simplified"

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

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

"Schalk I s.89 Bsp 104a (1) (y \<up> 2=2*p*x)";

"Schalk I s.89 Bsp 104a (1) (y \<up> 2=2*p*x)";

"Schalk I s.89 Bsp 104a (1) (y \<up> 2=2*p*x)";

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

val fmz = ["equality (y \<up> 2=2*p*x)",

	   "solveFor p", "solutions L"];

val (dI',pI',mI') = ("PolyEq",["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;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

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

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

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

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

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

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

val (p,_,f,nxt,_,pt) = me 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' (Test_Out.FormKF (_,_,0,_,"[p = y \<up> 2 / (2 * x)]")) => ()

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

if Ctree.get_assumptions pt p = [TermC.parse_test @{context}"- 2 * x ~= 0"] 

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

else 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 \<up> 2=2*p*x)";

"Schalk I s.89 Bsp 104a (2) (y \<up> 2=2*p*x)";

"Schalk I s.89 Bsp 104a (2) (y \<up> 2=2*p*x)";

(*EO ??*)

val fmz = ["equality (y \<up> 2=2*p*x)",

	   "solveFor y", "solutions L"];

val (dI',pI',mI') = ("PolyEq",["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;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;

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

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

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

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

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

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

val (p,_,f,nxt,_,pt) = me 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' (Test_Out.FormKF (_,_,0,_,"[y = sqrt (2 * p * x), y = - 1 * sqrt (2 * p * x)]")) => ()

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

if Ctree.get_assumptions pt p = [TermC.parse_test @{context}"0 <= - 1 * (- 2 * p * x)",

                            TermC.parse_test @{context}"0 <= - 1 * (- 2 * p * x)"] 

then writeln "asm should be simplified\nshould be simplified"

else 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 \<up> 2*x \<up> 2 + a \<up> 2*y \<up> 2 = a \<up> 2*b \<up> 2)";

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

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

(*EO-8*)

val fmz = ["equality (b \<up> 2*x \<up> 2 + a \<up> 2*y \<up> 2 = a \<up> 2*b \<up> 2)",

	   "solveFor x", "solutions L"];

val (dI',pI',mI') = ("PolyEq",["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;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;Ctree.get_assumptions pt p;

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

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

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

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;f2str f;UnparseC.terms (*WN1104changed*) (Ctree.get_assumptions pt p);

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;f2str f;UnparseC.terms (*WN1104changed*) (Ctree.get_assumptions pt p);

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

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

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

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

val asms = Ctree.get_assumptions pt p;

if asms = 

  [TermC.parse_test @{context}"0 * b \<up> 2 <= - 1 * (a \<up> 2 * y \<up> 2 + - 1 * a \<up> 2 * b \<up> 2)",

   TermC.parse_test @{context}"b \<up> 2 ~= 0",

   TermC.parse_test @{context}"0 * b \<up> 2 <= - 1 * (a \<up> 2 * y \<up> 2 + - 1 * a \<up> 2 * b \<up> 2)",

   TermC.parse_test @{context}"b \<up> 2 ~= 0"] then writeln"should be simplified MG"

else 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,_,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' (Test_Out.FormKF (~1,EdUndef,0,Nundef,"[x2 =\n (- 2 * A + x1 * y2 + x3 * y1 + - 1 * x1 * y3 + - 1 * x3 * y2) /\n (y1 + - 1 * y3)]")) => ()

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

if Ctree.get_assumptions pt p = [TermC.parse_test @{context}"y1 / 2 + - 1 * y3 / 2 ~= 0"] then ()

else 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,_,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' (Test_Out.FormKF (~1, EdUndef, 0, Nundef, "- 2 + x = 0")) then ()

else 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' (Test_Out.FormKF (~1,EdUndef,0,Nundef,"[x = 2]")) => ()

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

(* val nxt = ("Model_Problem",Model_Problem ["normalise", "rootX", "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", "rootX", "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", "rootX", "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;

Ctree.get_assumptions pt p;

(* val nxt = ("Model_Problem",  Model_Problem ["normalise", "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'

      (Test_Out.FormKF

         (~1, EdUndef, 0, Nundef, "256 + - 2368 * x + 576 * x \<up> 2 = 0"))then()

else 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;

Ctree.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;

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

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

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

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

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

Ctree.get_assumptions pt p;

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

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

val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me 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' (Test_Out.FormKF (~1,EdUndef,0,Nundef,"[x = 4, x = 1 / 9]")) 

then writeln "only [x = 4] !\nonly [x = 4] !\nonly [x = 4] !\n"

else error "rlang.sml: diff.behav. in II 68a";

val asms = Ctree.get_assumptions pt p;

if UnparseC.terms (*WN1104changed*) asms = 

"[0 <= (25 * (1 / 9) + - 1 * (16 + 49 * (1 / 9))) * -56,\

 \0 <= 1 / 9,\

 \0 <= 1 / 9,\

 \0 <= (-5 + 7 * sqrt (1 / 9) + 1) * 5,\

 \0 <= 1 / 9,\

 \0 <= (25 * (1 / 9) + - 1 * (16 + 49 * (1 / 9))) * -56,\

 \0 <= 1 / 9]"

(*WN050916 before correction 'rewrite__set_ called with 'Rule_Set.Empty' for ..'

  thus: maybe the rls for the asms is Rule_Set.Empty ??:

   [(TermC.parse_test @{context}"0 <= (25 * (1 / 9) + - 1 * (16 + 49 * (1 / 9))) * -56", []),

    (TermC.parse_test @{context}"9 ~= 0", []),

    (TermC.parse_test @{context}"0 <= (-5 + 7 * sqrt (1 / 9) + 1) * 5", []),

    (TermC.parse_test @{context}"9 ~= 0", []),

    (TermC.parse_test @{context}"0 <= (25 * (1 / 9) + - 1 * (16 + 49 * (1 / 9))) * -56", [])]*)

    then "should get True * False!!!"

else error "rlang.sml: diff.behav. in II 68a asms";

(*-----------------  Schalk II s.56 Bsp 73b ------------------------*)

"Schalk II s.56 Bsp 73b (sqrt(x+1)+sqrt(4*x+4)=sqrt(9*x+9))";

"Schalk II s.56 Bsp 73b (sqrt(x+1)+sqrt(4*x+4)=sqrt(9*x+9))";

"Schalk II s.56 Bsp 73b (sqrt(x+1)+sqrt(4*x+4)=sqrt(9*x+9))";

(*EO- 2*)

val fmz = ["equality (sqrt(x+1)+sqrt(4*x+4)=sqrt(9*x+9))",

	   "solveFor x", "solutions L"];

val (dI',pI',mI') = ("RootEq",["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;

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

(*"13 + 13 * x + - 2 * sqrt ((4 + 4 * x) * (9 + 9 * x)) = 1 + x" 

-> Subproblem ("RootEq", ["univariate", ...])*)

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

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

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

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

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

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

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

(*"144 + 288 * x + 144 * x \<up> 2 = 144 + x \<up> 2 + 288 * x + 143 * x \<up> 2"

-> Subproblem ("RootEq", ["univariate", ...])*)

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

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

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

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

val (p,_,f,nxt,_,pt) = me 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' (Test_Out.FormKF (~1, EdUndef, 0, Nundef, "0 = 0")) then ()

else error "rlang.sml: diff.behav. in Schalk II s.56 Bsp 73b";

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

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

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

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

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

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

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

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

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

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

val asm = Ctree.get_assumptions pt p;

if asm=[] andalso f = Form' (Test_Out.FormKF (~1,EdUndef,0,Nundef,"UniversalList")) andalso nxt = ("End_Proof'",End_Proof') then ()

else error "rlang.sml: diff.behav. in UniversalList 2";

(*-----------------  Schalk II s.56 Bsp 74a ------------------------*)

"Schalk II s.56 Bsp 74a (sqrt(4*x+1) - sqrt(x+3) = sqrt(x - 2))";

"Schalk II s.56 Bsp 74a (sqrt(4*x+1) - sqrt(x+3) = sqrt(x - 2))";

"Schalk II s.56 Bsp 74a (sqrt(4*x+1) - sqrt(x+3) = sqrt(x - 2))";

(*EO-3*)

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

	   "solveFor x", "solutions L"];

val (dI',pI',mI') = ("RootEq",["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;

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

(*4 + 5 * x + - 2 * sqrt (3 + 13 * x + 4 * x \<up> 2) = - 2 + x" 

-> Subproblem ("RootEq", ["univariate", ...])*)

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

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

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

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

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

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

val (p,_,f,nxt,_,pt) = me 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 + 52 * x + 16 * x \<up> 2 = 36 + x \<up> 2 + 48 * x + 15 * x \<up> 2"

-> Subproblem ("RootEq", ["univariate", ...])*)

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

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

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

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

val (p,_,f,nxt,_,pt) = me 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' (Test_Out.FormKF (~1, EdUndef, 0, Nundef, "- 24 + 4 * x = 0")) then ()

else error "rlang.sml: diff.behav. in Schalk II s.56 Bsp 74a";

(*-> ubproblem ("PolyEq", ["degree_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;

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

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

	 | _ => error "rlang.sml: diff.behav. in  Schalk II s.56 Bsp 74a [x = 6]";

(*-----------------  Schalk II s.56 Bsp 77b ------------------------*)

"Schalk II s.56 Bsp 77b (sqrt(x+12)+sqrt(x - 3) = sqrt(x + 32) - sqrt(5+x))";

"Schalk II s.56 Bsp 77b (sqrt(x+12)+sqrt(x - 3) = sqrt(x + 32) - sqrt(5+x))";

"Schalk II s.56 Bsp 77b (sqrt(x+12)+sqrt(x - 3) = sqrt(x + 32) - sqrt(5+x))";

(*EO-4*)

val fmz = ["equality (sqrt(x+12)+sqrt(x - 3) = sqrt(x + 32) - sqrt(5+x))",

	   "solveFor x", "solutions L"];

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

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

(* val nxt = ("Model_Problem",Model_Problem ["sq", "rootX", "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 nxt = ("Model_Problem",Model_Problem ["sq", "rootX", "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; f2str f;

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

(* val nxt = ("Model_Problem",Model_Problem ["sq", "rootX", "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 nxt = ("Model_Problem", 

 Model_Problem ["normalise", "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; since MGs norm_Rational*)

if f = Form'(Test_Out.FormKF (~1, EdUndef, 0, Nundef, "451584 + - 112896 * x = 0"))then()

else error "rlang.sml: diff.behav. in Schalk II s.56 Bsp 77b";

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

(* val nxt = ("Model_Problem",

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

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

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

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

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

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