test/Tools/isac/Knowledge/rlang.sml
branchisac-update-Isa09-2
changeset 38031 460c24a6a6ba
parent 37991 028442673981
child 41928 20138d6136cd
equal deleted inserted replaced
38030:95d956108461 38031:460c24a6a6ba
    77 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
    77 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
    78 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
    78 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
    79 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
    79 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
    80 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
    80 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
    81 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2]")) => ()
    81 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2]")) => ()
    82 	 | _ => raise error "rlang.sml: diff.behav. in Schalk I s.86 Bsp 5 [x = 2]";
    82 	 | _ => error "rlang.sml: diff.behav. in Schalk I s.86 Bsp 5 [x = 2]";
    83 
    83 
    84 (*-----------------  Schalk I s.86 Bsp 19 ------------------------*)
    84 (*-----------------  Schalk I s.86 Bsp 19 ------------------------*)
    85 "Schalk I s.86 Bsp 19 (x - 5)*(10 - x) = (3 - x)*(2 + x) + 2*(x + 20)";
    85 "Schalk I s.86 Bsp 19 (x - 5)*(10 - x) = (3 - x)*(2 + x) + 2*(x + 20)";
    86 "Schalk I s.86 Bsp 19 (x - 5)*(10 - x) = (3 - x)*(2 + x) + 2*(x + 20)";
    86 "Schalk I s.86 Bsp 19 (x - 5)*(10 - x) = (3 - x)*(2 + x) + 2*(x + 20)";
    87 "Schalk I s.86 Bsp 19 (x - 5)*(10 - x) = (3 - x)*(2 + x) + 2*(x + 20)";
    87 "Schalk I s.86 Bsp 19 (x - 5)*(10 - x) = (3 - x)*(2 + x) + 2*(x + 20)";
   107 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   107 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   108 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   108 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   109 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   109 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   110 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   110 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   111 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 8]")) => ()
   111 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 8]")) => ()
   112 	 | _ => raise error "rlang.sml: diff.behav. in Schalk I s.86 Bsp 19 [x = 8]";
   112 	 | _ => error "rlang.sml: diff.behav. in Schalk I s.86 Bsp 19 [x = 8]";
   113 
   113 
   114 (*-----------------  Schalk I s.86 Bsp 23 ------------------------*)
   114 (*-----------------  Schalk I s.86 Bsp 23 ------------------------*)
   115 "Schalk I s.86 Bsp 19 ((2*x+5)^^^2+(3*x+4)^^^2=(13*x+2)*(x+1)+2*(15+14*x))";
   115 "Schalk I s.86 Bsp 19 ((2*x+5)^^^2+(3*x+4)^^^2=(13*x+2)*(x+1)+2*(15+14*x))";
   116 "Schalk I s.86 Bsp 19 ((2*x+5)^^^2+(3*x+4)^^^2=(13*x+2)*(x+1)+2*(15+14*x))";
   116 "Schalk I s.86 Bsp 19 ((2*x+5)^^^2+(3*x+4)^^^2=(13*x+2)*(x+1)+2*(15+14*x))";
   117 "Schalk I s.86 Bsp 19 ((2*x+5)^^^2+(3*x+4)^^^2=(13*x+2)*(x+1)+2*(15+14*x))";
   117 "Schalk I s.86 Bsp 19 ((2*x+5)^^^2+(3*x+4)^^^2=(13*x+2)*(x+1)+2*(15+14*x))";
   137 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   137 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   138 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   138 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   139 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   139 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   140 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   140 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   141 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = -9]")) => ()
   141 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = -9]")) => ()
   142 	 | _ => raise error "rlang.sml: diff.behav. in Schalk I s.86 Bsp 23 [x = -9]";
   142 	 | _ => error "rlang.sml: diff.behav. in Schalk I s.86 Bsp 23 [x = -9]";
   143 
   143 
   144 (*-----------------  Schalk I s.86 Bsp 25 ------------------------*)
   144 (*-----------------  Schalk I s.86 Bsp 25 ------------------------*)
   145 "Schalk I s.86 Bsp 25 ((2*x+1)^^^3+(x+1)^^^3=(2*x+1)^^^2*2*x+(x+2)^^^3+x^^^2)";
   145 "Schalk I s.86 Bsp 25 ((2*x+1)^^^3+(x+1)^^^3=(2*x+1)^^^2*2*x+(x+2)^^^3+x^^^2)";
   146 "Schalk I s.86 Bsp 25 ((2*x+1)^^^3+(x+1)^^^3=(2*x+1)^^^2*2*x+(x+2)^^^3+x^^^2)";
   146 "Schalk I s.86 Bsp 25 ((2*x+1)^^^3+(x+1)^^^3=(2*x+1)^^^2*2*x+(x+2)^^^3+x^^^2)";
   147 "Schalk I s.86 Bsp 25 ((2*x+1)^^^3+(x+1)^^^3=(2*x+1)^^^2*2*x+(x+2)^^^3+x^^^2)";
   147 "Schalk I s.86 Bsp 25 ((2*x+1)^^^3+(x+1)^^^3=(2*x+1)^^^2*2*x+(x+2)^^^3+x^^^2)";
   167 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   167 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   168 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   168 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   169 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   169 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   170 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   170 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   171 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = -6 / 5]")) => ()
   171 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = -6 / 5]")) => ()
   172 	 | _ => raise error "rlang.sml: diff.behav. in Schalk I s.86 Bsp 25 [x = -6 / 5]";
   172 	 | _ => error "rlang.sml: diff.behav. in Schalk I s.86 Bsp 25 [x = -6 / 5]";
   173 
   173 
   174 (*-----------------  Schalk I s.86 Bsp 28b ------------------------*)
   174 (*-----------------  Schalk I s.86 Bsp 28b ------------------------*)
   175 "Schalk I s.86 Bsp 28b ((3*x+5)/18 - x/2 = -((3*x - 2)/9))";
   175 "Schalk I s.86 Bsp 28b ((3*x+5)/18 - x/2 = -((3*x - 2)/9))";
   176 "Schalk I s.86 Bsp 28b ((3*x+5)/18 - x/2 = -((3*x - 2)/9))";
   176 "Schalk I s.86 Bsp 28b ((3*x+5)/18 - x/2 = -((3*x - 2)/9))";
   177 "Schalk I s.86 Bsp 28b ((3*x+5)/18 - x/2 = -((3*x - 2)/9))";
   177 "Schalk I s.86 Bsp 28b ((3*x+5)/18 - x/2 = -((3*x - 2)/9))";
   195 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   195 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   196 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   196 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   197 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   197 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   198 val (p,_,f,nxt,_,pt) = me nxt p [1] pt; f2str f;
   198 val (p,_,f,nxt,_,pt) = me nxt p [1] pt; f2str f;
   199 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[]")) => ()
   199 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[]")) => ()
   200 	 | _ => raise error "rlang.sml: diff.behav. in Schalk I s.86 Bsp 28b []";
   200 	 | _ => error "rlang.sml: diff.behav. in Schalk I s.86 Bsp 28b []";
   201 
   201 
   202 (*WN---v *)
   202 (*WN---v *)
   203 val bdv= (term_of o the o (parse thy)) "bdv";
   203 val bdv= (term_of o the o (parse thy)) "bdv";
   204 val v = (term_of o the o (parse thy)) "x";
   204 val v = (term_of o the o (parse thy)) "x";
   205 val t = (term_of o the o (parse thy)) "3 * x / 5";
   205 val t = (term_of o the o (parse thy)) "3 * x / 5";
   206 val SOME (t',_) = rewrite_set_inst_ PolyEq.thy true 
   206 val SOME (t',_) = rewrite_set_inst_ PolyEq.thy true 
   207 				    [(bdv, v)] make_ratpoly_in t;
   207 				    [(bdv, v)] make_ratpoly_in t;
   208 if term2str t' = "3 / 5 * x" then () else raise error "rlang.sml: 1";
   208 if term2str t' = "3 / 5 * x" then () else error "rlang.sml: 1";
   209 
   209 
   210 val t = str2term "(3*x+5)/18 - x/2  - -(3*x - 2)/9 = 0";
   210 val t = str2term "(3*x+5)/18 - x/2  - -(3*x - 2)/9 = 0";
   211 val subst = [(str2term "bdv", str2term "x")];
   211 val subst = [(str2term "bdv", str2term "x")];
   212 val SOME (t',_) = rewrite_set_inst_ thy false subst make_ratpoly_in t;
   212 val SOME (t',_) = rewrite_set_inst_ thy false subst make_ratpoly_in t;
   213 if term2str t' = "1 / 18 = 0" then () else raise error "rlang.sml: 2";
   213 if term2str t' = "1 / 18 = 0" then () else error "rlang.sml: 2";
   214 (*WN---^ *)
   214 (*WN---^ *)
   215 
   215 
   216 (*-----------------  Schalk I s.87 Bsp 36b ------------------------*)
   216 (*-----------------  Schalk I s.87 Bsp 36b ------------------------*)
   217 "Schalk I s.87 Bsp 36b ((17*x - 51)/9 - (-(13*x - 3)/6) + 11 -(9*x- 7)/4 = 0)";
   217 "Schalk I s.87 Bsp 36b ((17*x - 51)/9 - (-(13*x - 3)/6) + 11 -(9*x- 7)/4 = 0)";
   218 "Schalk I s.87 Bsp 36b ((17*x - 51)/9 - (-(13*x - 3)/6) + 11 -(9*x- 7)/4 = 0)";
   218 "Schalk I s.87 Bsp 36b ((17*x - 51)/9 - (-(13*x - 3)/6) + 11 -(9*x- 7)/4 = 0)";
   238 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   238 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   239 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   239 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   240 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   240 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   241 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   241 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   242 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = -237 / 65]")) => ()
   242 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = -237 / 65]")) => ()
   243 	 | _ => raise error "rlang.sml: diff.behav. in Schalk I s.86 Bsp 36b [x = -237 / 65]";
   243 	 | _ => error "rlang.sml: diff.behav. in Schalk I s.86 Bsp 36b [x = -237 / 65]";
   244 
   244 
   245 
   245 
   246 (*WN---v *)
   246 (*WN---v *)
   247 val t = str2term "(17*x - 51)/9 - (-(13*x - 3)/6) + 11 - (9*x - 7)/4 = 0";
   247 val t = str2term "(17*x - 51)/9 - (-(13*x - 3)/6) + 11 - (9*x - 7)/4 = 0";
   248 val subst = [(str2term "bdv", str2term "x")];
   248 val subst = [(str2term "bdv", str2term "x")];
   249 val SOME (t',_) = rewrite_set_inst_ thy false subst make_ratpoly_in t;
   249 val SOME (t',_) = rewrite_set_inst_ thy false subst make_ratpoly_in t;
   250 term2str t';
   250 term2str t';
   251 if term2str t' = "79 / 12 + 65 / 36 * x = 0" then () 
   251 if term2str t' = "79 / 12 + 65 / 36 * x = 0" then () 
   252 else raise error "rlang.sml: 3";
   252 else error "rlang.sml: 3";
   253 (*WN---^ *)
   253 (*WN---^ *)
   254 
   254 
   255 
   255 
   256 (*-----------------  Schalk I s.87 Bsp 38b ------------------------*)
   256 (*-----------------  Schalk I s.87 Bsp 38b ------------------------*)
   257 "Schalk I s.87 Bsp 38b (-(2/x) + 3/(2*x) - 4/(3*x) + 5/(4*x) + 6/(5*x) =65/8)";
   257 "Schalk I s.87 Bsp 38b (-(2/x) + 3/(2*x) - 4/(3*x) + 5/(4*x) + 6/(5*x) =65/8)";
   277 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   277 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   278 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   278 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   279 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   279 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   280 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   280 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   281 if f = Form' (FormKF (~1, EdUndef, 0, Nundef, "296 + -3900 * x = 0")) then ()
   281 if f = Form' (FormKF (~1, EdUndef, 0, Nundef, "296 + -3900 * x = 0")) then ()
   282 else raise error "rlang.sml: diff.behav. in Schalk I s.87 Bsp 38b";
   282 else error "rlang.sml: diff.behav. in Schalk I s.87 Bsp 38b";
   283 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   283 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   284 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   284 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   285 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   285 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   286 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   286 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   287 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   287 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   289 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   289 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   290 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   290 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   291 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   291 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   292 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   292 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   293 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 74 / 975]")) => ()
   293 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 74 / 975]")) => ()
   294 	 | _ => raise error "rlang.sml: diff.behav. in Schalk I s.86 Bsp 38b [x = 74 / 975]";
   294 	 | _ => error "rlang.sml: diff.behav. in Schalk I s.86 Bsp 38b [x = 74 / 975]";
   295 
   295 
   296 (*-----------------  Schalk I s.87 Bsp 40b ------------------------*)
   296 (*-----------------  Schalk I s.87 Bsp 40b ------------------------*)
   297 "Schalk I s.87 Bsp 40b ((x+3)/(2*x - 4)=3)";
   297 "Schalk I s.87 Bsp 40b ((x+3)/(2*x - 4)=3)";
   298 "Schalk I s.87 Bsp 40b ((x+3)/(2*x - 4)=3)";
   298 "Schalk I s.87 Bsp 40b ((x+3)/(2*x - 4)=3)";
   299 "Schalk I s.87 Bsp 40b ((x+3)/(2*x - 4)=3)";
   299 "Schalk I s.87 Bsp 40b ((x+3)/(2*x - 4)=3)";
   319 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   319 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   320 val (p,_,f,nxt,_,pt) = me nxt p [1] pt; f2str f;
   320 val (p,_,f,nxt,_,pt) = me nxt p [1] pt; f2str f;
   321 (*val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   321 (*val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   322 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;*)
   322 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;*)
   323 if f = Form' (FormKF (~1, EdUndef, 0, Nundef, "15 + -5 * x = 0")) then ()
   323 if f = Form' (FormKF (~1, EdUndef, 0, Nundef, "15 + -5 * x = 0")) then ()
   324 else raise error "rlang.sml: diff.behav. in Schalk I s.87 Bsp 40b";
   324 else error "rlang.sml: diff.behav. in Schalk I s.87 Bsp 40b";
   325 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   325 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   326 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   326 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   327 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   327 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   328 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   328 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   329 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   329 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   330 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   330 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   331 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   331 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   332 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   332 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   333 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   333 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   334 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 3]")) => ()
   334 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 3]")) => ()
   335 	 | _ => raise error "rlang.sml: diff.behav. in Schalk I s.87 Bsp 40b [x = 3]";
   335 	 | _ => error "rlang.sml: diff.behav. in Schalk I s.87 Bsp 40b [x = 3]";
   336 
   336 
   337 
   337 
   338 (*-----------------  Schalk I s.87 Bsp 44a ------------------------*)
   338 (*-----------------  Schalk I s.87 Bsp 44a ------------------------*)
   339 "Schalk I s.87 Bsp 44a ((1/2+(5*x)/2)^^^2 -((13*x)/2- 5/2)^^^2 -(6*x)^^^2+29)";
   339 "Schalk I s.87 Bsp 44a ((1/2+(5*x)/2)^^^2 -((13*x)/2- 5/2)^^^2 -(6*x)^^^2+29)";
   340 "Schalk I s.87 Bsp 44a ((1/2+(5*x)/2)^^^2 -((13*x)/2- 5/2)^^^2 -(6*x)^^^2+29)";
   340 "Schalk I s.87 Bsp 44a ((1/2+(5*x)/2)^^^2 -((13*x)/2- 5/2)^^^2 -(6*x)^^^2+29)";
   363 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   363 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   364 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   364 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   365 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   365 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   366 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   366 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   367 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 1]")) => ()
   367 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 1]")) => ()
   368 	 | _ => raise error "rlang.sml: diff.behav. in Schalk I s.87 Bsp 44a [x = 1]";
   368 	 | _ => error "rlang.sml: diff.behav. in Schalk I s.87 Bsp 44a [x = 1]";
   369 
   369 
   370 (*WN---v *)
   370 (*WN---v *)
   371 val t = str2term "(1/2 + (5*x)/2)^^^2 - ((13*x)/2 - 5/2)^^^2 - (6*x)^^^2 + 29";
   371 val t = str2term "(1/2 + (5*x)/2)^^^2 - ((13*x)/2 - 5/2)^^^2 - (6*x)^^^2 + 29";
   372 val subst = [(str2term "bdv", str2term "x")];
   372 val subst = [(str2term "bdv", str2term "x")];
   373 val SOME (t',_) = rewrite_set_inst_ thy false subst make_ratpoly_in t;
   373 val SOME (t',_) = rewrite_set_inst_ thy false subst make_ratpoly_in t;
   374 if term2str t' = "23 + 35 * x + -72 * x ^^^ 2" then () 
   374 if term2str t' = "23 + 35 * x + -72 * x ^^^ 2" then () 
   375 else raise error "rlang.sml: 4";
   375 else error "rlang.sml: 4";
   376 
   376 
   377 val t = str2term "(1/2 + (5*x)/2)^^^2 - ((13*x)/2 - 5/2)^^^2 + (6*x)^^^2 - 29";
   377 val t = str2term "(1/2 + (5*x)/2)^^^2 - ((13*x)/2 - 5/2)^^^2 + (6*x)^^^2 - 29";
   378 val subst = [(str2term "bdv", str2term "x")];
   378 val subst = [(str2term "bdv", str2term "x")];
   379 val SOME (t',_) = rewrite_set_inst_ thy false subst make_ratpoly_in t;
   379 val SOME (t',_) = rewrite_set_inst_ thy false subst make_ratpoly_in t;
   380 if term2str t' = "-35 + 35 * x" then () 
   380 if term2str t' = "-35 + 35 * x" then () 
   381 else raise error "rlang.sml: 4.1";
   381 else error "rlang.sml: 4.1";
   382 (*WN---^ *)
   382 (*WN---^ *)
   383 
   383 
   384 (*-----------------  Schalk I s.87 Bsp 52a ------------------------*)
   384 (*-----------------  Schalk I s.87 Bsp 52a ------------------------*)
   385 "Schalk I s.87 Bsp 52a ((5*x)/(x - 2) - x/(x+2)=4)";
   385 "Schalk I s.87 Bsp 52a ((5*x)/(x - 2) - x/(x+2)=4)";
   386 "Schalk I s.87 Bsp 52a ((5*x)/(x - 2) - x/(x+2)=4)";
   386 "Schalk I s.87 Bsp 52a ((5*x)/(x - 2) - x/(x+2)=4)";
   402 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   402 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   403 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   403 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   404 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   404 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   405 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   405 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   406 if f = Form' (FormKF (~1, EdUndef, 0, Nundef, "16 + 12 * x = 0")) then ()
   406 if f = Form' (FormKF (~1, EdUndef, 0, Nundef, "16 + 12 * x = 0")) then ()
   407 else raise error "rlang.sml: diff.behav. in Schalk I s.87 Bsp 52a";
   407 else error "rlang.sml: diff.behav. in Schalk I s.87 Bsp 52a";
   408             (*Subproblem["degree_1", "polynomial", "univariate", "equation"]*)
   408             (*Subproblem["degree_1", "polynomial", "univariate", "equation"]*)
   409 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   409 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   410 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   410 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   411 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   411 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   412 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   412 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   414 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   414 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   415 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   415 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   416 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   416 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   417 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   417 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   418 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = -4 / 3]")) => ()
   418 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = -4 / 3]")) => ()
   419 	 | _ => raise error "rlang.sml: diff.behav. in  Schalk I s.87 Bsp 52a [x = -4 / 3]";
   419 	 | _ => error "rlang.sml: diff.behav. in  Schalk I s.87 Bsp 52a [x = -4 / 3]";
   420 
   420 
   421 (*-----------------  Schalk I s.87 Bsp 55b ------------------------*)
   421 (*-----------------  Schalk I s.87 Bsp 55b ------------------------*)
   422 "Schalk I s.87 Bsp 55b (x/(x^^^2 - 6*x+9) - 1/(x^^^2 - 3*x) =1/x)";
   422 "Schalk I s.87 Bsp 55b (x/(x^^^2 - 6*x+9) - 1/(x^^^2 - 3*x) =1/x)";
   423 "Schalk I s.87 Bsp 55b (x/(x^^^2 - 6*x+9) - 1/(x^^^2 - 3*x) =1/x)";
   423 "Schalk I s.87 Bsp 55b (x/(x^^^2 - 6*x+9) - 1/(x^^^2 - 3*x) =1/x)";
   424 "Schalk I s.87 Bsp 55b (x/(x^^^2 - 6*x+9) - 1/(x^^^2 - 3*x) =1/x)";
   424 "Schalk I s.87 Bsp 55b (x/(x^^^2 - 6*x+9) - 1/(x^^^2 - 3*x) =1/x)";
   445 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   445 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   446 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   446 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   447 (*val (p,_,f,nxt,_,pt) = me nxt p [1] pt; 040209 MGs norm_Rational*)
   447 (*val (p,_,f,nxt,_,pt) = me nxt p [1] pt; 040209 MGs norm_Rational*)
   448 (* val nxt = Subproblem ("PolyEq",["polynomial","univariate","equation"])*)
   448 (* val nxt = Subproblem ("PolyEq",["polynomial","univariate","equation"])*)
   449 if f= Form' (FormKF (~1, EdUndef, 0, Nundef, "-6 * x + 5 * x ^^^ 2 = 0"))then()
   449 if f= Form' (FormKF (~1, EdUndef, 0, Nundef, "-6 * x + 5 * x ^^^ 2 = 0"))then()
   450 else raise error "rlang.sml: diff.behav. in Schalk I s.87 Bsp 55b";
   450 else error "rlang.sml: diff.behav. in Schalk I s.87 Bsp 55b";
   451 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   451 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   452 (*nxt=Model_Problem["bdv_only","degree_2","polynomial","univariate","equation*)
   452 (*nxt=Model_Problem["bdv_only","degree_2","polynomial","univariate","equation*)
   453 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   453 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   454 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   454 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   455 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   455 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   475 (*val p = ([6],Res) : pos'
   475 (*val p = ([6],Res) : pos'
   476 val f = Form' (FormKF (~1,EdUndef,1,Nundef,"[x = 0, x = 6 / 5]")) : mout
   476 val f = Form' (FormKF (~1,EdUndef,1,Nundef,"[x = 0, x = 6 / 5]")) : mout
   477 val nxt = ("Check_elementwise",Check_elementwise "Assumptions")*)
   477 val nxt = ("Check_elementwise",Check_elementwise "Assumptions")*)
   478 val [(aaa,ppp)] = get_assumptions_ pt p;
   478 val [(aaa,ppp)] = get_assumptions_ pt p;
   479 if term2str aaa = "9 * x + -6 * x ^^^ 2 + x ^^^ 3 ~= 0" then ()
   479 if term2str aaa = "9 * x + -6 * x ^^^ 2 + x ^^^ 3 ~= 0" then ()
   480 else raise error "rlang.sml: diff.behav. in I s.87 Bsp 55b [x = 6 / 5], asms";
   480 else error "rlang.sml: diff.behav. in I s.87 Bsp 55b [x = 6 / 5], asms";
   481 (*WN060717 unintentionally changed some rls/ord while 
   481 (*WN060717 unintentionally changed some rls/ord while 
   482      completing knowl. for thes2file...
   482      completing knowl. for thes2file...
   483 if term2str aaa = "9 * x + (x ^^^ 3 + -6 * x ^^^ 2) ~= 0" then ()
   483 if term2str aaa = "9 * x + (x ^^^ 3 + -6 * x ^^^ 2) ~= 0" then ()
   484 else raise error "rlang.sml: diff.behav. in I s.87 Bsp 55b [x = 6 / 5], asms";
   484 else error "rlang.sml: diff.behav. in I s.87 Bsp 55b [x = 6 / 5], asms";
   485 .... but it became even better*)
   485 .... but it became even better*)
   486 
   486 
   487 (*22.10.03:
   487 (*22.10.03:
   488 val it = "9 * x + (x ^^^ 3 + -6 * x ^^^ 2) ~= 0" : string;
   488 val it = "9 * x + (x ^^^ 3 + -6 * x ^^^ 2) ~= 0" : string;
   489   before 22.10.03:
   489   before 22.10.03:
   500 (*val p = ([7],Res) : pos'
   500 (*val p = ([7],Res) : pos'
   501 val f = Form' (FormKF (~1,EdUndef,1,Nundef,"[x = 6 / 5]")) : mout
   501 val f = Form' (FormKF (~1,EdUndef,1,Nundef,"[x = 6 / 5]")) : mout
   502 val nxt =Check_Postcond ["rational","univariate","equation"])        *)
   502 val nxt =Check_Postcond ["rational","univariate","equation"])        *)
   503 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   503 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   504 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 6 / 5]")) => ()
   504 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 6 / 5]")) => ()
   505 	| _ => raise error "rlang.sml: diff.behav. in  Schalk I s.87 Bsp 55b [x = 6 / 5]";
   505 	| _ => error "rlang.sml: diff.behav. in  Schalk I s.87 Bsp 55b [x = 6 / 5]";
   506 
   506 
   507 (*-----------------  Schalk I s.88 Bsp 64c ------------------------*)
   507 (*-----------------  Schalk I s.88 Bsp 64c ------------------------*)
   508 "Schalk I s.88 Bsp 64c (((x - 1)/(x+1)+1)/((x - 1)/(x+1) - (x+1)/(x - 1))=2)";
   508 "Schalk I s.88 Bsp 64c (((x - 1)/(x+1)+1)/((x - 1)/(x+1) - (x+1)/(x - 1))=2)";
   509 "Schalk I s.88 Bsp 64c (((x - 1)/(x+1)+1)/((x - 1)/(x+1) - (x+1)/(x - 1))=2)";
   509 "Schalk I s.88 Bsp 64c (((x - 1)/(x+1)+1)/((x - 1)/(x+1) - (x+1)/(x - 1))=2)";
   510 "Schalk I s.88 Bsp 64c (((x - 1)/(x+1)+1)/((x - 1)/(x+1) - (x+1)/(x - 1))=2)";
   510 "Schalk I s.88 Bsp 64c (((x - 1)/(x+1)+1)/((x - 1)/(x+1) - (x+1)/(x - 1))=2)";
   528 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   528 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   529 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   529 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   530 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   530 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   531 val (p,_,f,nxt,_,pt) = me nxt p [1] pt; f2str f;
   531 val (p,_,f,nxt,_,pt) = me nxt p [1] pt; f2str f;
   532 if f = Form' (FormKF (~1, EdUndef, 0, Nundef, "-3 + -1 * x = 0")) then ()
   532 if f = Form' (FormKF (~1, EdUndef, 0, Nundef, "-3 + -1 * x = 0")) then ()
   533 else raise error "rlangsml: diff.behav. in Schalk I s.88 Bsp 64c";
   533 else error "rlangsml: diff.behav. in Schalk I s.88 Bsp 64c";
   534 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   534 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   535 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   535 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   536 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   536 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   537 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   537 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   538 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   538 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   540 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   540 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   541 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   541 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   542 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   542 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   543 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   543 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   544 case f of Form' (FormKF (_,_,0,_,"[x = -3]")) => ()
   544 case f of Form' (FormKF (_,_,0,_,"[x = -3]")) => ()
   545 	 | _ => raise error "rlang.sml: diff.behav. in  Schalk I s.88 Bsp 64c [x = -3]";
   545 	 | _ => error "rlang.sml: diff.behav. in  Schalk I s.88 Bsp 64c [x = -3]";
   546 
   546 
   547 (*-----------------  Schalk I s.88 Bsp 79a (2) ------------------------*)
   547 (*-----------------  Schalk I s.88 Bsp 79a (2) ------------------------*)
   548 "Schalk I s.88 Bsp 79a (2) (m1*v1+m2*v2=0)";
   548 "Schalk I s.88 Bsp 79a (2) (m1*v1+m2*v2=0)";
   549 "Schalk I s.88 Bsp 79a (2) (m1*v1+m2*v2=0)";
   549 "Schalk I s.88 Bsp 79a (2) (m1*v1+m2*v2=0)";
   550 "Schalk I s.88 Bsp 79a (2) (m1*v1+m2*v2=0)";
   550 "Schalk I s.88 Bsp 79a (2) (m1*v1+m2*v2=0)";
   569 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   569 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   570 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   570 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   571 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   571 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   572 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   572 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   573 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[m1 = -1 * m2 * v2 / v1]")) => ()
   573 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[m1 = -1 * m2 * v2 / v1]")) => ()
   574 	 | _ => raise error "rlang.sml: diff.behav. in  Schalk I s.88 Bsp 79a (2) [m1 = -1 * m2 * v2 / v1]";
   574 	 | _ => error "rlang.sml: diff.behav. in  Schalk I s.88 Bsp 79a (2) [m1 = -1 * m2 * v2 / v1]";
   575 
   575 
   576 (*-----------------  Schalk I s.89 Bsp 90a(1) ------------------------*)
   576 (*-----------------  Schalk I s.89 Bsp 90a(1) ------------------------*)
   577 "Schalk I s.89 Bsp 90a (1) (f=((w+u)/(w+v))*v0)";
   577 "Schalk I s.89 Bsp 90a (1) (f=((w+u)/(w+v))*v0)";
   578 "Schalk I s.89 Bsp 90a (1) (f=((w+u)/(w+v))*v0)";
   578 "Schalk I s.89 Bsp 90a (1) (f=((w+u)/(w+v))*v0)";
   579 "Schalk I s.89 Bsp 90a (1) (f=((w+u)/(w+v))*v0)";
   579 "Schalk I s.89 Bsp 90a (1) (f=((w+u)/(w+v))*v0)";
   611          (~1,
   611          (~1,
   612             EdUndef,
   612             EdUndef,
   613             0,
   613             0,
   614             Nundef,
   614             Nundef,
   615             "f * w + -1 * u * v0 + -1 * v0 * w + f * v = 0")) then ()
   615             "f * w + -1 * u * v0 + -1 * v0 * w + f * v = 0")) then ()
   616 else raise error "rlang.sml: diff.behav. in Schalk I s.89 Bsp 90a";
   616 else error "rlang.sml: diff.behav. in Schalk I s.89 Bsp 90a";
   617 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   617 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   618 (*val nxt = Model_Problem ["degree_1","polynomial","univariate","equation"])*)
   618 (*val nxt = Model_Problem ["degree_1","polynomial","univariate","equation"])*)
   619 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   619 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   620 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   620 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   621 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   621 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   644 (*val f = Form' (FormKF (~1,EdUndef,1,Nundef,"[]")) : mout
   644 (*val f = Form' (FormKF (~1,EdUndef,1,Nundef,"[]")) : mout
   645 val nxt = Check_Postcond ["rational","univariate","equation"])        *)
   645 val nxt = Check_Postcond ["rational","univariate","equation"])        *)
   646 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   646 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   647 case f of Form'  (FormKF (~1,EdUndef,0,Nundef,
   647 case f of Form'  (FormKF (~1,EdUndef,0,Nundef,
   648         "[v = (u * v0 + v0 * w + -1 * f * w) / f]")) => ()
   648         "[v = (u * v0 + v0 * w + -1 * f * w) / f]")) => ()
   649 	 | _ => raise error "rlang.sml: diff.behav. in  Schalk I s.89 Bsp 90a (1) [v=...]";
   649 	 | _ => error "rlang.sml: diff.behav. in  Schalk I s.89 Bsp 90a (1) [v=...]";
   650 if get_assumptions_ pt p = 
   650 if get_assumptions_ pt p = 
   651    [(str2term"(u * v0 + v0 * w + -1 * f * w) / f + w ~= 0",[])] then () 
   651    [(str2term"(u * v0 + v0 * w + -1 * f * w) / f + w ~= 0",[])] then () 
   652 else raise error "rlang.sml: diff.behav. in I s.89 Bsp 90a (1) [v=...] asm";
   652 else error "rlang.sml: diff.behav. in I s.89 Bsp 90a (1) [v=...] asm";
   653 
   653 
   654 
   654 
   655 (*-----------------  Schalk I s.89 Bsp 90a(2) ------------------------*)
   655 (*-----------------  Schalk I s.89 Bsp 90a(2) ------------------------*)
   656 "Schalk I s.89 Bsp 90a (2) (f=((w+u)/(w+v))*v0)";
   656 "Schalk I s.89 Bsp 90a (2) (f=((w+u)/(w+v))*v0)";
   657 "Schalk I s.89 Bsp 90a (2) (f=((w+u)/(w+v))*v0)";
   657 "Schalk I s.89 Bsp 90a (2) (f=((w+u)/(w+v))*v0)";
   680          (~1,
   680          (~1,
   681             EdUndef,
   681             EdUndef,
   682             0,
   682             0,
   683             Nundef,
   683             Nundef,
   684             "f * v + -1 * u * v0 + (f + -1 * v0) * w = 0")) then ()
   684             "f * v + -1 * u * v0 + (f + -1 * v0) * w = 0")) then ()
   685 else raise error "rlang.sml: diff.behav. in Schalk I s.89 Bsp 90a (2)";
   685 else error "rlang.sml: diff.behav. in Schalk I s.89 Bsp 90a (2)";
   686 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   686 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   687 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   687 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   688 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   688 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   689 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   689 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   690 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   690 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   691 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   691 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   692 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   692 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   693 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   693 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   694 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   694 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   695 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[w = (u * v0 + -1 * f * v) / (f + -1 * v0)]")) => ()
   695 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[w = (u * v0 + -1 * f * v) / (f + -1 * v0)]")) => ()
   696 	 | _ => raise error "rlang.sml: diff.behav. in Schalk I Bsp 90a(2)";
   696 	 | _ => error "rlang.sml: diff.behav. in Schalk I Bsp 90a(2)";
   697 if get_assumptions_ pt p = 
   697 if get_assumptions_ pt p = 
   698 [(str2term"v + (u * v0 + -1 * f * v) / (f + -1 * v0) ~= 0",[]),
   698 [(str2term"v + (u * v0 + -1 * f * v) / (f + -1 * v0) ~= 0",[]),
   699  (str2term"f + -1 * v0 ~= 0",[])]
   699  (str2term"f + -1 * v0 ~= 0",[])]
   700 then writeln "asm should be simplified ???" 
   700 then writeln "asm should be simplified ???" 
   701 else raise error "rlang.sml: diff.behav. in Schalk I Bsp 90a(2) asm";
   701 else error "rlang.sml: diff.behav. in Schalk I Bsp 90a(2) asm";
   702 
   702 
   703 (*-----------------  Schalk I s.89 Bsp 98a(1) ------------------------*)
   703 (*-----------------  Schalk I s.89 Bsp 98a(1) ------------------------*)
   704 "Schalk I s.89 Bsp 98a (1) (1/R=1/R1+1/R2)";
   704 "Schalk I s.89 Bsp 98a (1) (1/R=1/R1+1/R2)";
   705 "Schalk I s.89 Bsp 98a (1) (1/R=1/R1+1/R2)";
   705 "Schalk I s.89 Bsp 98a (1) (1/R=1/R1+1/R2)";
   706 "Schalk I s.89 Bsp 98a (1) (1/R=1/R1+1/R2)";
   706 "Schalk I s.89 Bsp 98a (1) (1/R=1/R1+1/R2)";
   725 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   725 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   726 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   726 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   727 if f = Form'
   727 if f = Form'
   728       (FormKF
   728       (FormKF
   729         (~1, EdUndef, 0, Nundef, "-1 * R * R2 + (R2 + -1 * R) * R1 = 0"))then()
   729         (~1, EdUndef, 0, Nundef, "-1 * R * R2 + (R2 + -1 * R) * R1 = 0"))then()
   730 else raise error "rlang.sml: diff.behav. in Schalk I s.89 Bsp 98a (1)";
   730 else error "rlang.sml: diff.behav. in Schalk I s.89 Bsp 98a (1)";
   731 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   731 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   732 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   732 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   733 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   733 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   734 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   734 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   735 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   735 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   736 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   736 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   737 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   737 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   738 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   738 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   739 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   739 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   740 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[R1 = R * R2 / (R2 + -1 * R)]")) => ()
   740 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[R1 = R * R2 / (R2 + -1 * R)]")) => ()
   741 	 | _ => raise error "rlang.sml: diff.behav. in 98a(1) [R1 = ...]";
   741 	 | _ => error "rlang.sml: diff.behav. in 98a(1) [R1 = ...]";
   742 if get_assumptions_ pt p = [(str2term"R * R2 * R2 ~= (R2 + -1 * R) * 0",[]),
   742 if get_assumptions_ pt p = [(str2term"R * R2 * R2 ~= (R2 + -1 * R) * 0",[]),
   743 			    (str2term"R2 + -1 * R ~= 0",[]),
   743 			    (str2term"R2 + -1 * R ~= 0",[]),
   744 			    (str2term"R2 + -1 * R ~= 0",[])] 
   744 			    (str2term"R2 + -1 * R ~= 0",[])] 
   745     then writeln "asm should be simplified"
   745     then writeln "asm should be simplified"
   746 else raise error "rlang.sml: diff.behav. in 98a(1) asm";
   746 else error "rlang.sml: diff.behav. in 98a(1) asm";
   747 
   747 
   748 (*-----------------  Schalk I s.89 Bsp 104a(1) ------------------------*)
   748 (*-----------------  Schalk I s.89 Bsp 104a(1) ------------------------*)
   749 "Schalk I s.89 Bsp 104a (1) (y^^^2=2*p*x)";
   749 "Schalk I s.89 Bsp 104a (1) (y^^^2=2*p*x)";
   750 "Schalk I s.89 Bsp 104a (1) (y^^^2=2*p*x)";
   750 "Schalk I s.89 Bsp 104a (1) (y^^^2=2*p*x)";
   751 "Schalk I s.89 Bsp 104a (1) (y^^^2=2*p*x)";
   751 "Schalk I s.89 Bsp 104a (1) (y^^^2=2*p*x)";
   770 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt; 
   770 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt; 
   771 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   771 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   772 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   772 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   773 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   773 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   774 case f of Form' (FormKF (_,_,0,_,"[p = y ^^^ 2 / (2 * x)]")) => ()
   774 case f of Form' (FormKF (_,_,0,_,"[p = y ^^^ 2 / (2 * x)]")) => ()
   775 	 | _ => raise error "rlang.sml: diff.behav. in  Schalk I s.89 Bsp 104a (1) [p = y^2/(2*x)]";
   775 	 | _ => error "rlang.sml: diff.behav. in  Schalk I s.89 Bsp 104a (1) [p = y^2/(2*x)]";
   776 if get_assumptions_ pt p = [(str2term"-2 * x ~= 0",[])] 
   776 if get_assumptions_ pt p = [(str2term"-2 * x ~= 0",[])] 
   777 then writeln"should be x ~= 0\nshould be x ~= 0\nshould be x ~= 0\n" 
   777 then writeln"should be x ~= 0\nshould be x ~= 0\nshould be x ~= 0\n" 
   778 else raise error "rlang.sml: diff.behav. in  I s.89 Bsp 104a(1) asm";
   778 else error "rlang.sml: diff.behav. in  I s.89 Bsp 104a(1) asm";
   779 
   779 
   780 
   780 
   781 (*-----------------  Schalk I s.89 Bsp 104a(2) ------------------------*)
   781 (*-----------------  Schalk I s.89 Bsp 104a(2) ------------------------*)
   782 "Schalk I s.89 Bsp 104a (2) (y^^^2=2*p*x)";
   782 "Schalk I s.89 Bsp 104a (2) (y^^^2=2*p*x)";
   783 "Schalk I s.89 Bsp 104a (2) (y^^^2=2*p*x)";
   783 "Schalk I s.89 Bsp 104a (2) (y^^^2=2*p*x)";
   804 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   804 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   805 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   805 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   806 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   806 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   807 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   807 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   808 case f of Form' (FormKF (_,_,0,_,"[y = sqrt (2 * p * x), y = -1 * sqrt (2 * p * x)]")) => ()
   808 case f of Form' (FormKF (_,_,0,_,"[y = sqrt (2 * p * x), y = -1 * sqrt (2 * p * x)]")) => ()
   809 | _ => raise error "rlang.sml: diff.behav. Schalk I s.89 Bsp 104a(2) [x = ]";
   809 | _ => error "rlang.sml: diff.behav. Schalk I s.89 Bsp 104a(2) [x = ]";
   810 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"
   810 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"
   811 else raise error "rlang.sml: diff.behav. in I s.89 Bsp 104a(2) asm";
   811 else error "rlang.sml: diff.behav. in I s.89 Bsp 104a(2) asm";
   812 
   812 
   813 
   813 
   814 (*-----------------  Schalk I s.90 Bsp 118a (1) ------------------------*)
   814 (*-----------------  Schalk I s.90 Bsp 118a (1) ------------------------*)
   815 "Schalk I s.90 Bsp 118a (1) (b^^^2*x^^^2 + a^^^2*y^^^2 = a^^^2*b^^^2)";
   815 "Schalk I s.90 Bsp 118a (1) (b^^^2*x^^^2 + a^^^2*y^^^2 = a^^^2*b^^^2)";
   816 "Schalk I s.90 Bsp 118a (1) (b^^^2*x^^^2 + a^^^2*y^^^2 = a^^^2*b^^^2)";
   816 "Schalk I s.90 Bsp 118a (1) (b^^^2*x^^^2 + a^^^2*y^^^2 = a^^^2*b^^^2)";
   850 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;f2str f;asms2str (get_asm (fst p, fst p) pt);
   850 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;f2str f;asms2str (get_asm (fst p, fst p) pt);
   851 
   851 
   852 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;f2str f;get_asm (fst p, fst p) pt;
   852 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;f2str f;get_asm (fst p, fst p) pt;
   853 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;f2str f;get_asm (fst p, fst p) pt;
   853 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;f2str f;get_asm (fst p, fst p) pt;
   854 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"
   854 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"
   855 | _ => raise error "rlang.sml: diff.behav. in  Schalk I s.89 Bsp 118a(2) [x = ]";
   855 | _ => error "rlang.sml: diff.behav. in  Schalk I s.89 Bsp 118a(2) [x = ]";
   856 val asms = get_assumptions_ pt p;
   856 val asms = get_assumptions_ pt p;
   857 if asms = [(str2term"0 * b ^^^ 2 <= -1 * (a ^^^ 2 * y ^^^ 2 + -1 * a ^^^ 2 * b ^^^ 2)", []),
   857 if asms = [(str2term"0 * b ^^^ 2 <= -1 * (a ^^^ 2 * y ^^^ 2 + -1 * a ^^^ 2 * b ^^^ 2)", []),
   858 	   (str2term"b ^^^ 2 ~= 0", []),
   858 	   (str2term"b ^^^ 2 ~= 0", []),
   859 	   (str2term"0 * b ^^^ 2 <= -1 * (a ^^^ 2 * y ^^^ 2 + -1 * a ^^^ 2 * b ^^^ 2)", []),
   859 	   (str2term"0 * b ^^^ 2 <= -1 * (a ^^^ 2 * y ^^^ 2 + -1 * a ^^^ 2 * b ^^^ 2)", []),
   860 	   (str2term"b ^^^ 2 ~= 0", [])
   860 	   (str2term"b ^^^ 2 ~= 0", [])
   861 	   ] then writeln"should be simplified MG"
   861 	   ] then writeln"should be simplified MG"
   862 else raise error "rlang.sml: diff.behav. in Schalk I s.89 Bsp 118a(2) asms";
   862 else error "rlang.sml: diff.behav. in Schalk I s.89 Bsp 118a(2) asms";
   863 
   863 
   864 (*-----------------  Schalk I s.102 Bsp 268(1) ------------------------*)
   864 (*-----------------  Schalk I s.102 Bsp 268(1) ------------------------*)
   865 "Schalk I s.102 Bsp 268(1) (A = (1/2)*(x1*(y2-y3)+x2*(y3 - y1)+x3*(y1 - y2)))";
   865 "Schalk I s.102 Bsp 268(1) (A = (1/2)*(x1*(y2-y3)+x2*(y3 - y1)+x3*(y1 - y2)))";
   866 "Schalk I s.102 Bsp 268(1) (A = (1/2)*(x1*(y2-y3)+x2*(y3 - y1)+x3*(y1 - y2)))";
   866 "Schalk I s.102 Bsp 268(1) (A = (1/2)*(x1*(y2-y3)+x2*(y3 - y1)+x3*(y1 - y2)))";
   867 "Schalk I s.102 Bsp 268(1) (A = (1/2)*(x1*(y2-y3)+x2*(y3 - y1)+x3*(y1 - y2)))";
   867 "Schalk I s.102 Bsp 268(1) (A = (1/2)*(x1*(y2-y3)+x2*(y3 - y1)+x3*(y1 - y2)))";
   887 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   887 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   888 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   888 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   889 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   889 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   890 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   890 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   891 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)]")) => ()
   891 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)]")) => ()
   892 | _ => raise error "rlang.sml: diff.behav. Schalk I s.102 Bsp 268(1) [x2=...]";
   892 | _ => error "rlang.sml: diff.behav. Schalk I s.102 Bsp 268(1) [x2=...]";
   893 if get_assumptions_ pt p = [(str2term"y1 / 2 + -1 * y3 / 2 ~= 0",[])] then ()
   893 if get_assumptions_ pt p = [(str2term"y1 / 2 + -1 * y3 / 2 ~= 0",[])] then ()
   894 else raise error "rlang.sml: diff.behav. in I s.102 Bsp 268(1) asm";
   894 else error "rlang.sml: diff.behav. in I s.102 Bsp 268(1) asm";
   895 
   895 
   896 (*--------------------  Schalk II ----------------------------*)
   896 (*--------------------  Schalk II ----------------------------*)
   897 (*--------------------  Schalk II ----------------------------*)
   897 (*--------------------  Schalk II ----------------------------*)
   898 (*--------------------  Schalk II ----------------------------*)
   898 (*--------------------  Schalk II ----------------------------*)
   899 (*--------------------  Schalk II ----------------------------*)
   899 (*--------------------  Schalk II ----------------------------*)
   924 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   924 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   925 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   925 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   926 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   926 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   927 val (p,_,f,nxt,_,pt) = me nxt p [1] pt; f2str f;
   927 val (p,_,f,nxt,_,pt) = me nxt p [1] pt; f2str f;
   928 if f = Form' (FormKF (~1, EdUndef, 0, Nundef, "-2 + x = 0")) then ()
   928 if f = Form' (FormKF (~1, EdUndef, 0, Nundef, "-2 + x = 0")) then ()
   929 else raise error "rlang.sml: diff.behav. in Schalk II s.56 Bsp 67b";
   929 else error "rlang.sml: diff.behav. in Schalk II s.56 Bsp 67b";
   930 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   930 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   931 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   931 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   932 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   932 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   933 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   933 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   934 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   934 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   935 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   935 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   936 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   936 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   937 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   937 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   938 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   938 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   939 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2]")) => ()
   939 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2]")) => ()
   940 	 | _ => raise error "rlang.sml: diff.behav. in  Schalk II s.56 Bsp 67b [x=2]";
   940 	 | _ => error "rlang.sml: diff.behav. in  Schalk II s.56 Bsp 67b [x=2]";
   941 
   941 
   942 (*-----------------  Schalk II s.56 Bsp 68a ------------------------*)
   942 (*-----------------  Schalk II s.56 Bsp 68a ------------------------*)
   943 "Schalk II s.56 Bsp 68a (5*sqrt(x) - 1 = 7*sqrt(x) - 5)";
   943 "Schalk II s.56 Bsp 68a (5*sqrt(x) - 1 = 7*sqrt(x) - 5)";
   944 "Schalk II s.56 Bsp 68a (5*sqrt(x) - 1 = 7*sqrt(x) - 5)";
   944 "Schalk II s.56 Bsp 68a (5*sqrt(x) - 1 = 7*sqrt(x) - 5)";
   945 "Schalk II s.56 Bsp 68a (5*sqrt(x) - 1 = 7*sqrt(x) - 5)";
   945 "Schalk II s.56 Bsp 68a (5*sqrt(x) - 1 = 7*sqrt(x) - 5)";
   981 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   981 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   982 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   982 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   983 if f = Form'
   983 if f = Form'
   984       (FormKF
   984       (FormKF
   985          (~1, EdUndef, 0, Nundef, "256 + -2368 * x + 576 * x ^^^ 2 = 0"))then()
   985          (~1, EdUndef, 0, Nundef, "256 + -2368 * x + 576 * x ^^^ 2 = 0"))then()
   986 else raise error "rlang.sml: diff.behav. in Schalk II s.56 Bsp 68a";
   986 else error "rlang.sml: diff.behav. in Schalk II s.56 Bsp 68a";
   987 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   987 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   988 get_assumptions_ pt p;
   988 get_assumptions_ pt p;
   989 (* val nxt = ("Model_Problem",  Model_Problem
   989 (* val nxt = ("Model_Problem",  Model_Problem
   990      ["abcFormula","degree_2","polynomial","univariate","equation"])*)
   990      ["abcFormula","degree_2","polynomial","univariate","equation"])*)
   991 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   991 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   999 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   999 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1000 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1000 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1001 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1001 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1002 if f = Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 4, x = 1 / 9]")) 
  1002 if f = Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 4, x = 1 / 9]")) 
  1003 then writeln "only [x = 4] !\nonly [x = 4] !\nonly [x = 4] !\n"
  1003 then writeln "only [x = 4] !\nonly [x = 4] !\nonly [x = 4] !\n"
  1004 else raise error "rlang.sml: diff.behav. in II 68a";
  1004 else error "rlang.sml: diff.behav. in II 68a";
  1005 val asms = get_assumptions_ pt p;
  1005 val asms = get_assumptions_ pt p;
  1006 if asms2str asms = 
  1006 if asms2str asms = 
  1007 "[(0 <= (25 * (1 / 9) + -1 * (16 + 49 * (1 / 9))) * -56, []),\
  1007 "[(0 <= (25 * (1 / 9) + -1 * (16 + 49 * (1 / 9))) * -56, []),\
  1008  \(0 <= 1 / 9, []),\
  1008  \(0 <= 1 / 9, []),\
  1009  \(0 <= 1 / 9, []),\
  1009  \(0 <= 1 / 9, []),\
  1017     (str2term"9 ~= 0", []),
  1017     (str2term"9 ~= 0", []),
  1018     (str2term"0 <= (-5 + 7 * sqrt (1 / 9) + 1) * 5", []),
  1018     (str2term"0 <= (-5 + 7 * sqrt (1 / 9) + 1) * 5", []),
  1019     (str2term"9 ~= 0", []),
  1019     (str2term"9 ~= 0", []),
  1020     (str2term"0 <= (25 * (1 / 9) + -1 * (16 + 49 * (1 / 9))) * -56", [])]*)
  1020     (str2term"0 <= (25 * (1 / 9) + -1 * (16 + 49 * (1 / 9))) * -56", [])]*)
  1021     then "should get True * False!!!"
  1021     then "should get True * False!!!"
  1022 else raise error "rlang.sml: diff.behav. in II 68a asms";
  1022 else error "rlang.sml: diff.behav. in II 68a asms";
  1023 
  1023 
  1024 (*-----------------  Schalk II s.56 Bsp 73b ------------------------*)
  1024 (*-----------------  Schalk II s.56 Bsp 73b ------------------------*)
  1025 "Schalk II s.56 Bsp 73b (sqrt(x+1)+sqrt(4*x+4)=sqrt(9*x+9))";
  1025 "Schalk II s.56 Bsp 73b (sqrt(x+1)+sqrt(4*x+4)=sqrt(9*x+9))";
  1026 "Schalk II s.56 Bsp 73b (sqrt(x+1)+sqrt(4*x+4)=sqrt(9*x+9))";
  1026 "Schalk II s.56 Bsp 73b (sqrt(x+1)+sqrt(4*x+4)=sqrt(9*x+9))";
  1027 "Schalk II s.56 Bsp 73b (sqrt(x+1)+sqrt(4*x+4)=sqrt(9*x+9))";
  1027 "Schalk II s.56 Bsp 73b (sqrt(x+1)+sqrt(4*x+4)=sqrt(9*x+9))";
  1054 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1054 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1055 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1055 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1056 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1056 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1057 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1057 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1058 if f = Form' (FormKF (~1, EdUndef, 0, Nundef, "0 = 0")) then ()
  1058 if f = Form' (FormKF (~1, EdUndef, 0, Nundef, "0 = 0")) then ()
  1059 else raise error "rlang.sml: diff.behav. in Schalk II s.56 Bsp 73b";
  1059 else error "rlang.sml: diff.behav. in Schalk II s.56 Bsp 73b";
  1060 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1060 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1061 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1061 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1062 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1062 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1063 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1063 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1064 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1064 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1067 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1067 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1068 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1068 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1069 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1069 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1070 val asm = get_assumptions_ pt p;
  1070 val asm = get_assumptions_ pt p;
  1071 if asm=[] andalso f = Form' (FormKF (~1,EdUndef,0,Nundef,"UniversalList")) andalso nxt = ("End_Proof'",End_Proof') then ()
  1071 if asm=[] andalso f = Form' (FormKF (~1,EdUndef,0,Nundef,"UniversalList")) andalso nxt = ("End_Proof'",End_Proof') then ()
  1072 else raise error "rlang.sml: diff.behav. in UniversalList 2";
  1072 else error "rlang.sml: diff.behav. in UniversalList 2";
  1073 
  1073 
  1074 (*-----------------  Schalk II s.56 Bsp 74a ------------------------*)
  1074 (*-----------------  Schalk II s.56 Bsp 74a ------------------------*)
  1075 "Schalk II s.56 Bsp 74a (sqrt(4*x+1) - sqrt(x+3) = sqrt(x - 2))";
  1075 "Schalk II s.56 Bsp 74a (sqrt(4*x+1) - sqrt(x+3) = sqrt(x - 2))";
  1076 "Schalk II s.56 Bsp 74a (sqrt(4*x+1) - sqrt(x+3) = sqrt(x - 2))";
  1076 "Schalk II s.56 Bsp 74a (sqrt(4*x+1) - sqrt(x+3) = sqrt(x - 2))";
  1077 "Schalk II s.56 Bsp 74a (sqrt(4*x+1) - sqrt(x+3) = sqrt(x - 2))";
  1077 "Schalk II s.56 Bsp 74a (sqrt(4*x+1) - sqrt(x+3) = sqrt(x - 2))";
  1105 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1105 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1106 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1106 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1107 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1107 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1108 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1108 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1109 if f = Form' (FormKF (~1, EdUndef, 0, Nundef, "-24 + 4 * x = 0")) then ()
  1109 if f = Form' (FormKF (~1, EdUndef, 0, Nundef, "-24 + 4 * x = 0")) then ()
  1110 else raise error "rlang.sml: diff.behav. in Schalk II s.56 Bsp 74a";
  1110 else error "rlang.sml: diff.behav. in Schalk II s.56 Bsp 74a";
  1111 (*-> ubproblem ("PolyEq", ["degree_1", ...]*)
  1111 (*-> ubproblem ("PolyEq", ["degree_1", ...]*)
  1112 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1112 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1113 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1113 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1114 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1114 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1115 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1115 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1118 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1118 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1119 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1119 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1120 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1120 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1121 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1121 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1122 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 6]")) => ()
  1122 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 6]")) => ()
  1123 	 | _ => raise error "rlang.sml: diff.behav. in  Schalk II s.56 Bsp 74a [x = 6]";
  1123 	 | _ => error "rlang.sml: diff.behav. in  Schalk II s.56 Bsp 74a [x = 6]";
  1124 
  1124 
  1125 
  1125 
  1126 (*-----------------  Schalk II s.56 Bsp 77b ------------------------*)
  1126 (*-----------------  Schalk II s.56 Bsp 77b ------------------------*)
  1127 "Schalk II s.56 Bsp 77b (sqrt(x+12)+sqrt(x - 3) = sqrt(x + 32) - sqrt(5+x))";
  1127 "Schalk II s.56 Bsp 77b (sqrt(x+12)+sqrt(x - 3) = sqrt(x + 32) - sqrt(5+x))";
  1128 "Schalk II s.56 Bsp 77b (sqrt(x+12)+sqrt(x - 3) = sqrt(x + 32) - sqrt(5+x))";
  1128 "Schalk II s.56 Bsp 77b (sqrt(x+12)+sqrt(x - 3) = sqrt(x + 32) - sqrt(5+x))";
  1165 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1165 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1166 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1166 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1167 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1167 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1168 (*val (p,_,f,nxt,_,pt) = me nxt p [1] pt; since MGs norm_Rational*)
  1168 (*val (p,_,f,nxt,_,pt) = me nxt p [1] pt; since MGs norm_Rational*)
  1169 if f = Form'(FormKF (~1, EdUndef, 0, Nundef, "451584 + -112896 * x = 0"))then()
  1169 if f = Form'(FormKF (~1, EdUndef, 0, Nundef, "451584 + -112896 * x = 0"))then()
  1170 else raise error "rlang.sml: diff.behav. in Schalk II s.56 Bsp 77b";
  1170 else error "rlang.sml: diff.behav. in Schalk II s.56 Bsp 77b";
  1171 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1171 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1172 (* val nxt = ("Model_Problem",
  1172 (* val nxt = ("Model_Problem",
  1173    Model_Problem ["degree_1","polynomial","univariate","equation"])*)
  1173    Model_Problem ["degree_1","polynomial","univariate","equation"])*)
  1174 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1174 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1175 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1175 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1179 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1179 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1180 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1180 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1181 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1181 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1182 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1182 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1183 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[]")) => ()
  1183 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[]")) => ()
  1184 	 | _ => raise error "rlang.sml: diff.behav. in  Schalk II s.56 Bsp 77b []";
  1184 	 | _ => error "rlang.sml: diff.behav. in  Schalk II s.56 Bsp 77b []";
  1185 (*added 040209 at introducing MGs norm_Rational ?!*)
  1185 (*added 040209 at introducing MGs norm_Rational ?!*)
  1186 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1186 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1187 
  1187 
  1188 
  1188 
  1189 (*-----------------  Schalk II s.66 Bsp 4 ------------------------*)
  1189 (*-----------------  Schalk II s.66 Bsp 4 ------------------------*)
  1212 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1212 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1213 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1213 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1214 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1214 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1215 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1215 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1216 case f of   Form' (FormKF (_,_,0,_,"[x = 5, x = -5]")) => ()
  1216 case f of   Form' (FormKF (_,_,0,_,"[x = 5, x = -5]")) => ()
  1217   | _ => raise error "rlang.sml: diff.behav. in  Schalk II s.66 Bsp 4 []";
  1217   | _ => error "rlang.sml: diff.behav. in  Schalk II s.66 Bsp 4 []";
  1218 
  1218 
  1219 
  1219 
  1220 (*-----------------  Schalk II s.66 Bsp 8a ------------------------*)
  1220 (*-----------------  Schalk II s.66 Bsp 8a ------------------------*)
  1221 "Schalk II s.66 Bsp 8a ((x - 4)/(x+4) = (1 - x)/(1+x))";
  1221 "Schalk II s.66 Bsp 8a ((x - 4)/(x+4) = (1 - x)/(1+x))";
  1222 (*ER-15*)
  1222 (*ER-15*)
  1240 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1240 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1241 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1241 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1242 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1242 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1243 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1243 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1244 if f = Form' (FormKF (~1, EdUndef, 0, Nundef, "-8 + 2 * x ^^^ 2 = 0")) then ()
  1244 if f = Form' (FormKF (~1, EdUndef, 0, Nundef, "-8 + 2 * x ^^^ 2 = 0")) then ()
  1245 else raise error "rlang.sml: diff.behav. in Schalk II s.66 Bsp 8a";
  1245 else error "rlang.sml: diff.behav. in Schalk II s.66 Bsp 8a";
  1246 (*-> Subproblem ("PolyEq", ["polynomial", ...])*)
  1246 (*-> Subproblem ("PolyEq", ["polynomial", ...])*)
  1247 (* 
  1247 (* 
  1248  val Form' (FormKF (~1, EdUndef, 0, Nundef, str)) = f;
  1248  val Form' (FormKF (~1, EdUndef, 0, Nundef, str)) = f;
  1249  *)
  1249  *)
  1250 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1250 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1255 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1255 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1256 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1256 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1257 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1257 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1258 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1258 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1259 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2, x = -2]")) => ()
  1259 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2, x = -2]")) => ()
  1260 	 | _ => raise error "rlang.sml: diff.behav. in  Schalk II s.66 Bsp 8a [x = 2, x = -2]";
  1260 	 | _ => error "rlang.sml: diff.behav. in  Schalk II s.66 Bsp 8a [x = 2, x = -2]";
  1261 
  1261 
  1262 (*-----------------  Schalk II s.66 Bsp 10b ------------------------*)
  1262 (*-----------------  Schalk II s.66 Bsp 10b ------------------------*)
  1263 "Schalk II s.66 Bsp 10b (1/(x^^^2 - 9)+(2*x+3)/(x+3)=(3*x+4)/(x - 3))";
  1263 "Schalk II s.66 Bsp 10b (1/(x^^^2 - 9)+(2*x+3)/(x+3)=(3*x+4)/(x - 3))";
  1264 "Schalk II s.66 Bsp 10b (1/(x^^^2 - 9)+(2*x+3)/(x+3)=(3*x+4)/(x - 3))";
  1264 "Schalk II s.66 Bsp 10b (1/(x^^^2 - 9)+(2*x+3)/(x+3)=(3*x+4)/(x - 3))";
  1265 "Schalk II s.66 Bsp 10b (1/(x^^^2 - 9)+(2*x+3)/(x+3)=(3*x+4)/(x - 3))";
  1265 "Schalk II s.66 Bsp 10b (1/(x^^^2 - 9)+(2*x+3)/(x+3)=(3*x+4)/(x - 3))";
  1288          (~1,
  1288          (~1,
  1289             EdUndef,
  1289             EdUndef,
  1290             0,
  1290             0,
  1291             Nundef,
  1291             Nundef,
  1292             "60 + 28 * x + -13 * x ^^^ 2 + -1 * x ^^^ 3 = 0")) then ()
  1292             "60 + 28 * x + -13 * x ^^^ 2 + -1 * x ^^^ 3 = 0")) then ()
  1293 else raise error "rlang.sml: diff.behav. in Schalk II s.66 Bsp 10b";
  1293 else error "rlang.sml: diff.behav. in Schalk II s.66 Bsp 10b";
  1294 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1294 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1295 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1295 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1296 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1296 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1297 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1297 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1298 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1298 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1330 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1330 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1331 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1331 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1332 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1332 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1333 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1333 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1334 if f = Form' (FormKF (~1, EdUndef, 0, Nundef, "-25 + x ^^^ 2 = 0")) then ()
  1334 if f = Form' (FormKF (~1, EdUndef, 0, Nundef, "-25 + x ^^^ 2 = 0")) then ()
  1335 else raise error "rlang.sml: diff.behav. in Schalk II s.66 Bsp 20a";
  1335 else error "rlang.sml: diff.behav. in Schalk II s.66 Bsp 20a";
  1336 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1336 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1337 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1337 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1338 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1338 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1339 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1339 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1340 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1340 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1343 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1343 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1344 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1344 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1345 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1345 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1346 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1346 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1347 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 5, x = -5]")) => ()
  1347 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 5, x = -5]")) => ()
  1348 	 | _ => raise error "rlang.sml: diff.behav. in  Schalk II s.66 Bsp 20a [x = 5, x = -5]";
  1348 	 | _ => error "rlang.sml: diff.behav. in  Schalk II s.66 Bsp 20a [x = 5, x = -5]";
  1349 
  1349 
  1350 (*-----------------  Schalk II s.66 Bsp 23b ------------------------*)
  1350 (*-----------------  Schalk II s.66 Bsp 23b ------------------------*)
  1351 "Schalk II s.66 Bsp 23b (2*sqrt(261 - x) - sqrt(2+2*x)=sqrt(2)*sqrt(5 - 3*x))";
  1351 "Schalk II s.66 Bsp 23b (2*sqrt(261 - x) - sqrt(2+2*x)=sqrt(2)*sqrt(5 - 3*x))";
  1352 "Schalk II s.66 Bsp 23b (2*sqrt(261 - x) - sqrt(2+2*x)=sqrt(2)*sqrt(5 - 3*x))";
  1352 "Schalk II s.66 Bsp 23b (2*sqrt(261 - x) - sqrt(2+2*x)=sqrt(2)*sqrt(5 - 3*x))";
  1353 "Schalk II s.66 Bsp 23b (2*sqrt(261 - x) - sqrt(2+2*x)=sqrt(2)*sqrt(5 - 3*x))";
  1353 "Schalk II s.66 Bsp 23b (2*sqrt(261 - x) - sqrt(2+2*x)=sqrt(2)*sqrt(5 - 3*x))";
  1382 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1382 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1383 val (p,_,f,nxt,_,pt) = me nxt p [1] pt; f2str f;
  1383 val (p,_,f,nxt,_,pt) = me nxt p [1] pt; f2str f;
  1384 if f = Form'
  1384 if f = Form'
  1385       (FormKF
  1385       (FormKF
  1386        (~1, EdUndef, 0, Nundef, "-1064944 + 32 * x + -48 * x ^^^ 2 = 0"))then()
  1386        (~1, EdUndef, 0, Nundef, "-1064944 + 32 * x + -48 * x ^^^ 2 = 0"))then()
  1387 else raise error "rlang.sml: diff.behav. in Schalk II s.66 Bsp 23b";
  1387 else error "rlang.sml: diff.behav. in Schalk II s.66 Bsp 23b";
  1388 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1388 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1389 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1389 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1390 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1390 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1391 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1391 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1392 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1392 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1393 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1393 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1394 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1394 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1395 case f of Form' (FormKF (~1,EdUndef,_,Nundef,"[]")) => ()
  1395 case f of Form' (FormKF (~1,EdUndef,_,Nundef,"[]")) => ()
  1396 	 | _ => raise error "rlang.sml: diff.behav. in  Schalk II s.66 Bsp 23b []";
  1396 	 | _ => error "rlang.sml: diff.behav. in  Schalk II s.66 Bsp 23b []";
  1397 
  1397 
  1398 (*-----------------  Schalk II s.66 Bsp 28a ------------------------*)
  1398 (*-----------------  Schalk II s.66 Bsp 28a ------------------------*)
  1399 "Schalk II s.66 Bsp 28a (A=(c/d)*sqrt(4*a^^^2 - c^^^2))";
  1399 "Schalk II s.66 Bsp 28a (A=(c/d)*sqrt(4*a^^^2 - c^^^2))";
  1400 "Schalk II s.66 Bsp 28a (A=(c/d)*sqrt(4*a^^^2 - c^^^2))";
  1400 "Schalk II s.66 Bsp 28a (A=(c/d)*sqrt(4*a^^^2 - c^^^2))";
  1401 "Schalk II s.66 Bsp 28a (A=(c/d)*sqrt(4*a^^^2 - c^^^2))";
  1401 "Schalk II s.66 Bsp 28a (A=(c/d)*sqrt(4*a^^^2 - c^^^2))";
  1425             0,
  1425             0,
  1426             Nundef,
  1426             Nundef,
  1427             "c ^^^ 4 / d ^^^ 2 + A ^^^ 2 * d ^^^ 2 / d ^^^ 2 +\n-4 * c ^^^ 2 / d ^^^ 2 * a ^^^ 2 =\n0")) then ()*)
  1427             "c ^^^ 4 / d ^^^ 2 + A ^^^ 2 * d ^^^ 2 / d ^^^ 2 +\n-4 * c ^^^ 2 / d ^^^ 2 * a ^^^ 2 =\n0")) then ()*)
  1428 if f2str f = 
  1428 if f2str f = 
  1429    "c ^^^ 4 / d ^^^ 2 + A ^^^ 2 / 1 + -4 * c ^^^ 2 / d ^^^ 2 * a ^^^ 2 = 0"
  1429    "c ^^^ 4 / d ^^^ 2 + A ^^^ 2 / 1 + -4 * c ^^^ 2 / d ^^^ 2 * a ^^^ 2 = 0"
  1430 then () else raise error "rlang.sml: diff.behav. in Schalk II s.66 Bsp 28a";
  1430 then () else error "rlang.sml: diff.behav. in Schalk II s.66 Bsp 28a";
  1431 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1431 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1432 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1432 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1433 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1433 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1434 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1434 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1435 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1435 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1436 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1436 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1437 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1437 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1438 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1438 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1439 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1439 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1440 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[a = sqrt ((c ^^^ 4 + A ^^^ 2 * d ^^^ 2) / (4 * c ^^^ 2)),\n a = -1 * sqrt ((c ^^^ 4 + A ^^^ 2 * d ^^^ 2) / (4 * c ^^^ 2))]")) => ()
  1440 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[a = sqrt ((c ^^^ 4 + A ^^^ 2 * d ^^^ 2) / (4 * c ^^^ 2)),\n a = -1 * sqrt ((c ^^^ 4 + A ^^^ 2 * d ^^^ 2) / (4 * c ^^^ 2))]")) => ()
  1441 | _ => raise error "rlang.sml: diff.behav. in  Schalk II s.66 Bsp 28a [a=...]";
  1441 | _ => error "rlang.sml: diff.behav. in  Schalk II s.66 Bsp 28a [a=...]";
  1442 
  1442 
  1443 
  1443 
  1444 
  1444 
  1445 (*-----------------  Schalk II s.68 Bsp 52b ------------------------*)
  1445 (*-----------------  Schalk II s.68 Bsp 52b ------------------------*)
  1446 "Schalk II s.68 Bsp 52b (1/(x - a+b)=1/x - 1/a + 1/b)";
  1446 "Schalk II s.68 Bsp 52b (1/(x - a+b)=1/x - 1/a + 1/b)";
  1477          (~1,
  1477          (~1,
  1478             EdUndef,
  1478             EdUndef,
  1479             0,
  1479             0,
  1480             Nundef,
  1480             Nundef,
  1481             "b * a ^^^ 2 + -1 * a * b ^^^ 2 + (a ^^^ 2 + b ^^^ 2 + -2 * a * b) * x +\n(b + -1 * a) * x ^^^ 2 =\n0")) then ()
  1481             "b * a ^^^ 2 + -1 * a * b ^^^ 2 + (a ^^^ 2 + b ^^^ 2 + -2 * a * b) * x +\n(b + -1 * a) * x ^^^ 2 =\n0")) then ()
  1482 else raise error "rlang.sml: diff.behav. in chalk I s.87 Bsp 38b";
  1482 else error "rlang.sml: diff.behav. in chalk I s.87 Bsp 38b";
  1483 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1483 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1484 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1484 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1485 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1485 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1486 (*val nxt = ("Specify_Theory",Specify_Theory "PolyEq")*)
  1486 (*val nxt = ("Specify_Theory",Specify_Theory "PolyEq")*)
  1487 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1487 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1500 val nxt =Check_Postcond ["normalize","polynomial","univariate","equation"])*)
  1500 val nxt =Check_Postcond ["normalize","polynomial","univariate","equation"])*)
  1501 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1501 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1502 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;(*1 additional for MGs norm_Rational*)
  1502 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;(*1 additional for MGs norm_Rational*)
  1503 if p = ([],Res) andalso f = Form' (FormKF (~1,EdUndef,0,Nundef,
  1503 if p = ([],Res) andalso f = Form' (FormKF (~1,EdUndef,0,Nundef,
  1504 "[x =\n (2 * a * b + -1 * a ^^^ 2 + -1 * b ^^^ 2 +\n  sqrt\n   (a ^^^ 4 + b ^^^ 4 + -4 * a * a * b ^^^ 2 + -4 * a * b * a ^^^ 2 +\n    -4 * b * b * a ^^^ 2 +\n    4 * a * a * b ^^^ 2 +\n    4 * a * b * a ^^^ 2 +\n    2 * a ^^^ 2 * b ^^^ 2)) /\n (-2 * a + 2 * b),\n x =\n (2 * a * b + -1 * a ^^^ 2 + -1 * b ^^^ 2 +\n  -1 *\n  sqrt\n   (a ^^^ 4 + b ^^^ 4 + -4 * a * a * b ^^^ 2 + -4 * a * b * a ^^^ 2 +\n    -4 * b * b * a ^^^ 2 +\n    4 * a * a * b ^^^ 2 +\n    4 * a * b * a ^^^ 2 +\n    2 * a ^^^ 2 * b ^^^ 2)) /\n (-2 * a + 2 * b)]")) andalso nxt = ("End_Proof'",End_Proof') then writeln"simplify MG"
  1504 "[x =\n (2 * a * b + -1 * a ^^^ 2 + -1 * b ^^^ 2 +\n  sqrt\n   (a ^^^ 4 + b ^^^ 4 + -4 * a * a * b ^^^ 2 + -4 * a * b * a ^^^ 2 +\n    -4 * b * b * a ^^^ 2 +\n    4 * a * a * b ^^^ 2 +\n    4 * a * b * a ^^^ 2 +\n    2 * a ^^^ 2 * b ^^^ 2)) /\n (-2 * a + 2 * b),\n x =\n (2 * a * b + -1 * a ^^^ 2 + -1 * b ^^^ 2 +\n  -1 *\n  sqrt\n   (a ^^^ 4 + b ^^^ 4 + -4 * a * a * b ^^^ 2 + -4 * a * b * a ^^^ 2 +\n    -4 * b * b * a ^^^ 2 +\n    4 * a * a * b ^^^ 2 +\n    4 * a * b * a ^^^ 2 +\n    2 * a ^^^ 2 * b ^^^ 2)) /\n (-2 * a + 2 * b)]")) andalso nxt = ("End_Proof'",End_Proof') then writeln"simplify MG"
  1505 else raise error "rlang.sml: diff.behav. in rational-a-b";
  1505 else error "rlang.sml: diff.behav. in rational-a-b";
  1506 
  1506 
  1507 (*-----------------  Schalk II s.68 Bsp 56a ------------------------*)
  1507 (*-----------------  Schalk II s.68 Bsp 56a ------------------------*)
  1508 "Schalk II s.68 Bsp 56a ((a+b*x)/(a-b*x) - (a - b*x)/(a+b*x)= (4*a*b)/(a^^^2 - b^^^2))";
  1508 "Schalk II s.68 Bsp 56a ((a+b*x)/(a-b*x) - (a - b*x)/(a+b*x)= (4*a*b)/(a^^^2 - b^^^2))";
  1509 val fmz = ["equality ((a+b*x)/(a-b*x) - (a - b*x)/(a+b*x)= (4*a*b)/(a^^^2 - b^^^2))","solveFor x","solutions L"];
  1509 val fmz = ["equality ((a+b*x)/(a-b*x) - (a - b*x)/(a+b*x)= (4*a*b)/(a^^^2 - b^^^2))","solveFor x","solutions L"];
  1510 val (dI',pI',mI') = ("RatEq",["univariate","equation"],["no_met"]);
  1510 val (dI',pI',mI') = ("RatEq",["univariate","equation"],["no_met"]);
  1627             EdUndef,
  1627             EdUndef,
  1628             0,
  1628             0,
  1629             Nundef,
  1629             Nundef,
  1630             (*"-4 * b ^^^ 2 + -4 * a * b + 4 * b ^^^ 2 + 8 * a * b +\n(-2 * a + -4 * a + -4 * b + 2 * a + 8 * b) * x +\n-4 * x ^^^ 2 =\n0" before MG*)
  1630             (*"-4 * b ^^^ 2 + -4 * a * b + 4 * b ^^^ 2 + 8 * a * b +\n(-2 * a + -4 * a + -4 * b + 2 * a + 8 * b) * x +\n-4 * x ^^^ 2 =\n0" before MG*)
  1631 	    "4 * a * b + (-4 * a + 4 * b) * x + -4 * x ^^^ 2 = 0")) then ()
  1631 	    "4 * a * b + (-4 * a + 4 * b) * x + -4 * x ^^^ 2 = 0")) then ()
  1632 else raise error "rlang.sml: diff.behav. in Schalk II s.68 Bsp 61b";
  1632 else error "rlang.sml: diff.behav. in Schalk II s.68 Bsp 61b";
  1633 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1633 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1634 (*val nxt = ("Model_Problem", Model_Problem
  1634 (*val nxt = ("Model_Problem", Model_Problem
  1635      ["abcFormula","degree_2","polynomial","univariate","equation"])*)
  1635      ["abcFormula","degree_2","polynomial","univariate","equation"])*)
  1636 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1636 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1637 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1637 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1647 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1647 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1648 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1648 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1649 (*if f = Form' (FormKF (~1,EdUndef,0,Nundef, with norm_Rational before MG
  1649 (*if f = Form' (FormKF (~1,EdUndef,0,Nundef, with norm_Rational before MG
  1650 "[x =\n (-2 * a + -4 * b + 6 * a +\n  sqrt\n   (32 * a * b + -16 * a ^^^ 2 + -48 * b ^^^ 2 + 24 * a ^^^ 2 +\n    64 * b ^^^ 2 +\n    8 * a ^^^ 2)) /\n -8,\n x =\n (-2 * a + -4 * b + 6 * a +\n  -1 *\n  sqrt\n   (32 * a * b + -16 * a ^^^ 2 + -48 * b ^^^ 2 + 24 * a ^^^ 2 +\n    64 * b ^^^ 2 +\n    8 * a ^^^ 2)) /\n -8]")) then writeln"simplify MG"*)
  1650 "[x =\n (-2 * a + -4 * b + 6 * a +\n  sqrt\n   (32 * a * b + -16 * a ^^^ 2 + -48 * b ^^^ 2 + 24 * a ^^^ 2 +\n    64 * b ^^^ 2 +\n    8 * a ^^^ 2)) /\n -8,\n x =\n (-2 * a + -4 * b + 6 * a +\n  -1 *\n  sqrt\n   (32 * a * b + -16 * a ^^^ 2 + -48 * b ^^^ 2 + 24 * a ^^^ 2 +\n    64 * b ^^^ 2 +\n    8 * a ^^^ 2)) /\n -8]")) then writeln"simplify MG"*)
  1651 if f = Form' (FormKF (~1,EdUndef,0,Nundef,"[x =\n (-4 * b + 4 * a + sqrt (32 * a * b + 16 * a ^^^ 2 + 16 * b ^^^ 2)) / -8,\n x =\n (-4 * b + 4 * a + -1 * sqrt (32 * a * b + 16 * a ^^^ 2 + 16 * b ^^^ 2)) /\n -8]")) then ()
  1651 if f = Form' (FormKF (~1,EdUndef,0,Nundef,"[x =\n (-4 * b + 4 * a + sqrt (32 * a * b + 16 * a ^^^ 2 + 16 * b ^^^ 2)) / -8,\n x =\n (-4 * b + 4 * a + -1 * sqrt (32 * a * b + 16 * a ^^^ 2 + 16 * b ^^^ 2)) /\n -8]")) then ()
  1652 else raise error "rlang.sml: diff.behav. Bsp 61b";
  1652 else error "rlang.sml: diff.behav. Bsp 61b";
  1653 (*WN.18.12.03: extreme run-time !!!*)
  1653 (*WN.18.12.03: extreme run-time !!!*)
  1654 
  1654 
  1655 
  1655 
  1656 (*-----------------  Schalk II s.68 Bsp 62b ------------------------*)
  1656 (*-----------------  Schalk II s.68 Bsp 62b ------------------------*)
  1657 "Schalk II s.68 Bsp 62b (sqrt((x+a)^^^2+(x - 2*b)^^^2)=a+2*b)";
  1657 "Schalk II s.68 Bsp 62b (sqrt((x+a)^^^2+(x - 2*b)^^^2)=a+2*b)";
  1679          (~1,
  1679          (~1,
  1680             EdUndef,
  1680             EdUndef,
  1681             0,
  1681             0,
  1682             Nundef,
  1682             Nundef,
  1683             "-4 * a * b + (-4 * b + 2 * a) * x + 2 * x ^^^ 2 = 0")) then ()
  1683             "-4 * a * b + (-4 * b + 2 * a) * x + 2 * x ^^^ 2 = 0")) then ()
  1684 else raise error "rlang.sml: diff.behav. in Schalk II s.68 Bsp 62b";
  1684 else error "rlang.sml: diff.behav. in Schalk II s.68 Bsp 62b";
  1685 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1685 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1686 (*val nxt =  ("Model_Problem", Model_Problem
  1686 (*val nxt =  ("Model_Problem", Model_Problem
  1687      ["abcFormula","degree_2","polynomial","univariate","equation"])*)
  1687      ["abcFormula","degree_2","polynomial","univariate","equation"])*)
  1688 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1688 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1689 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1689 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1697 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1697 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1698 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1698 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1699 (*val (p,_,f,nxt,_,pt) = me nxt p [1] pt;introduc.MGs norm_Rational*)
  1699 (*val (p,_,f,nxt,_,pt) = me nxt p [1] pt;introduc.MGs norm_Rational*)
  1700 if f = Form' (FormKF (~1,EdUndef,0,Nundef,
  1700 if f = Form' (FormKF (~1,EdUndef,0,Nundef,
  1701         "[x = (-2 * a + 4 * b + sqrt (16 * a * b + 16 * b ^^^ 2 + 4 * a ^^^ 2)) / 4,\n x =\n (-2 * a + 4 * b + -1 * sqrt (16 * a * b + 16 * b ^^^ 2 + 4 * a ^^^ 2)) / 4]")) then writeln "simplify MG"
  1701         "[x = (-2 * a + 4 * b + sqrt (16 * a * b + 16 * b ^^^ 2 + 4 * a ^^^ 2)) / 4,\n x =\n (-2 * a + 4 * b + -1 * sqrt (16 * a * b + 16 * b ^^^ 2 + 4 * a ^^^ 2)) / 4]")) then writeln "simplify MG"
  1702 else raise error "rlang.sml: diff.behav. in II 62b [x=...]";
  1702 else error "rlang.sml: diff.behav. in II 62b [x=...]";
  1703 val asms = get_assumptions_ pt p;
  1703 val asms = get_assumptions_ pt p;
  1704 if asms = [(str2term"0 <= ((-2 * a + 4 * b + sqrt (16 * a * b + 16 * b ^^^ 2 + 4 * a ^^^ 2)) / 4 + a) ^^^ 2 + ((-2 * a + 4 * b + sqrt (16 * a * b + 16 * b ^^^ 2 + 4 * a ^^^ 2)) / 4 - 2 * b) ^^^ 2", []),
  1704 if asms = [(str2term"0 <= ((-2 * a + 4 * b + sqrt (16 * a * b + 16 * b ^^^ 2 + 4 * a ^^^ 2)) / 4 + a) ^^^ 2 + ((-2 * a + 4 * b + sqrt (16 * a * b + 16 * b ^^^ 2 + 4 * a ^^^ 2)) / 4 - 2 * b) ^^^ 2", []),
  1705 	   (str2term"0 <= a + 2 * b", []),
  1705 	   (str2term"0 <= a + 2 * b", []),
  1706 	   (str2term"8 * (-4 * a * b) <= (-4 * b + 2 * a) ^^^ 2", []),
  1706 	   (str2term"8 * (-4 * a * b) <= (-4 * b + 2 * a) ^^^ 2", []),
  1707 	   (str2term"8 * (-4 * a * b) <= (-4 * b + 2 * a) ^^^ 2", []),
  1707 	   (str2term"8 * (-4 * a * b) <= (-4 * b + 2 * a) ^^^ 2", []),
  1708 	   (str2term"0 <= ((-2 * a + 4 * b + -1 * sqrt (16 * a * b + 16 * b ^^^ 2 + 4 * a ^^^ 2)) / 4 + a) ^^^ 2 + ((-2 * a + 4 * b + -1 * sqrt (16 * a * b + 16 * b ^^^ 2 + 4 * a ^^^ 2)) / 4 - 2 * b) ^^^ 2", []),
  1708 	   (str2term"0 <= ((-2 * a + 4 * b + -1 * sqrt (16 * a * b + 16 * b ^^^ 2 + 4 * a ^^^ 2)) / 4 + a) ^^^ 2 + ((-2 * a + 4 * b + -1 * sqrt (16 * a * b + 16 * b ^^^ 2 + 4 * a ^^^ 2)) / 4 - 2 * b) ^^^ 2", []),
  1709 	   (str2term"0 <= a + 2 * b", []),
  1709 	   (str2term"0 <= a + 2 * b", []),
  1710 	   (str2term"8 * (-4 * a * b) <= (-4 * b + 2 * a) ^^^ 2", []),
  1710 	   (str2term"8 * (-4 * a * b) <= (-4 * b + 2 * a) ^^^ 2", []),
  1711 	   (str2term"8 * (-4 * a * b) <= (-4 * b + 2 * a) ^^^ 2", [])] 
  1711 	   (str2term"8 * (-4 * a * b) <= (-4 * b + 2 * a) ^^^ 2", [])] 
  1712 then writeln "should be simplified MG"
  1712 then writeln "should be simplified MG"
  1713 else raise error "rlang.sml: diff.behav. in II 62b asms";
  1713 else error "rlang.sml: diff.behav. in II 62b asms";
  1714 
  1714 
  1715 "------ WN.TEST---------------------------------";
  1715 "------ WN.TEST---------------------------------";
  1716 "------ WN.TEST---------------------------------";
  1716 "------ WN.TEST---------------------------------";
  1717 "------ WN.TEST---------------------------------";
  1717 "------ WN.TEST---------------------------------";
  1718 (*EO-7*)
  1718 (*EO-7*)
  1730 normiert nicht ... korr.WN:
  1730 normiert nicht ... korr.WN:
  1731 val t = str2term "(2*x+1)*x^^^2 = 0";
  1731 val t = str2term "(2*x+1)*x^^^2 = 0";
  1732 val subst = [(str2term "bdv", str2term "x")];
  1732 val subst = [(str2term "bdv", str2term "x")];
  1733 val SOME (t',_) = rewrite_set_inst_ thy false subst make_ratpoly_in t;
  1733 val SOME (t',_) = rewrite_set_inst_ thy false subst make_ratpoly_in t;
  1734 if term2str t' = "x ^^^ 2 + 2 * x ^^^ 3 = 0" then () 
  1734 if term2str t' = "x ^^^ 2 + 2 * x ^^^ 3 = 0" then () 
  1735 else raise error "rlang.sml: 7";
  1735 else error "rlang.sml: 7";
  1736 *)
  1736 *)
  1737 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1737 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1738 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1738 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1739 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1739 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1740 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1740 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1744 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1744 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1745 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1745 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1746 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1746 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1747 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1747 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1748 if f = Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 0, x = 0, x = -1 / 2]")) then()
  1748 if f = Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 0, x = 0, x = -1 / 2]")) then()
  1749 else raise error "rlang.sml WN.TEST new behaviour";
  1749 else error "rlang.sml WN.TEST new behaviour";
  1750 
  1750 
  1751 "------ rlang.sml end---------------------------------";
  1751 "------ rlang.sml end---------------------------------";
  1752 
  1752 
  1753 (*------------------------------vvv-Rewrite_Set "rat_eliminate"---------
  1753 (*------------------------------vvv-Rewrite_Set "rat_eliminate"---------
  1754 > trace_rewrite:=true;
  1754 > trace_rewrite:=true;
  1796 val (p,_,f,nxt,_,pt) = me nxt p c pt;
  1796 val (p,_,f,nxt,_,pt) = me nxt p c pt;
  1797 val (p,_,f,nxt,_,pt) = me nxt p c pt;
  1797 val (p,_,f,nxt,_,pt) = me nxt p c pt;
  1798 if f = Form' (FormKF (~1,EdUndef,0,Nundef,
  1798 if f = Form' (FormKF (~1,EdUndef,0,Nundef,
  1799 "[a = sqrt ((-1 * b ^^^ 2 + 4 * r ^^^ 2) / 1),\n a = -1 * sqrt ((-1 * b ^^^ 2 + 4 * r ^^^ 2) / 1)]")) andalso nxt = ("End_Proof'",End_Proof')
  1799 "[a = sqrt ((-1 * b ^^^ 2 + 4 * r ^^^ 2) / 1),\n a = -1 * sqrt ((-1 * b ^^^ 2 + 4 * r ^^^ 2) / 1)]")) andalso nxt = ("End_Proof'",End_Proof')
  1800 then writeln"simplify result\nsimplify result\nsimplify result"
  1800 then writeln"simplify result\nsimplify result\nsimplify result"
  1801 else raise error "rlang.sml: diff.behav. in Pythagoras";
  1801 else error "rlang.sml: diff.behav. in Pythagoras";
  1802 val asms = get_assumptions_ pt p;
  1802 val asms = get_assumptions_ pt p;
  1803 (*if asms = [(str2term"0 <= -4 * (b ^^^ 2 / 4 + -4 * r ^^^ 2 / 4)", []),
  1803 (*if asms = [(str2term"0 <= -4 * (b ^^^ 2 / 4 + -4 * r ^^^ 2 / 4)", []),
  1804            (str2term"0 <= -4 * (b ^^^ 2 / 4 + -4 * r ^^^ 2 / 4)", [])]*)
  1804            (str2term"0 <= -4 * (b ^^^ 2 / 4 + -4 * r ^^^ 2 / 4)", [])]*)
  1805 if asms2str asms = 
  1805 if asms2str asms = 
  1806    "[(0 <= -4 * (b ^^^ 2 / 4 + -1 * r ^^^ 2 / 1), []),\
  1806    "[(0 <= -4 * (b ^^^ 2 / 4 + -1 * r ^^^ 2 / 1), []),\
  1807    \(0 <= -4 * (b ^^^ 2 / 4 + -1 * r ^^^ 2 / 1), [])]"
  1807    \(0 <= -4 * (b ^^^ 2 / 4 + -1 * r ^^^ 2 / 1), [])]"
  1808 then writeln"simplify result\nsimplify result\nsimplify result"
  1808 then writeln"simplify result\nsimplify result\nsimplify result"
  1809 else raise error "rlang.sml: diff.behav. in Pythagoras asms";
  1809 else error "rlang.sml: diff.behav. in Pythagoras asms";
  1810 
  1810 
  1811 
  1811 
  1812 "-------------------- WN.15.5.03: equation within the maximum example ------";
  1812 "-------------------- WN.15.5.03: equation within the maximum example ------";
  1813 "-------------------- WN.15.5.03: equation within the maximum example ------";
  1813 "-------------------- WN.15.5.03: equation within the maximum example ------";
  1814 "-------------------- WN.15.5.03: equation within the maximum example ------";
  1814 "-------------------- WN.15.5.03: equation within the maximum example ------";
  1862          (~1,
  1862          (~1,
  1863             EdUndef,
  1863             EdUndef,
  1864             0,
  1864             0,
  1865             Nundef,
  1865             Nundef,
  1866             "-16 * r ^^^ 4 + 8 * r ^^^ 2 * u ^^^ 2 = 0")) then ()
  1866             "-16 * r ^^^ 4 + 8 * r ^^^ 2 * u ^^^ 2 = 0")) then ()
  1867 else raise error "rlang.sml: diff.behav. in Schalk I s.87 Bsp 38b";
  1867 else error "rlang.sml: diff.behav. in Schalk I s.87 Bsp 38b";
  1868 val (p,_,f,nxt,_,pt) = me nxt p c pt;
  1868 val (p,_,f,nxt,_,pt) = me nxt p c pt;
  1869 (*val nxt = Model_Problem ["sq_only","degree_2","polynomial","univariate","equation"]) *)
  1869 (*val nxt = Model_Problem ["sq_only","degree_2","polynomial","univariate","equation"]) *)
  1870 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
  1870 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
  1871 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
  1871 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
  1872 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
  1872 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
  1878 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
  1878 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
  1879 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
  1879 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
  1880 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
  1880 val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
  1881 val (p,_,f,nxt,_,pt) = me nxt p c pt;
  1881 val (p,_,f,nxt,_,pt) = me nxt p c pt;
  1882 if f = Form' (FormKF (~1,EdUndef,0,Nundef,"[u = sqrt (2 * r ^^^ 2 / 1), u = -1 * sqrt (2 * r ^^^ 2 / 1)]")) then()
  1882 if f = Form' (FormKF (~1,EdUndef,0,Nundef,"[u = sqrt (2 * r ^^^ 2 / 1), u = -1 * sqrt (2 * r ^^^ 2 / 1)]")) then()
  1883 else raise error "rlang.sml WN.TEST new behaviour in max-rooteq";
  1883 else error "rlang.sml WN.TEST new behaviour in max-rooteq";