test/Tools/isac/Knowledge/polyeq-1.sml
changeset 60242 73ee61385493
parent 60237 e534316f9e07
child 60309 70a1d102660d
child 60329 0c10aeff57d7
     1.1 --- a/test/Tools/isac/Knowledge/polyeq-1.sml	Mon Apr 19 20:44:18 2021 +0200
     1.2 +++ b/test/Tools/isac/Knowledge/polyeq-1.sml	Tue Apr 20 16:58:44 2021 +0200
     1.3 @@ -16,30 +16,30 @@
     1.4  "----------- Matthias Goldgruber 2003 trials on rewrite orders -------------------------------";
     1.5  "----------- lin.eq degree_0 -------------------------------------";
     1.6  "----------- test thm's d2_pq_formulsxx[_neg]---------------------";
     1.7 -"----------- equality (2 +(-1)*x + x^^^2 = (0::real)) ----------------------------------------";
     1.8 -"----------- equality (-2 +(-1)*x + 1*x^^^2 = 0) ---------------------------------------------";
     1.9 -"----------- equality (-2 + x + x^^^2 = 0) ---------------------------------------------------";
    1.10 -"----------- equality (2 + x + x^^^2 = 0) ----------------------------------------------------";
    1.11 -"----------- equality (-2 + x + 1*x^^^2 = 0)) ------------------------------------------------";
    1.12 -"----------- equality (1*x +   x^^^2 = 0) ----------------------------------------------------";
    1.13 -"----------- equality (1*x + 1*x^^^2 = 0) ----------------------------------------------------";
    1.14 -"----------- equality (x +   x^^^2 = 0) ------------------------------------------------------";
    1.15 -"----------- equality (x + 1*x^^^2 = 0) ------------------------------------------------------";
    1.16 -"----------- equality (-4 + x^^^2 = 0) -------------------------------------------------------";
    1.17 -"----------- equality (4 + 1*x^^^2 = 0) -------------------------------------------------------";
    1.18 -"----------- equality (1 +(-1)*x + 2*x^^^2 = 0) ----------------------------------------------";
    1.19 -"----------- equality (-1 + x + 2*x^^^2 = 0) -------------------------------------------------";
    1.20 -"----------- equality (1 + x + 2*x^^^2 = 0) --------------------------------------------------";
    1.21 -"----------- (-8 - 2*x + x^^^2 = 0),  (*Schalk 2, S.67 Nr.31.b----";
    1.22 -"----------- (-8 - 2*x + x^^^2 = 0),  by rewriting ---------------";
    1.23 -"----------- (-16 + 4*x + 2*x^^^2 = 0), --------------------------";
    1.24 +"----------- equality (2 +(-1)*x + x \<up> 2 = (0::real)) ----------------------------------------";
    1.25 +"----------- equality (-2 +(-1)*x + 1*x \<up> 2 = 0) ---------------------------------------------";
    1.26 +"----------- equality (-2 + x + x \<up> 2 = 0) ---------------------------------------------------";
    1.27 +"----------- equality (2 + x + x \<up> 2 = 0) ----------------------------------------------------";
    1.28 +"----------- equality (-2 + x + 1*x \<up> 2 = 0)) ------------------------------------------------";
    1.29 +"----------- equality (1*x +   x \<up> 2 = 0) ----------------------------------------------------";
    1.30 +"----------- equality (1*x + 1*x \<up> 2 = 0) ----------------------------------------------------";
    1.31 +"----------- equality (x +   x \<up> 2 = 0) ------------------------------------------------------";
    1.32 +"----------- equality (x + 1*x \<up> 2 = 0) ------------------------------------------------------";
    1.33 +"----------- equality (-4 + x \<up> 2 = 0) -------------------------------------------------------";
    1.34 +"----------- equality (4 + 1*x \<up> 2 = 0) -------------------------------------------------------";
    1.35 +"----------- equality (1 +(-1)*x + 2*x \<up> 2 = 0) ----------------------------------------------";
    1.36 +"----------- equality (-1 + x + 2*x \<up> 2 = 0) -------------------------------------------------";
    1.37 +"----------- equality (1 + x + 2*x \<up> 2 = 0) --------------------------------------------------";
    1.38 +"----------- (-8 - 2*x + x \<up> 2 = 0),  (*Schalk 2, S.67 Nr.31.b----";
    1.39 +"----------- (-8 - 2*x + x \<up> 2 = 0),  by rewriting ---------------";
    1.40 +"----------- (-16 + 4*x + 2*x \<up> 2 = 0), --------------------------";
    1.41  "-----------------------------------------------------------------";
    1.42  "------ polyeq-2.sml ---------------------------------------------";
    1.43 -"----------- (a*b - (a+b)*x + x^^^2 = 0), (*Schalk 2,S.68Nr.44.a*)";
    1.44 -"----------- (-64 + x^^^2 = 0), (*Schalk 2, S.66 Nr.1.a~--------*)";
    1.45 -"----------- (-147 + 3*x^^^2 = 0), (*Schalk 2, S.66 Nr.1.b------*)";
    1.46 +"----------- (a*b - (a+b)*x + x \<up> 2 = 0), (*Schalk 2,S.68Nr.44.a*)";
    1.47 +"----------- (-64 + x \<up> 2 = 0), (*Schalk 2, S.66 Nr.1.a~--------*)";
    1.48 +"----------- (-147 + 3*x \<up> 2 = 0), (*Schalk 2, S.66 Nr.1.b------*)";
    1.49  "----------- (3*x - 1 - (5*x - (2 - 4*x)) = -11),(*Schalk Is86Bsp5";
    1.50 -"----------- ((x+1)*(x+2) - (3*x - 2)^^^2=.. Schalk II s.68 Bsp 37";
    1.51 +"----------- ((x+1)*(x+2) - (3*x - 2) \<up> 2=.. Schalk II s.68 Bsp 37";
    1.52  "----------- rls make_polynomial_in ------------------------------";
    1.53  "----------- interSteps ([1],Res); on Schalk Is86Bsp5-------------";
    1.54  "----------- rls d2_polyeq_bdv_only_simplify ---------------------";
    1.55 @@ -52,12 +52,12 @@
    1.56  (* Rewrite.trace_on:=true;
    1.57   Rewrite.trace_on:=false;
    1.58  *)
    1.59 - val t1 = (Thm.term_of o the o (TermC.parse thy)) "lhs (-8 - 2*x + x^^^2 = 0)";
    1.60 + val t1 = (Thm.term_of o the o (TermC.parse thy)) "lhs (-8 - 2*x + x \<up> 2 = 0)";
    1.61   val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t1;
    1.62 - if ((UnparseC.term t) = "-8 - 2 * x + x ^^^ 2") then ()
    1.63 + if ((UnparseC.term t) = "-8 - 2 * x + x \<up> 2") then ()
    1.64   else  error "polyeq.sml: diff.behav. in lhs";
    1.65  
    1.66 - val t2 = (Thm.term_of o the o (TermC.parse thy)) "(-8 - 2*x + x^^^2) is_expanded_in x";
    1.67 + val t2 = (Thm.term_of o the o (TermC.parse thy)) "(-8 - 2*x + x \<up> 2) is_expanded_in x";
    1.68   val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t2;
    1.69   if (UnparseC.term t) = "True" then ()
    1.70   else  error "polyeq.sml: diff.behav. 1 in is_expended_in";
    1.71 @@ -67,23 +67,23 @@
    1.72   if (UnparseC.term t) = "False" then ()
    1.73   else  error "polyeq.sml: diff.behav. 2 in is_poly_in";
    1.74  
    1.75 - val t3 = (Thm.term_of o the o (TermC.parse thy)) "(-8 + (-1)*2*x + x^^^2) is_poly_in x";
    1.76 + val t3 = (Thm.term_of o the o (TermC.parse thy)) "(-8 + (-1)*2*x + x \<up> 2) is_poly_in x";
    1.77   val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t3;
    1.78   if (UnparseC.term t) = "True" then ()
    1.79   else  error "polyeq.sml: diff.behav. 3 in is_poly_in";
    1.80  
    1.81 - val t4 = (Thm.term_of o the o (TermC.parse thy)) "(lhs (-8 + (-1)*2*x + x^^^2 = 0)) is_expanded_in x";
    1.82 + val t4 = (Thm.term_of o the o (TermC.parse thy)) "(lhs (-8 + (-1)*2*x + x \<up> 2 = 0)) is_expanded_in x";
    1.83   val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t4;
    1.84   if (UnparseC.term t) = "True" then ()
    1.85   else  error "polyeq.sml: diff.behav. 4 in is_expended_in";
    1.86  
    1.87  
    1.88 - val t6 = (Thm.term_of o the o (TermC.parse thy)) "(lhs (-8 - 2*x + x^^^2 = 0)) is_expanded_in x";
    1.89 + val t6 = (Thm.term_of o the o (TermC.parse thy)) "(lhs (-8 - 2*x + x \<up> 2 = 0)) is_expanded_in x";
    1.90   val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t6;
    1.91   if (UnparseC.term t) = "True" then ()
    1.92   else  error "polyeq.sml: diff.behav. 5 in is_expended_in";
    1.93   
    1.94 - val t3 = (Thm.term_of o the o (TermC.parse thy))"((-8 - 2*x + x^^^2) has_degree_in x) = 2";
    1.95 + val t3 = (Thm.term_of o the o (TermC.parse thy))"((-8 - 2*x + x \<up> 2) has_degree_in x) = 2";
    1.96   val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t3;
    1.97   if (UnparseC.term t) = "True" then ()
    1.98   else  error "polyeq.sml: diff.behav. in has_degree_in_in";
    1.99 @@ -94,13 +94,13 @@
   1.100   else  error "polyeq.sml: diff.behav. 6 in has_degree_in_in";
   1.101  
   1.102   val t4 = (Thm.term_of o the o (TermC.parse thy)) 
   1.103 -	      "((-8 - 2*x + x^^^2) has_degree_in x) = 1";
   1.104 +	      "((-8 - 2*x + x \<up> 2) has_degree_in x) = 1";
   1.105   val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t4;
   1.106   if (UnparseC.term t) = "False" then ()
   1.107   else  error "polyeq.sml: diff.behav. 7 in has_degree_in_in";
   1.108  
   1.109   val t5 = (Thm.term_of o the o (TermC.parse thy)) 
   1.110 -	      "((-8 - 2*x + x^^^2) has_degree_in x) = 2";
   1.111 +	      "((-8 - 2*x + x \<up> 2) has_degree_in x) = 2";
   1.112   val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t5;
   1.113   if (UnparseC.term t) = "True" then ()
   1.114   else  error "polyeq.sml: diff.behav. 8 in has_degree_in_in";
   1.115 @@ -108,21 +108,21 @@
   1.116  "----------- test matching problems --------------------------0---";
   1.117  "----------- test matching problems --------------------------0---";
   1.118  "----------- test matching problems --------------------------0---";
   1.119 -val fmz = ["equality (-8 - 2*x + x^^^2 = 0)", "solveFor x", "solutions L"];
   1.120 +val fmz = ["equality (-8 - 2*x + x \<up> 2 = 0)", "solveFor x", "solutions L"];
   1.121  if M_Match.match_pbl fmz (Problem.from_store ["expanded", "univariate", "equation"]) =
   1.122    M_Match.Matches' {Find = [Correct "solutions L"], 
   1.123              With = [], 
   1.124 -            Given = [Correct "equality (-8 - 2 * x + x ^^^ 2 = 0)", Correct "solveFor x"], 
   1.125 -            Where = [Correct "matches (?a = 0) (-8 - 2 * x + x ^^^ 2 = 0)", 
   1.126 -                     Correct "lhs (-8 - 2 * x + x ^^^ 2 = 0) is_expanded_in x"], 
   1.127 +            Given = [Correct "equality (-8 - 2 * x + x \<up> 2 = 0)", Correct "solveFor x"], 
   1.128 +            Where = [Correct "matches (?a = 0) (-8 - 2 * x + x \<up> 2 = 0)", 
   1.129 +                     Correct "lhs (-8 - 2 * x + x \<up> 2 = 0) is_expanded_in x"], 
   1.130              Relate = []}
   1.131  then () else error "M_Match.match_pbl [expanded,univariate,equation]";
   1.132  
   1.133  if M_Match.match_pbl fmz (Problem.from_store ["degree_2", "expanded", "univariate", "equation"]) =
   1.134    M_Match.Matches' {Find = [Correct "solutions L"], 
   1.135              With = [], 
   1.136 -            Given = [Correct "equality (-8 - 2 * x + x ^^^ 2 = 0)", Correct "solveFor x"], 
   1.137 -            Where = [Correct "lhs (-8 - 2 * x + x ^^^ 2 = 0) has_degree_in x = 2"], 
   1.138 +            Given = [Correct "equality (-8 - 2 * x + x \<up> 2 = 0)", Correct "solveFor x"], 
   1.139 +            Where = [Correct "lhs (-8 - 2 * x + x \<up> 2 = 0) has_degree_in x = 2"], 
   1.140              Relate = []}              (*before WN110906 was: has_degree_in x =!= 2"]*)
   1.141  then () else error "M_Match.match_pbl [degree_2,expanded,univariate,equation]";
   1.142  
   1.143 @@ -134,30 +134,30 @@
   1.144  -----------28.2.03: war nicht upgedatet und ausgeklammert in ROOT.ML-->Test_Isac.thy
   1.145  
   1.146    (*Aufgabe zum Einstieg in die Arbeit...*)
   1.147 -  val t = (Thm.term_of o the o (TermC.parse thy)) "a*b - (a+b)*x + x^^^2 = 0";
   1.148 +  val t = (Thm.term_of o the o (TermC.parse thy)) "a*b - (a+b)*x + x \<up> 2 = 0";
   1.149    (*ein 'ruleset' aus Poly.ML wird angewandt...*)
   1.150    val SOME (t,_) = rewrite_set_ thy Poly_erls false make_polynomial t;
   1.151    UnparseC.term t;
   1.152 -  "a * b + (-1 * (a * x) + (-1 * (b * x) + x ^^^ 2)) = 0";
   1.153 +  "a * b + (-1 * (a * x) + (-1 * (b * x) + x \<up> 2)) = 0";
   1.154    val SOME (t,_) = 
   1.155        rewrite_set_inst_ thy Poly_erls false [("bdv", "a")] make_polynomial_in t;
   1.156    UnparseC.term t;
   1.157 -  "x ^^^ 2 + (-1 * (b * x) + (-1 * (x * a) + b * a)) = 0";
   1.158 +  "x \<up> 2 + (-1 * (b * x) + (-1 * (x * a) + b * a)) = 0";
   1.159  (* bei Verwendung von "size_of-term" nach MG :*)
   1.160 -(*"x ^^^ 2 + (-1 * (b * x) + (b * a + -1 * (x * a))) = 0"  !!! *)
   1.161 +(*"x \<up> 2 + (-1 * (b * x) + (b * a + -1 * (x * a))) = 0"  !!! *)
   1.162  
   1.163    (*wir holen 'a' wieder aus der Klammerung heraus...*)
   1.164    val SOME (t,_) = rewrite_set_ thy Poly_erls false discard_parentheses t;
   1.165    UnparseC.term t;
   1.166 -   "x ^^^ 2 + -1 * b * x + -1 * x * a + b * a = 0";
   1.167 -(* "x ^^^ 2 + -1 * b * x + b * a + -1 * x * a = 0" !!! *)
   1.168 +   "x \<up> 2 + -1 * b * x + -1 * x * a + b * a = 0";
   1.169 +(* "x \<up> 2 + -1 * b * x + b * a + -1 * x * a = 0" !!! *)
   1.170  
   1.171    val SOME (t,_) =
   1.172        rewrite_set_inst_ thy Poly_erls false [("bdv", "a")] make_polynomial_in t;
   1.173    UnparseC.term t;
   1.174 -  "x ^^^ 2 + (-1 * (b * x) + a * (b + -1 * x)) = 0"; 
   1.175 +  "x \<up> 2 + (-1 * (b * x) + a * (b + -1 * x)) = 0"; 
   1.176    (*da sind wir fast am Ziel: make_polynomial_in 'a' sollte ergeben
   1.177 -  "x ^^^ 2 + (-1 * (b * x)) + (b + -1 * x) * a = 0"*)
   1.178 +  "x \<up> 2 + (-1 * (b * x)) + (b + -1 * x) * a = 0"*)
   1.179  
   1.180    (*das rewriting l"asst sich beobachten mit
   1.181  Rewrite.trace_on := false;
   1.182 @@ -178,23 +178,23 @@
   1.183   UnparseC.term t;
   1.184  "1 + b * x + x * a";
   1.185  
   1.186 - val t = (Thm.term_of o the o (TermC.parse thy)) "1 + a * (x + b * x) + a^^^2";
   1.187 + val t = (Thm.term_of o the o (TermC.parse thy)) "1 + a * (x + b * x) + a \<up> 2";
   1.188   val SOME (t,_) =
   1.189       rewrite_set_inst_ thy false [(bdv,a)] make_polynomial_in t;
   1.190   UnparseC.term t;
   1.191   val SOME (t,_) =
   1.192       rewrite_set_ thy false discard_parentheses t;
   1.193   UnparseC.term t;
   1.194 -"1 + (x + b * x) * a + a ^^^ 2";
   1.195 +"1 + (x + b * x) * a + a \<up> 2";
   1.196  
   1.197 - val t = (Thm.term_of o the o (TermC.parse thy)) "1 + a ^^^2 * x + b * a + 7*a^^^2";
   1.198 + val t = (Thm.term_of o the o (TermC.parse thy)) "1 + a  \<up> 2 * x + b * a + 7*a \<up> 2";
   1.199   val SOME (t,_) =
   1.200       rewrite_set_inst_ thy false [(bdv,a)] make_polynomial_in t;
   1.201   UnparseC.term t;
   1.202   val SOME (t,_) =
   1.203       rewrite_set_ thy false discard_parentheses t;
   1.204   UnparseC.term t;
   1.205 -"1 + b * a + (7 + x) * a ^^^ 2";
   1.206 +"1 + b * a + (7 + x) * a \<up> 2";
   1.207  
   1.208  (* MG2003
   1.209   Prog_Expr.thy       grundlegende Algebra
   1.210 @@ -207,14 +207,14 @@
   1.211   get_thm Termorder.thy "bdv_n_collect";
   1.212   get_thm (theory "Isac_Knowledge") "bdv_n_collect";
   1.213  *)
   1.214 - val t = (Thm.term_of o the o (TermC.parse thy)) "a ^^^2 * x + 7 * a^^^2";
   1.215 + val t = (Thm.term_of o the o (TermC.parse thy)) "a  \<up> 2 * x + 7 * a \<up> 2";
   1.216   val SOME (t,_) =
   1.217       rewrite_set_inst_ thy false [(bdv,a)] make_polynomial_in t;
   1.218   UnparseC.term t;
   1.219   val SOME (t,_) =
   1.220       rewrite_set_ thy false discard_parentheses t;
   1.221   UnparseC.term t;
   1.222 -"(7 + x) * a ^^^ 2";
   1.223 +"(7 + x) * a \<up> 2";
   1.224  
   1.225   val t = (Thm.term_of o the o (TermC.parse Termorder.thy)) "Pi";
   1.226  
   1.227 @@ -244,12 +244,12 @@
   1.228  else error "termorder.sml diff.behav ord_make_polynomial_in #3";
   1.229  
   1.230    val aa = (Thm.term_of o the o (TermC.parse thy)) "-1 * a * x";
   1.231 -  val bb = (Thm.term_of o the o (TermC.parse thy)) "x^^^3";
   1.232 +  val bb = (Thm.term_of o the o (TermC.parse thy)) "x \<up> 3";
   1.233    ord_make_polynomial_in true thy substx (aa, bb);
   1.234    true; (* => LESS *) 
   1.235    
   1.236    val aa = (Thm.term_of o the o (TermC.parse thy)) "-1 * a * x";
   1.237 -  val bb = (Thm.term_of o the o (TermC.parse thy)) "x^^^3";
   1.238 +  val bb = (Thm.term_of o the o (TermC.parse thy)) "x \<up> 3";
   1.239    ord_make_polynomial_in true thy substa (aa, bb);
   1.240    false; (* => GREATER *)
   1.241  
   1.242 @@ -269,14 +269,14 @@
   1.243  if UnparseC.term t' = "a + b + x" then ()
   1.244  else error "termorder.sml diff.behav ord_make_polynomial_in #13";
   1.245  
   1.246 -  val ppp' = "-6 + -5*x + x^^^3 + -1*x^^^2 + -1*x^^^3 + -14*x^^^2";
   1.247 +  val ppp' = "-6 + -5*x + x \<up> 3 + -1*x \<up> 2 + -1*x \<up> 3 + -14*x \<up> 2";
   1.248    val ppp  = (Thm.term_of o the o (TermC.parse thy)) ppp';
   1.249  val SOME (t',_) = rewrite_set_inst_ thy false [(bdv,x)] make_polynomial_in ppp;
   1.250 -if UnparseC.term t' = "-6 + -5 * x + -15 * x ^^^ 2 + 0" then ()
   1.251 +if UnparseC.term t' = "-6 + -5 * x + -15 * x \<up> 2 + 0" then ()
   1.252  else error "termorder.sml diff.behav ord_make_polynomial_in #14";
   1.253  
   1.254  val SOME (t', _) = rewrite_set_inst_ thy false [(bdv,x)] make_polynomial_in ppp;
   1.255 -if UnparseC.term t' = "-6 + -5 * x + -15 * x ^^^ 2 + 0" then ()
   1.256 +if UnparseC.term t' = "-6 + -5 * x + -15 * x \<up> 2 + 0" then ()
   1.257  else error "termorder.sml diff.behav ord_make_polynomial_in #15";
   1.258  
   1.259    val ttt' = "(3*x + 5)/18";
   1.260 @@ -332,7 +332,7 @@
   1.261  "----------- test thm's d2_pq_formulsxx[_neg]---------------------";
   1.262  "----------- test thm's d2_pq_formulsxx[_neg]---------------------";
   1.263  "----- d2_pqformula1 ------!!!!";
   1.264 -val fmz = ["equality (-1/8 + (-1/4)*z + z^^^2 = (0::real))", "solveFor z", "solutions L"];
   1.265 +val fmz = ["equality (-1/8 + (-1/4)*z + z \<up> 2 = (0::real))", "solveFor z", "solutions L"];
   1.266  val (dI',pI',mI') =
   1.267    ("Isac_Knowledge", ["pqFormula", "degree_2", "polynomial", "univariate", "equation"], ["no_met"]);
   1.268  val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
   1.269 @@ -355,14 +355,14 @@
   1.270  
   1.271  if p = ([], Res) andalso
   1.272    f2str f = "[z = 1 / 8 + sqrt (9 / 16) / 2, z = 1 / 8 + -1 * sqrt (9 / 16) / 2]" then
   1.273 -    case nxt of End_Proof' => () | _ => error "(-1/8 + (-1/4)*z + z^^^2 = (0::real)) CHANGED 1"
   1.274 -else error "(-1/8 + (-1/4)*z + z^^^2 = (0::real)) CHANGED 2";
   1.275 +    case nxt of End_Proof' => () | _ => error "(-1/8 + (-1/4)*z + z \<up> 2 = (0::real)) CHANGED 1"
   1.276 +else error "(-1/8 + (-1/4)*z + z \<up> 2 = (0::real)) CHANGED 2";
   1.277  
   1.278 -"----------- equality (2 +(-1)*x + x^^^2 = (0::real)) ----------------------------------------";
   1.279 -"----------- equality (2 +(-1)*x + x^^^2 = (0::real)) ----------------------------------------";
   1.280 -"----------- equality (2 +(-1)*x + x^^^2 = (0::real)) ----------------------------------------";
   1.281 +"----------- equality (2 +(-1)*x + x \<up> 2 = (0::real)) ----------------------------------------";
   1.282 +"----------- equality (2 +(-1)*x + x \<up> 2 = (0::real)) ----------------------------------------";
   1.283 +"----------- equality (2 +(-1)*x + x \<up> 2 = (0::real)) ----------------------------------------";
   1.284  "----- d2_pqformula1_neg ------";
   1.285 -val fmz = ["equality (2 +(-1)*x + x^^^2 = (0::real))", "solveFor x", "solutions L"];
   1.286 +val fmz = ["equality (2 +(-1)*x + x \<up> 2 = (0::real))", "solveFor x", "solutions L"];
   1.287  val (dI',pI',mI') = ("PolyEq",["pqFormula", "degree_2", "polynomial", "univariate", "equation"], ["PolyEq", "solve_d2_polyeq_pq_equation"]);
   1.288  val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
   1.289  val (p,_,f,nxt,_,pt) = me nxt p [] pt;
   1.290 @@ -379,15 +379,15 @@
   1.291  val (p,_,f,nxt,_,pt) = me nxt p [] pt;
   1.292  val asm = Ctree.get_assumptions pt p;
   1.293  if f2str f = "[]" andalso 
   1.294 -  UnparseC.terms asm = "[\"lhs (2 + -1 * x + x ^^^ 2 = 0) is_poly_in x\", " ^
   1.295 -    "\"lhs (2 + -1 * x + x ^^^ 2 = 0) has_degree_in x = 2\"]" then ()
   1.296 -else error "polyeq.sml: diff.behav. in 2 +(-1)*x + x^^^2 = 0";
   1.297 +  UnparseC.terms asm = "[\"lhs (2 + -1 * x + x \<up> 2 = 0) is_poly_in x\", " ^
   1.298 +    "\"lhs (2 + -1 * x + x \<up> 2 = 0) has_degree_in x = 2\"]" then ()
   1.299 +else error "polyeq.sml: diff.behav. in 2 +(-1)*x + x \<up> 2 = 0";
   1.300  
   1.301 -"----------- equality (-2 +(-1)*x + 1*x^^^2 = 0) ---------------------------------------------";
   1.302 -"----------- equality (-2 +(-1)*x + 1*x^^^2 = 0) ---------------------------------------------";
   1.303 -"----------- equality (-2 +(-1)*x + 1*x^^^2 = 0) ---------------------------------------------";
   1.304 +"----------- equality (-2 +(-1)*x + 1*x \<up> 2 = 0) ---------------------------------------------";
   1.305 +"----------- equality (-2 +(-1)*x + 1*x \<up> 2 = 0) ---------------------------------------------";
   1.306 +"----------- equality (-2 +(-1)*x + 1*x \<up> 2 = 0) ---------------------------------------------";
   1.307  "----- d2_pqformula2 ------";
   1.308 -val fmz = ["equality (-2 +(-1)*x + 1*x^^^2 = 0)", "solveFor x", "solutions L"];
   1.309 +val fmz = ["equality (-2 +(-1)*x + 1*x \<up> 2 = 0)", "solveFor x", "solutions L"];
   1.310  val (dI',pI',mI') = ("PolyEq",["pqFormula", "degree_2", "polynomial", "univariate", "equation"],
   1.311                       ["PolyEq", "solve_d2_polyeq_pq_equation"]);
   1.312  val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
   1.313 @@ -404,12 +404,12 @@
   1.314  	 | _ => error "polyeq.sml: diff.behav. in -2 + (-1)*x + x^2 = 0 -> [x = 2, x = -1]";
   1.315  
   1.316  
   1.317 -"----------- equality (-2 + x + x^^^2 = 0) ---------------------------------------------------";
   1.318 -"----------- equality (-2 + x + x^^^2 = 0) ---------------------------------------------------";
   1.319 -"----------- equality (-2 + x + x^^^2 = 0) ---------------------------------------------------";
   1.320 +"----------- equality (-2 + x + x \<up> 2 = 0) ---------------------------------------------------";
   1.321 +"----------- equality (-2 + x + x \<up> 2 = 0) ---------------------------------------------------";
   1.322 +"----------- equality (-2 + x + x \<up> 2 = 0) ---------------------------------------------------";
   1.323  "----- d2_pqformula3 ------";
   1.324  (*EP-9*)
   1.325 -val fmz = ["equality (-2 + x + x^^^2 = 0)", "solveFor x", "solutions L"];
   1.326 +val fmz = ["equality (-2 + x + x \<up> 2 = 0)", "solveFor x", "solutions L"];
   1.327  val (dI',pI',mI') = ("PolyEq",["pqFormula", "degree_2", "polynomial", "univariate", "equation"],
   1.328                       ["PolyEq", "solve_d2_polyeq_pq_equation"]);
   1.329  val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
   1.330 @@ -426,11 +426,11 @@
   1.331  	 | _ => error "polyeq.sml: diff.behav. in  -2 + x + x^2 = 0-> [x = 1, x = -2]";
   1.332  
   1.333  
   1.334 -"----------- equality (2 + x + x^^^2 = 0) ----------------------------------------------------";
   1.335 -"----------- equality (2 + x + x^^^2 = 0) ----------------------------------------------------";
   1.336 -"----------- equality (2 + x + x^^^2 = 0) ----------------------------------------------------";
   1.337 +"----------- equality (2 + x + x \<up> 2 = 0) ----------------------------------------------------";
   1.338 +"----------- equality (2 + x + x \<up> 2 = 0) ----------------------------------------------------";
   1.339 +"----------- equality (2 + x + x \<up> 2 = 0) ----------------------------------------------------";
   1.340  "----- d2_pqformula3_neg ------";
   1.341 -val fmz = ["equality (2 + x + x^^^2 = 0)", "solveFor x", "solutions L"];
   1.342 +val fmz = ["equality (2 + x + x \<up> 2 = 0)", "solveFor x", "solutions L"];
   1.343  val (dI',pI',mI') = ("PolyEq",["pqFormula", "degree_2", "polynomial", "univariate", "equation"],
   1.344                       ["PolyEq", "solve_d2_polyeq_pq_equation"]);
   1.345  val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
   1.346 @@ -442,15 +442,15 @@
   1.347  
   1.348  val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
   1.349  val (p,_,f,nxt,_,pt) = me nxt p [] pt;
   1.350 -"TODO 2 + x + x^^^2 = 0";
   1.351 -"TODO 2 + x + x^^^2 = 0";
   1.352 -"TODO 2 + x + x^^^2 = 0";
   1.353 +"TODO 2 + x + x \<up> 2 = 0";
   1.354 +"TODO 2 + x + x \<up> 2 = 0";
   1.355 +"TODO 2 + x + x \<up> 2 = 0";
   1.356  
   1.357 -"----------- equality (-2 + x + 1*x^^^2 = 0)) ------------------------------------------------";
   1.358 -"----------- equality (-2 + x + 1*x^^^2 = 0)) ------------------------------------------------";
   1.359 -"----------- equality (-2 + x + 1*x^^^2 = 0)) ------------------------------------------------";
   1.360 +"----------- equality (-2 + x + 1*x \<up> 2 = 0)) ------------------------------------------------";
   1.361 +"----------- equality (-2 + x + 1*x \<up> 2 = 0)) ------------------------------------------------";
   1.362 +"----------- equality (-2 + x + 1*x \<up> 2 = 0)) ------------------------------------------------";
   1.363  "----- d2_pqformula4 ------";
   1.364 -val fmz = ["equality (-2 + x + 1*x^^^2 = 0)", "solveFor x", "solutions L"];
   1.365 +val fmz = ["equality (-2 + x + 1*x \<up> 2 = 0)", "solveFor x", "solutions L"];
   1.366  val (dI',pI',mI') = ("PolyEq",["pqFormula", "degree_2", "polynomial", "univariate", "equation"],
   1.367                       ["PolyEq", "solve_d2_polyeq_pq_equation"]);
   1.368  val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
   1.369 @@ -463,13 +463,13 @@
   1.370  val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
   1.371  val (p,_,f,nxt,_,pt) = me nxt p [] pt;
   1.372  case f of Test_Out.FormKF "[x = 1, x = -2]" => ()
   1.373 -	 | _ => error "polyeq.sml: diff.behav. in  -2 + x + 1*x^^^2 = 0 -> [x = 1, x = -2]";
   1.374 +	 | _ => error "polyeq.sml: diff.behav. in  -2 + x + 1*x \<up> 2 = 0 -> [x = 1, x = -2]";
   1.375  
   1.376 -"----------- equality (1*x +   x^^^2 = 0) ----------------------------------------------------";
   1.377 -"----------- equality (1*x +   x^^^2 = 0) ----------------------------------------------------";
   1.378 -"----------- equality (1*x +   x^^^2 = 0) ----------------------------------------------------";
   1.379 +"----------- equality (1*x +   x \<up> 2 = 0) ----------------------------------------------------";
   1.380 +"----------- equality (1*x +   x \<up> 2 = 0) ----------------------------------------------------";
   1.381 +"----------- equality (1*x +   x \<up> 2 = 0) ----------------------------------------------------";
   1.382  "----- d2_pqformula5 ------";
   1.383 -val fmz = ["equality (1*x +   x^^^2 = 0)", "solveFor x", "solutions L"];
   1.384 +val fmz = ["equality (1*x +   x \<up> 2 = 0)", "solveFor x", "solutions L"];
   1.385  val (dI',pI',mI') = ("PolyEq",["pqFormula", "degree_2", "polynomial", "univariate", "equation"],
   1.386                       ["PolyEq", "solve_d2_polyeq_pq_equation"]);
   1.387  val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
   1.388 @@ -484,11 +484,11 @@
   1.389  case f of Test_Out.FormKF "[x = 0, x = -1]" => ()
   1.390  	 | _ => error "polyeq.sml: diff.behav. in  1*x +   x^2 = 0 -> [x = 0, x = -1]";
   1.391  
   1.392 -"----------- equality (1*x + 1*x^^^2 = 0) ----------------------------------------------------";
   1.393 -"----------- equality (1*x + 1*x^^^2 = 0) ----------------------------------------------------";
   1.394 -"----------- equality (1*x + 1*x^^^2 = 0) ----------------------------------------------------";
   1.395 +"----------- equality (1*x + 1*x \<up> 2 = 0) ----------------------------------------------------";
   1.396 +"----------- equality (1*x + 1*x \<up> 2 = 0) ----------------------------------------------------";
   1.397 +"----------- equality (1*x + 1*x \<up> 2 = 0) ----------------------------------------------------";
   1.398  "----- d2_pqformula6 ------";
   1.399 -val fmz = ["equality (1*x + 1*x^^^2 = 0)", "solveFor x", "solutions L"];
   1.400 +val fmz = ["equality (1*x + 1*x \<up> 2 = 0)", "solveFor x", "solutions L"];
   1.401  val (dI',pI',mI') = ("PolyEq",["pqFormula", "degree_2", "polynomial", "univariate", "equation"],
   1.402                       ["PolyEq", "solve_d2_polyeq_pq_equation"]);
   1.403  val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
   1.404 @@ -503,12 +503,12 @@
   1.405  case f of Test_Out.FormKF "[x = 0, x = -1]" => ()
   1.406  	 | _ => error "polyeq.sml: diff.behav. in  1*x + 1*x^2 = 0 -> [x = 0, x = -1]";
   1.407  
   1.408 -"----------- equality (x +   x^^^2 = 0) ------------------------------------------------------";
   1.409 -"----------- equality (x +   x^^^2 = 0) ------------------------------------------------------";
   1.410 -"----------- equality (x +   x^^^2 = 0) ------------------------------------------------------";
   1.411 +"----------- equality (x +   x \<up> 2 = 0) ------------------------------------------------------";
   1.412 +"----------- equality (x +   x \<up> 2 = 0) ------------------------------------------------------";
   1.413 +"----------- equality (x +   x \<up> 2 = 0) ------------------------------------------------------";
   1.414  "----- d2_pqformula7 ------";
   1.415  (*EP-10*)
   1.416 -val fmz = ["equality (  x +   x^^^2 = 0)", "solveFor x", "solutions L"];
   1.417 +val fmz = ["equality (  x +   x \<up> 2 = 0)", "solveFor x", "solutions L"];
   1.418  val (dI',pI',mI') = ("PolyEq",["pqFormula", "degree_2", "polynomial", "univariate", "equation"],
   1.419                       ["PolyEq", "solve_d2_polyeq_pq_equation"]);
   1.420  val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
   1.421 @@ -523,11 +523,11 @@
   1.422  case f of Test_Out.FormKF "[x = 0, x = -1]" => ()
   1.423  	 | _ => error "polyeq.sml: diff.behav. in  x + x^2 = 0 -> [x = 0, x = -1]";
   1.424  
   1.425 -"----------- equality (x + 1*x^^^2 = 0) ------------------------------------------------------";
   1.426 -"----------- equality (x + 1*x^^^2 = 0) ------------------------------------------------------";
   1.427 -"----------- equality (x + 1*x^^^2 = 0) ------------------------------------------------------";
   1.428 +"----------- equality (x + 1*x \<up> 2 = 0) ------------------------------------------------------";
   1.429 +"----------- equality (x + 1*x \<up> 2 = 0) ------------------------------------------------------";
   1.430 +"----------- equality (x + 1*x \<up> 2 = 0) ------------------------------------------------------";
   1.431  "----- d2_pqformula8 ------";
   1.432 -val fmz = ["equality (x + 1*x^^^2 = 0)", "solveFor x", "solutions L"];
   1.433 +val fmz = ["equality (x + 1*x \<up> 2 = 0)", "solveFor x", "solutions L"];
   1.434  val (dI',pI',mI') = ("PolyEq",["pqFormula", "degree_2", "polynomial", "univariate", "equation"],
   1.435                       ["PolyEq", "solve_d2_polyeq_pq_equation"]);
   1.436  val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
   1.437 @@ -542,11 +542,11 @@
   1.438  case f of Test_Out.FormKF "[x = 0, x = -1]" => ()
   1.439  	 | _ => error "polyeq.sml: diff.behav. in  x + 1*x^2 = 0 -> [x = 0, x = -1]";
   1.440  
   1.441 -"----------- equality (-4 + x^^^2 = 0) -------------------------------------------------------";
   1.442 -"----------- equality (-4 + x^^^2 = 0) -------------------------------------------------------";
   1.443 -"----------- equality (-4 + x^^^2 = 0) -------------------------------------------------------";
   1.444 +"----------- equality (-4 + x \<up> 2 = 0) -------------------------------------------------------";
   1.445 +"----------- equality (-4 + x \<up> 2 = 0) -------------------------------------------------------";
   1.446 +"----------- equality (-4 + x \<up> 2 = 0) -------------------------------------------------------";
   1.447  "----- d2_pqformula9 ------";
   1.448 -val fmz = ["equality (-4 + x^^^2 = 0)", "solveFor x", "solutions L"];
   1.449 +val fmz = ["equality (-4 + x \<up> 2 = 0)", "solveFor x", "solutions L"];
   1.450  val (dI',pI',mI') = ("PolyEq",["pqFormula", "degree_2", "polynomial", "univariate", "equation"],
   1.451                       ["PolyEq", "solve_d2_polyeq_pq_equation"]);
   1.452  val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
   1.453 @@ -561,11 +561,11 @@
   1.454  	 | _ => error "polyeq.sml: diff.behav. in -4 + x^2 = 0 -> [x = 2, x = -2]";
   1.455  
   1.456  
   1.457 -"----------- equality (4 + 1*x^^^2 = 0) -------------------------------------------------------";
   1.458 -"----------- equality (4 + 1*x^^^2 = 0) -------------------------------------------------------";
   1.459 -"----------- equality (4 + 1*x^^^2 = 0) -------------------------------------------------------";
   1.460 +"----------- equality (4 + 1*x \<up> 2 = 0) -------------------------------------------------------";
   1.461 +"----------- equality (4 + 1*x \<up> 2 = 0) -------------------------------------------------------";
   1.462 +"----------- equality (4 + 1*x \<up> 2 = 0) -------------------------------------------------------";
   1.463  "----- d2_pqformula9_neg ------";
   1.464 -val fmz = ["equality (4 + 1*x^^^2 = 0)", "solveFor x", "solutions L"];
   1.465 +val fmz = ["equality (4 + 1*x \<up> 2 = 0)", "solveFor x", "solutions L"];
   1.466  val (dI',pI',mI') = ("PolyEq",["pqFormula", "degree_2", "polynomial", "univariate", "equation"],
   1.467                       ["PolyEq", "solve_d2_polyeq_pq_equation"]);
   1.468  val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
   1.469 @@ -575,14 +575,14 @@
   1.470  val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
   1.471  val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
   1.472  val (p,_,f,nxt,_,pt) = me nxt p [] pt;
   1.473 -"TODO 4 + 1*x^^^2 = 0";
   1.474 -"TODO 4 + 1*x^^^2 = 0";
   1.475 -"TODO 4 + 1*x^^^2 = 0";
   1.476 +"TODO 4 + 1*x \<up> 2 = 0";
   1.477 +"TODO 4 + 1*x \<up> 2 = 0";
   1.478 +"TODO 4 + 1*x \<up> 2 = 0";
   1.479  
   1.480  "-------------------- test thm's d2_abc_formulsxx[_neg]-----";
   1.481  "-------------------- test thm's d2_abc_formulsxx[_neg]-----";
   1.482  "-------------------- test thm's d2_abc_formulsxx[_neg]-----";
   1.483 -val fmz = ["equality (-1 +(-1)*x + 2*x^^^2 = 0)", "solveFor x", "solutions L"];
   1.484 +val fmz = ["equality (-1 +(-1)*x + 2*x \<up> 2 = 0)", "solveFor x", "solutions L"];
   1.485  val (dI',pI',mI') = ("PolyEq",["abcFormula", "degree_2", "polynomial", "univariate", "equation"],
   1.486                       ["PolyEq", "solve_d2_polyeq_abc_equation"]);
   1.487  val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
   1.488 @@ -596,10 +596,10 @@
   1.489  case f of Test_Out.FormKF "[x = 1, x = -1 / 2]" => ()
   1.490  	 | _ => error "polyeq.sml: diff.behav. in -1 + (-1)*x + 2*x^2 = 0 -> [x = 1, x = -1/2]";
   1.491  
   1.492 -"----------- equality (1 +(-1)*x + 2*x^^^2 = 0) ----------------------------------------------";
   1.493 -"----------- equality (1 +(-1)*x + 2*x^^^2 = 0) ----------------------------------------------";
   1.494 -"----------- equality (1 +(-1)*x + 2*x^^^2 = 0) ----------------------------------------------";
   1.495 -val fmz = ["equality (1 +(-1)*x + 2*x^^^2 = 0)", "solveFor x", "solutions L"];
   1.496 +"----------- equality (1 +(-1)*x + 2*x \<up> 2 = 0) ----------------------------------------------";
   1.497 +"----------- equality (1 +(-1)*x + 2*x \<up> 2 = 0) ----------------------------------------------";
   1.498 +"----------- equality (1 +(-1)*x + 2*x \<up> 2 = 0) ----------------------------------------------";
   1.499 +val fmz = ["equality (1 +(-1)*x + 2*x \<up> 2 = 0)", "solveFor x", "solutions L"];
   1.500  val (dI',pI',mI') = ("PolyEq",["abcFormula", "degree_2", "polynomial", "univariate", "equation"],
   1.501                       ["PolyEq", "solve_d2_polyeq_abc_equation"]);
   1.502  val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
   1.503 @@ -610,16 +610,16 @@
   1.504  val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
   1.505  val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
   1.506  val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
   1.507 -"TODO 1 +(-1)*x + 2*x^^^2 = 0";
   1.508 -"TODO 1 +(-1)*x + 2*x^^^2 = 0";
   1.509 -"TODO 1 +(-1)*x + 2*x^^^2 = 0";
   1.510 +"TODO 1 +(-1)*x + 2*x \<up> 2 = 0";
   1.511 +"TODO 1 +(-1)*x + 2*x \<up> 2 = 0";
   1.512 +"TODO 1 +(-1)*x + 2*x \<up> 2 = 0";
   1.513  
   1.514  
   1.515 -"----------- equality (-1 + x + 2*x^^^2 = 0) -------------------------------------------------";
   1.516 -"----------- equality (-1 + x + 2*x^^^2 = 0) -------------------------------------------------";
   1.517 -"----------- equality (-1 + x + 2*x^^^2 = 0) -------------------------------------------------";
   1.518 +"----------- equality (-1 + x + 2*x \<up> 2 = 0) -------------------------------------------------";
   1.519 +"----------- equality (-1 + x + 2*x \<up> 2 = 0) -------------------------------------------------";
   1.520 +"----------- equality (-1 + x + 2*x \<up> 2 = 0) -------------------------------------------------";
   1.521  (*EP-11*)
   1.522 -val fmz = ["equality (-1 + x + 2*x^^^2 = 0)", "solveFor x", "solutions L"];
   1.523 +val fmz = ["equality (-1 + x + 2*x \<up> 2 = 0)", "solveFor x", "solutions L"];
   1.524  val (dI',pI',mI') = ("PolyEq",["abcFormula", "degree_2", "polynomial", "univariate", "equation"],
   1.525                       ["PolyEq", "solve_d2_polyeq_abc_equation"]);
   1.526  val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
   1.527 @@ -636,10 +636,10 @@
   1.528  	 | _ => error "polyeq.sml: diff.behav. in -1 + x + 2*x^2 = 0 -> [x = 1/2, x = -1]";
   1.529  
   1.530  
   1.531 -"----------- equality (1 + x + 2*x^^^2 = 0) --------------------------------------------------";
   1.532 -"----------- equality (1 + x + 2*x^^^2 = 0) --------------------------------------------------";
   1.533 -"----------- equality (1 + x + 2*x^^^2 = 0) --------------------------------------------------";
   1.534 -val fmz = ["equality (1 + x + 2*x^^^2 = 0)", "solveFor x", "solutions L"];
   1.535 +"----------- equality (1 + x + 2*x \<up> 2 = 0) --------------------------------------------------";
   1.536 +"----------- equality (1 + x + 2*x \<up> 2 = 0) --------------------------------------------------";
   1.537 +"----------- equality (1 + x + 2*x \<up> 2 = 0) --------------------------------------------------";
   1.538 +val fmz = ["equality (1 + x + 2*x \<up> 2 = 0)", "solveFor x", "solutions L"];
   1.539  val (dI',pI',mI') = ("PolyEq",["abcFormula", "degree_2", "polynomial", "univariate", "equation"],
   1.540                       ["PolyEq", "solve_d2_polyeq_abc_equation"]);
   1.541  val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
   1.542 @@ -651,12 +651,12 @@
   1.543  val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
   1.544  val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
   1.545  val (p,_,f,nxt,_,pt) = me nxt p [] pt; 
   1.546 -"TODO 1 + x + 2*x^^^2 = 0";
   1.547 -"TODO 1 + x + 2*x^^^2 = 0";
   1.548 -"TODO 1 + x + 2*x^^^2 = 0";
   1.549 +"TODO 1 + x + 2*x \<up> 2 = 0";
   1.550 +"TODO 1 + x + 2*x \<up> 2 = 0";
   1.551 +"TODO 1 + x + 2*x \<up> 2 = 0";
   1.552  
   1.553  
   1.554 -val fmz = ["equality (-2 + 1*x + x^^^2 = 0)", "solveFor x", "solutions L"];
   1.555 +val fmz = ["equality (-2 + 1*x + x \<up> 2 = 0)", "solveFor x", "solutions L"];
   1.556  val (dI',pI',mI') = ("PolyEq",["abcFormula", "degree_2", "polynomial", "univariate", "equation"],
   1.557                       ["PolyEq", "solve_d2_polyeq_abc_equation"]);
   1.558  val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
   1.559 @@ -670,7 +670,7 @@
   1.560  case f of Test_Out.FormKF "[x = 1, x = -2]" => ()
   1.561  	 | _ => error "polyeq.sml: diff.behav. in -2 + 1*x + x^2 = 0 -> [x = 1, x = -2]";
   1.562  
   1.563 -val fmz = ["equality ( 2 + 1*x + x^^^2 = 0)", "solveFor x", "solutions L"];
   1.564 +val fmz = ["equality ( 2 + 1*x + x \<up> 2 = 0)", "solveFor x", "solutions L"];
   1.565  val (dI',pI',mI') = ("PolyEq",["abcFormula", "degree_2", "polynomial", "univariate", "equation"],
   1.566                       ["PolyEq", "solve_d2_polyeq_abc_equation"]);
   1.567  val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
   1.568 @@ -681,12 +681,12 @@
   1.569  val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
   1.570  val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
   1.571  val (p,_,f,nxt,_,pt) = me nxt p [] pt; 
   1.572 -"TODO 2 + 1*x + x^^^2 = 0";
   1.573 -"TODO 2 + 1*x + x^^^2 = 0";
   1.574 -"TODO 2 + 1*x + x^^^2 = 0";
   1.575 +"TODO 2 + 1*x + x \<up> 2 = 0";
   1.576 +"TODO 2 + 1*x + x \<up> 2 = 0";
   1.577 +"TODO 2 + 1*x + x \<up> 2 = 0";
   1.578  
   1.579  (*EP-12*)
   1.580 -val fmz = ["equality (-2 + x + x^^^2 = 0)", "solveFor x", "solutions L"];
   1.581 +val fmz = ["equality (-2 + x + x \<up> 2 = 0)", "solveFor x", "solutions L"];
   1.582  val (dI',pI',mI') = ("PolyEq",["abcFormula", "degree_2", "polynomial", "univariate", "equation"],
   1.583                       ["PolyEq", "solve_d2_polyeq_abc_equation"]);
   1.584  val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
   1.585 @@ -700,7 +700,7 @@
   1.586  case f of Test_Out.FormKF "[x = 1, x = -2]" => ()
   1.587  	 | _ => error "polyeq.sml: diff.behav. in -2 + x + x^2 = 0 -> [x = 1, x = -2]";
   1.588  
   1.589 -val fmz = ["equality ( 2 + x + x^^^2 = 0)", "solveFor x", "solutions L"];
   1.590 +val fmz = ["equality ( 2 + x + x \<up> 2 = 0)", "solveFor x", "solutions L"];
   1.591  val (dI',pI',mI') = ("PolyEq",["abcFormula", "degree_2", "polynomial", "univariate", "equation"],
   1.592                       ["PolyEq", "solve_d2_polyeq_abc_equation"]);
   1.593  val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
   1.594 @@ -711,12 +711,12 @@
   1.595  val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
   1.596  val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
   1.597  val (p,_,f,nxt,_,pt) = me nxt p [] pt; 
   1.598 -"TODO 2 + x + x^^^2 = 0";
   1.599 -"TODO 2 + x + x^^^2 = 0";
   1.600 -"TODO 2 + x + x^^^2 = 0";
   1.601 +"TODO 2 + x + x \<up> 2 = 0";
   1.602 +"TODO 2 + x + x \<up> 2 = 0";
   1.603 +"TODO 2 + x + x \<up> 2 = 0";
   1.604  
   1.605  (*EP-13*)
   1.606 -val fmz = ["equality (-8 + 2*x^^^2 = 0)", "solveFor x", "solutions L"];
   1.607 +val fmz = ["equality (-8 + 2*x \<up> 2 = 0)", "solveFor x", "solutions L"];
   1.608  val (dI',pI',mI') = ("PolyEq",["abcFormula", "degree_2", "polynomial", "univariate", "equation"],
   1.609                       ["PolyEq", "solve_d2_polyeq_abc_equation"]);
   1.610  val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
   1.611 @@ -730,7 +730,7 @@
   1.612  case f of Test_Out.FormKF "[x = 2, x = -2]" => ()
   1.613  	 | _ => error "polyeq.sml: diff.behav. in -8 + 2*x^2 = 0 -> [x = 2, x = -2]";
   1.614  
   1.615 -val fmz = ["equality ( 8+ 2*x^^^2 = 0)", "solveFor x", "solutions L"];
   1.616 +val fmz = ["equality ( 8+ 2*x \<up> 2 = 0)", "solveFor x", "solutions L"];
   1.617  val (dI',pI',mI') = ("PolyEq",["abcFormula", "degree_2", "polynomial", "univariate", "equation"],
   1.618                       ["PolyEq", "solve_d2_polyeq_abc_equation"]);
   1.619  val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
   1.620 @@ -740,12 +740,12 @@
   1.621  val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
   1.622  val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
   1.623  val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
   1.624 -"TODO 8+ 2*x^^^2 = 0";
   1.625 -"TODO 8+ 2*x^^^2 = 0";
   1.626 -"TODO 8+ 2*x^^^2 = 0";
   1.627 +"TODO 8+ 2*x \<up> 2 = 0";
   1.628 +"TODO 8+ 2*x \<up> 2 = 0";
   1.629 +"TODO 8+ 2*x \<up> 2 = 0";
   1.630  
   1.631  (*EP-14*)
   1.632 -val fmz = ["equality (-4 + x^^^2 = 0)", "solveFor x", "solutions L"];
   1.633 +val fmz = ["equality (-4 + x \<up> 2 = 0)", "solveFor x", "solutions L"];
   1.634  val (dI',pI',mI') = ("PolyEq",["abcFormula", "degree_2", "polynomial", "univariate", "equation"], ["PolyEq", "solve_d2_polyeq_abc_equation"]);
   1.635  val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
   1.636  val (p,_,f,nxt,_,pt) = me nxt p [] pt;
   1.637 @@ -759,7 +759,7 @@
   1.638  	 | _ => error "polyeq.sml: diff.behav. in -4 + x^2 = 0 -> [x = 2, x = -2]";
   1.639  
   1.640  
   1.641 -val fmz = ["equality ( 4+ x^^^2 = 0)", "solveFor x", "solutions L"];
   1.642 +val fmz = ["equality ( 4+ x \<up> 2 = 0)", "solveFor x", "solutions L"];
   1.643  val (dI',pI',mI') = ("PolyEq",["abcFormula", "degree_2", "polynomial", "univariate", "equation"], ["PolyEq", "solve_d2_polyeq_abc_equation"]);
   1.644  val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
   1.645  val (p,_,f,nxt,_,pt) = me nxt p [] pt;
   1.646 @@ -768,12 +768,12 @@
   1.647  val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
   1.648  val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
   1.649  val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
   1.650 -"TODO 4+ x^^^2 = 0";
   1.651 -"TODO 4+ x^^^2 = 0";
   1.652 -"TODO 4+ x^^^2 = 0";
   1.653 +"TODO 4+ x \<up> 2 = 0";
   1.654 +"TODO 4+ x \<up> 2 = 0";
   1.655 +"TODO 4+ x \<up> 2 = 0";
   1.656  
   1.657  (*EP-15*)
   1.658 -val fmz = ["equality (2*x + 2*x^^^2 = 0)", "solveFor x", "solutions L"];
   1.659 +val fmz = ["equality (2*x + 2*x \<up> 2 = 0)", "solveFor x", "solutions L"];
   1.660  val (dI',pI',mI') = ("PolyEq",["abcFormula", "degree_2", "polynomial", "univariate", "equation"],
   1.661                       ["PolyEq", "solve_d2_polyeq_abc_equation"]);
   1.662  val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
   1.663 @@ -787,7 +787,7 @@
   1.664  case f of Test_Out.FormKF "[x = 0, x = -1]" => ()
   1.665  	 | _ => error "polyeq.sml: diff.behav. in x + x^2 = 0 -> [x = 0, x = -1]";
   1.666  
   1.667 -val fmz = ["equality (1*x + x^^^2 = 0)", "solveFor x", "solutions L"];
   1.668 +val fmz = ["equality (1*x + x \<up> 2 = 0)", "solveFor x", "solutions L"];
   1.669  val (dI',pI',mI') = ("PolyEq",["abcFormula", "degree_2", "polynomial", "univariate", "equation"],
   1.670                       ["PolyEq", "solve_d2_polyeq_abc_equation"]);
   1.671  val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
   1.672 @@ -802,7 +802,7 @@
   1.673  	 | _ => error "polyeq.sml: diff.behav. in x + x^2 = 0 -> [x = 0, x = -1]";
   1.674  
   1.675  (*EP-16*)
   1.676 -val fmz = ["equality (x + 2*x^^^2 = 0)", "solveFor x", "solutions L"];
   1.677 +val fmz = ["equality (x + 2*x \<up> 2 = 0)", "solveFor x", "solutions L"];
   1.678  val (dI',pI',mI') = ("PolyEq",["abcFormula", "degree_2", "polynomial", "univariate", "equation"],
   1.679                       ["PolyEq", "solve_d2_polyeq_abc_equation"]);
   1.680  val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
   1.681 @@ -817,7 +817,7 @@
   1.682  	 | _ => error "polyeq.sml: diff.behav. in x + x^2 = 0 -> [x = 0, x = -1 / 2]";
   1.683  
   1.684  (*EP-//*)
   1.685 -val fmz = ["equality (x + x^^^2 = 0)", "solveFor x", "solutions L"];
   1.686 +val fmz = ["equality (x + x \<up> 2 = 0)", "solveFor x", "solutions L"];
   1.687  val (dI',pI',mI') = ("PolyEq",["abcFormula", "degree_2", "polynomial", "univariate", "equation"],
   1.688                       ["PolyEq", "solve_d2_polyeq_abc_equation"]);
   1.689  val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
   1.690 @@ -832,15 +832,15 @@
   1.691  	 | _ => error "polyeq.sml: diff.behav. in x + x^2 = 0 -> [x = 0, x = -1]";
   1.692  
   1.693  
   1.694 -"----------- (-8 - 2*x + x^^^2 = 0),  (*Schalk 2, S.67 Nr.31.b----";
   1.695 -"----------- (-8 - 2*x + x^^^2 = 0),  (*Schalk 2, S.67 Nr.31.b----";
   1.696 -"----------- (-8 - 2*x + x^^^2 = 0),  (*Schalk 2, S.67 Nr.31.b----";
   1.697 +"----------- (-8 - 2*x + x \<up> 2 = 0),  (*Schalk 2, S.67 Nr.31.b----";
   1.698 +"----------- (-8 - 2*x + x \<up> 2 = 0),  (*Schalk 2, S.67 Nr.31.b----";
   1.699 +"----------- (-8 - 2*x + x \<up> 2 = 0),  (*Schalk 2, S.67 Nr.31.b----";
   1.700  (*stopped du to TODO.txt WN111014.TODO calculate_Poly < calculate_Rational < calculate_RootRat
   1.701  see --- val rls = calculate_RootRat > calculate_Rational ---
   1.702  calculate_RootRat was a TODO with 2002, requires re-design.
   1.703 -see also --- (-8 - 2*x + x^^^2 = 0),  by rewriting --- below
   1.704 +see also --- (-8 - 2*x + x \<up> 2 = 0),  by rewriting --- below
   1.705  *)
   1.706 - val fmz = ["equality (-8 - 2*x + x^^^2 = 0)", (*Schalk 2, S.67 Nr.31.b*)
   1.707 + val fmz = ["equality (-8 - 2*x + x \<up> 2 = 0)", (*Schalk 2, S.67 Nr.31.b*)
   1.708   	    "solveFor x", "solutions L"];
   1.709   val (dI',pI',mI') =
   1.710       ("PolyEq",["degree_2", "expanded", "univariate", "equation"],
   1.711 @@ -853,27 +853,27 @@
   1.712  val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
   1.713  (*Apply_Method ("PolyEq", "complete_square")*)
   1.714  val (p,_,f,nxt,_,pt) = me nxt p [] pt;
   1.715 -(*"-8 - 2 * x + x ^^^ 2 = 0", nxt = Rewrite_Set_Inst ... "complete_square*)
   1.716 +(*"-8 - 2 * x + x \<up> 2 = 0", nxt = Rewrite_Set_Inst ... "complete_square*)
   1.717  val (p,_,f,nxt,_,pt) = me nxt p [] pt;
   1.718 -(*"-8 + (2 / 2 - x) ^^^ 2 = (2 / 2) ^^^ 2", nxt = Rewrite("square_explicit1"*)
   1.719 +(*"-8 + (2 / 2 - x) \<up> 2 = (2 / 2) \<up> 2", nxt = Rewrite("square_explicit1"*)
   1.720  val (p,_,f,nxt,_,pt) = me nxt p [] pt;
   1.721 -(*"(2 / 2 - x) ^^^ 2 = (2 / 2) ^^^ 2 - -8" nxt = Rewrite("root_plus_minus*)
   1.722 +(*"(2 / 2 - x) \<up> 2 = (2 / 2) \<up> 2 - -8" nxt = Rewrite("root_plus_minus*)
   1.723  val (p,_,f,nxt,_,pt) = me nxt p [] pt;
   1.724 -(*"2 / 2 - x = sqrt ((2 / 2) ^^^ 2 - -8) |
   1.725 -   2 / 2 - x = - sqrt ((2 / 2) ^^^ 2 - -8)" nxt = Rewr_Inst("bdv_explicit2"*)
   1.726 +(*"2 / 2 - x = sqrt ((2 / 2) \<up> 2 - -8) |
   1.727 +   2 / 2 - x = - sqrt ((2 / 2) \<up> 2 - -8)" nxt = Rewr_Inst("bdv_explicit2"*)
   1.728  val (p,_,f,nxt,_,pt) = me nxt p [] pt;
   1.729 -(*"2 / 2 - x = sqrt ((2 / 2) ^^^ 2 - -8) |
   1.730 -   -1*x = - (2 / 2) + - sqrt ((2 / 2) ^^^ 2 - -8)"nxt = R_Inst("bdv_explt2"*)
   1.731 +(*"2 / 2 - x = sqrt ((2 / 2) \<up> 2 - -8) |
   1.732 +   -1*x = - (2 / 2) + - sqrt ((2 / 2) \<up> 2 - -8)"nxt = R_Inst("bdv_explt2"*)
   1.733  val (p,_,f,nxt,_,pt) = me nxt p [] pt;
   1.734 -(*"-1 * x = - (2 / 2) + sqrt ((2 / 2) ^^^ 2 - -8) |
   1.735 -   -1 * x = (- (2 / 2) + - sqrt ((2 / 2) ^^^ 2 - -8))"nxt = bdv_explicit3*)
   1.736 +(*"-1 * x = - (2 / 2) + sqrt ((2 / 2) \<up> 2 - -8) |
   1.737 +   -1 * x = (- (2 / 2) + - sqrt ((2 / 2) \<up> 2 - -8))"nxt = bdv_explicit3*)
   1.738  val (p,_,f,nxt,_,pt) = me nxt p [] pt;
   1.739 -(*"-1 * x = - (2 / 2) + sqrt ((2 / 2) ^^^ 2 - -8) |
   1.740 -  x = -1 * (- (2 / 2) + - sqrt ((2 / 2) ^^^ 2 - -8))" nxt = bdv_explicit3*)
   1.741 +(*"-1 * x = - (2 / 2) + sqrt ((2 / 2) \<up> 2 - -8) |
   1.742 +  x = -1 * (- (2 / 2) + - sqrt ((2 / 2) \<up> 2 - -8))" nxt = bdv_explicit3*)
   1.743  val (p,_,f,nxt,_,pt) = me nxt p [] pt;
   1.744 -(*"x = -1 * (- (2 / 2) + sqrt ((2 / 2) ^^^ 2 - -8)) |
   1.745 -   x = -1 * (- (2 / 2) + - sqrt ((2 / 2) ^^^ 2 - -8))"nxt = calculate_Rational
   1.746 -   NOT IMPLEMENTED SINCE 2002 ------------------------------^^^^^^^^^^^^^^^^^^*)
   1.747 +(*"x = -1 * (- (2 / 2) + sqrt ((2 / 2) \<up> 2 - -8)) |
   1.748 +   x = -1 * (- (2 / 2) + - sqrt ((2 / 2) \<up> 2 - -8))"nxt = calculate_Rational
   1.749 +   NOT IMPLEMENTED SINCE 2002 ------------------------------ \<up> \<up> \<up> \<up> \<up>  \<up> *)
   1.750  val (p,_,f,nxt,_,pt) = me nxt p [] pt;
   1.751  (*"x = -2 | x = 4" nxt = Or_to_List*)
   1.752  val (p,_,f,nxt,_,pt) = me nxt p [] pt;
   1.753 @@ -884,70 +884,70 @@
   1.754  	 | _ => error "polyeq.sml: diff.behav. in [x = -2, x = 4]";
   1.755  *)
   1.756  if f2str f =
   1.757 -"[x = -1 * -1 + -1 * sqrt (2 ^^^ 2 / 2 ^^^ 2 - -8),\n x = -1 * -1 + -1 * (-1 * sqrt (2 ^^^ 2 / 2 ^^^ 2 - -8))]"
   1.758 -(*"[x = -1 * -1 + -1 * sqrt (1 ^^^ 2 - -8),\n x = -1 * -1 + -1 * (-1 * sqrt (1 ^^^ 2 - -8))]"*)
   1.759 +"[x = -1 * -1 + -1 * sqrt (2 \<up> 2 / 2 \<up> 2 - -8),\n x = -1 * -1 + -1 * (-1 * sqrt (2 \<up> 2 / 2 \<up> 2 - -8))]"
   1.760 +(*"[x = -1 * -1 + -1 * sqrt (1 \<up> 2 - -8),\n x = -1 * -1 + -1 * (-1 * sqrt (1 \<up> 2 - -8))]"*)
   1.761  then () else error "polyeq.sml corrected?behav. in [x = -2, x = 4]";
   1.762  
   1.763  
   1.764 -"----------- (-8 - 2*x + x^^^2 = 0),  by rewriting ---------------";
   1.765 -"----------- (-8 - 2*x + x^^^2 = 0),  by rewriting ---------------";
   1.766 -"----------- (-8 - 2*x + x^^^2 = 0),  by rewriting ---------------";
   1.767 +"----------- (-8 - 2*x + x \<up> 2 = 0),  by rewriting ---------------";
   1.768 +"----------- (-8 - 2*x + x \<up> 2 = 0),  by rewriting ---------------";
   1.769 +"----------- (-8 - 2*x + x \<up> 2 = 0),  by rewriting ---------------";
   1.770  (*stopped du to TODO.txt WN111014.TODO calculate_Poly < calculate_Rational < calculate_RootRat
   1.771  see --- val rls = calculate_RootRat > calculate_Rational ---*)
   1.772  val thy = @{theory PolyEq};
   1.773  val ctxt = Proof_Context.init_global thy;
   1.774  val inst = [((the o (parseNEW  ctxt)) "bdv::real", (the o (parseNEW  ctxt)) "x::real")];
   1.775 -val t = (the o (parseNEW  ctxt)) "-8 - 2*x + x^^^2 = (0::real)";
   1.776 +val t = (the o (parseNEW  ctxt)) "-8 - 2*x + x \<up> 2 = (0::real)";
   1.777  
   1.778  val rls = complete_square;
   1.779  val SOME (t,asm) = rewrite_set_inst_ thy true inst rls t;
   1.780 -UnparseC.term t = "-8 + (2 / 2 - x) ^^^ 2 = (2 / 2) ^^^ 2";
   1.781 +UnparseC.term t = "-8 + (2 / 2 - x) \<up> 2 = (2 / 2) \<up> 2";
   1.782  
   1.783  val thm = ThmC.numerals_to_Free @{thm square_explicit1};
   1.784  val SOME (t,asm) = rewrite_ thy dummy_ord Rule_Set.Empty true thm t;
   1.785 -UnparseC.term t = "(2 / 2 - x) ^^^ 2 = (2 / 2) ^^^ 2 - -8";
   1.786 +UnparseC.term t = "(2 / 2 - x) \<up> 2 = (2 / 2) \<up> 2 - -8";
   1.787  
   1.788  val thm = ThmC.numerals_to_Free @{thm root_plus_minus};
   1.789  val SOME (t,asm) = rewrite_ thy dummy_ord PolyEq_erls true thm t;
   1.790 -UnparseC.term t = "2 / 2 - x = sqrt ((2 / 2) ^^^ 2 - -8) |"^
   1.791 -           "\n2 / 2 - x = -1 * sqrt ((2 / 2) ^^^ 2 - -8)";
   1.792 +UnparseC.term t = "2 / 2 - x = sqrt ((2 / 2) \<up> 2 - -8) |"^
   1.793 +           "\n2 / 2 - x = -1 * sqrt ((2 / 2) \<up> 2 - -8)";
   1.794  
   1.795  (*the thm bdv_explicit2* here required to be constrained to ::real*)
   1.796  val thm = ThmC.numerals_to_Free @{thm bdv_explicit2};
   1.797  val SOME (t,asm) = rewrite_inst_ thy dummy_ord Rule_Set.Empty true inst thm t;
   1.798 -UnparseC.term t = "2 / 2 - x = sqrt ((2 / 2) ^^^ 2 - -8) |"^
   1.799 -              "\n-1 * x = - (2 / 2) + -1 * sqrt ((2 / 2) ^^^ 2 - -8)";
   1.800 +UnparseC.term t = "2 / 2 - x = sqrt ((2 / 2) \<up> 2 - -8) |"^
   1.801 +              "\n-1 * x = - (2 / 2) + -1 * sqrt ((2 / 2) \<up> 2 - -8)";
   1.802  
   1.803  val thm = ThmC.numerals_to_Free @{thm bdv_explicit3};
   1.804  val SOME (t,asm) = rewrite_inst_ thy dummy_ord Rule_Set.Empty true inst thm t;
   1.805 -UnparseC.term t = "2 / 2 - x = sqrt ((2 / 2) ^^^ 2 - -8) |"^
   1.806 -                   "\nx = -1 * (- (2 / 2) + -1 * sqrt ((2 / 2) ^^^ 2 - -8))";
   1.807 +UnparseC.term t = "2 / 2 - x = sqrt ((2 / 2) \<up> 2 - -8) |"^
   1.808 +                   "\nx = -1 * (- (2 / 2) + -1 * sqrt ((2 / 2) \<up> 2 - -8))";
   1.809  
   1.810  val thm = ThmC.numerals_to_Free @{thm bdv_explicit2};
   1.811  val SOME (t,asm) = rewrite_inst_ thy dummy_ord Rule_Set.Empty true inst thm t;
   1.812 -UnparseC.term t = "-1 * x = - (2 / 2) + sqrt ((2 / 2) ^^^ 2 - -8) |"^
   1.813 -                "\nx = -1 * (- (2 / 2) + -1 * sqrt ((2 / 2) ^^^ 2 - -8))";
   1.814 +UnparseC.term t = "-1 * x = - (2 / 2) + sqrt ((2 / 2) \<up> 2 - -8) |"^
   1.815 +                "\nx = -1 * (- (2 / 2) + -1 * sqrt ((2 / 2) \<up> 2 - -8))";
   1.816  
   1.817  val rls = calculate_RootRat;
   1.818  val SOME (t,asm) = rewrite_set_ thy true rls t;
   1.819  if UnparseC.term t =
   1.820 -  "-1 * x = -1 + sqrt (2 ^^^ 2 / 2 ^^^ 2 - -8) \<or>\nx = -1 * -1 + -1 * (-1 * sqrt (2 ^^^ 2 / 2 ^^^ 2 - -8))"
   1.821 -(*"-1 * x = -1 + sqrt (2 ^^^ 2 / 2 ^^^ 2 - -8) |\nx = -1 * -1 + -1 * (-1 * sqrt (2 ^^^ 2 / 2 ^^^ 2 - -8))"..isabisac15*)
   1.822 -then () else error "(-8 - 2*x + x^^^2 = 0),  by rewriting -- ERROR INDICATES IMPROVEMENT";
   1.823 +  "-1 * x = -1 + sqrt (2 \<up> 2 / 2 \<up> 2 - -8) \<or>\nx = -1 * -1 + -1 * (-1 * sqrt (2 \<up> 2 / 2 \<up> 2 - -8))"
   1.824 +(*"-1 * x = -1 + sqrt (2 \<up> 2 / 2 \<up> 2 - -8) |\nx = -1 * -1 + -1 * (-1 * sqrt (2 \<up> 2 / 2 \<up> 2 - -8))"..isabisac15*)
   1.825 +then () else error "(-8 - 2*x + x \<up> 2 = 0),  by rewriting -- ERROR INDICATES IMPROVEMENT";
   1.826  (*SHOULD BE: UnparseC.term = "x = -2 | x = 4;*)
   1.827  
   1.828  
   1.829 -"-------------------- (3 - 10*x + 3*x^^^2 = 0), ----------------------";
   1.830 -"-------------------- (3 - 10*x + 3*x^^^2 = 0), ----------------------";
   1.831 -"-------------------- (3 - 10*x + 3*x^^^2 = 0), ----------------------";
   1.832 +"-------------------- (3 - 10*x + 3*x \<up> 2 = 0), ----------------------";
   1.833 +"-------------------- (3 - 10*x + 3*x \<up> 2 = 0), ----------------------";
   1.834 +"-------------------- (3 - 10*x + 3*x \<up> 2 = 0), ----------------------";
   1.835  "---- test the erls ----";
   1.836 - val t1 = (Thm.term_of o the o (TermC.parse thy)) "0 <= (10/3/2)^^^2 - 1";
   1.837 + val t1 = (Thm.term_of o the o (TermC.parse thy)) "0 <= (10/3/2) \<up> 2 - 1";
   1.838   val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_erls t1;
   1.839   val t' = UnparseC.term t;
   1.840   (*if t'= "HOL.True" then ()
   1.841   else error "polyeq.sml: diff.behav. in 'rewrite_set_.. PolyEq_erls";*)
   1.842  (* *)
   1.843 - val fmz = ["equality (3 - 10*x + 3*x^^^2 = 0)",
   1.844 + val fmz = ["equality (3 - 10*x + 3*x \<up> 2 = 0)",
   1.845   	    "solveFor x", "solutions L"];
   1.846   val (dI',pI',mI') =
   1.847       ("PolyEq",["degree_2", "expanded", "univariate", "equation"],
   1.848 @@ -963,10 +963,10 @@
   1.849   (*Apply_Method ("PolyEq", "complete_square")*)
   1.850   val (p,_,f,nxt,_,pt) = me nxt p [] pt; f2str f;
   1.851  
   1.852 -"----------- (-16 + 4*x + 2*x^^^2 = 0), --------------------------";
   1.853 -"----------- (-16 + 4*x + 2*x^^^2 = 0), --------------------------";
   1.854 -"----------- (-16 + 4*x + 2*x^^^2 = 0), --------------------------";
   1.855 - val fmz = ["equality (-16 + 4*x + 2*x^^^2 = 0)",
   1.856 +"----------- (-16 + 4*x + 2*x \<up> 2 = 0), --------------------------";
   1.857 +"----------- (-16 + 4*x + 2*x \<up> 2 = 0), --------------------------";
   1.858 +"----------- (-16 + 4*x + 2*x \<up> 2 = 0), --------------------------";
   1.859 + val fmz = ["equality (-16 + 4*x + 2*x \<up> 2 = 0)",
   1.860   	    "solveFor x", "solutions L"];
   1.861   val (dI',pI',mI') =
   1.862       ("PolyEq",["degree_2", "expanded", "univariate", "equation"],