test/Tools/isac/Knowledge/polyeq.sml
branchisac-update-Isa09-2
changeset 38031 460c24a6a6ba
parent 37991 028442673981
child 41928 20138d6136cd
equal deleted inserted replaced
38030:95d956108461 38031:460c24a6a6ba
    39  trace_rewrite:=false;
    39  trace_rewrite:=false;
    40 *)
    40 *)
    41  val t1 = (term_of o the o (parse thy)) "lhs (-8 - 2*x + x^^^2 = 0)";
    41  val t1 = (term_of o the o (parse thy)) "lhs (-8 - 2*x + x^^^2 = 0)";
    42  val SOME (t,_) = rewrite_set_ PolyEq.thy false PolyEq_prls t1;
    42  val SOME (t,_) = rewrite_set_ PolyEq.thy false PolyEq_prls t1;
    43  if ((term2str t) = "-8 - 2 * x + x ^^^ 2") then ()
    43  if ((term2str t) = "-8 - 2 * x + x ^^^ 2") then ()
    44  else  raise error "polyeq.sml: diff.behav. in lhs";
    44  else  error "polyeq.sml: diff.behav. in lhs";
    45 
    45 
    46 
    46 
    47  val t2 = (term_of o the o (parse thy)) "(-8 - 2*x + x^^^2) is_expanded_in x";
    47  val t2 = (term_of o the o (parse thy)) "(-8 - 2*x + x^^^2) is_expanded_in x";
    48  val SOME (t,_) = rewrite_set_ PolyEq.thy false PolyEq_prls t2;
    48  val SOME (t,_) = rewrite_set_ PolyEq.thy false PolyEq_prls t2;
    49  if (term2str t) = "True" then ()
    49  if (term2str t) = "True" then ()
    50  else  raise error "polyeq.sml: diff.behav. 1 in is_expended_in";
    50  else  error "polyeq.sml: diff.behav. 1 in is_expended_in";
    51 
    51 
    52  val t0 = (term_of o the o (parse thy)) "(sqrt(x)) is_poly_in x";
    52  val t0 = (term_of o the o (parse thy)) "(sqrt(x)) is_poly_in x";
    53  val SOME (t,_) = rewrite_set_ PolyEq.thy false PolyEq_prls t0;
    53  val SOME (t,_) = rewrite_set_ PolyEq.thy false PolyEq_prls t0;
    54  if (term2str t) = "False" then ()
    54  if (term2str t) = "False" then ()
    55  else  raise error "polyeq.sml: diff.behav. 2 in is_poly_in";
    55  else  error "polyeq.sml: diff.behav. 2 in is_poly_in";
    56 
    56 
    57 
    57 
    58  val t3 = (term_of o the o (parse thy)) "(-8 + (-1)*2*x + x^^^2) is_poly_in x";
    58  val t3 = (term_of o the o (parse thy)) "(-8 + (-1)*2*x + x^^^2) is_poly_in x";
    59  val SOME (t,_) = rewrite_set_ PolyEq.thy false PolyEq_prls t3;
    59  val SOME (t,_) = rewrite_set_ PolyEq.thy false PolyEq_prls t3;
    60  if (term2str t) = "True" then ()
    60  if (term2str t) = "True" then ()
    61  else  raise error "polyeq.sml: diff.behav. 3 in is_poly_in";
    61  else  error "polyeq.sml: diff.behav. 3 in is_poly_in";
    62 
    62 
    63 
    63 
    64  val t4 = (term_of o the o (parse thy)) "(lhs (-8 + (-1)*2*x + x^^^2 = 0)) is_expanded_in x";
    64  val t4 = (term_of o the o (parse thy)) "(lhs (-8 + (-1)*2*x + x^^^2 = 0)) is_expanded_in x";
    65  val SOME (t,_) = rewrite_set_ PolyEq.thy false PolyEq_prls t4;
    65  val SOME (t,_) = rewrite_set_ PolyEq.thy false PolyEq_prls t4;
    66  if (term2str t) = "True" then ()
    66  if (term2str t) = "True" then ()
    67  else  raise error "polyeq.sml: diff.behav. 4 in is_expended_in";
    67  else  error "polyeq.sml: diff.behav. 4 in is_expended_in";
    68 
    68 
    69 
    69 
    70  val t6 = (term_of o the o (parse thy)) "(lhs (-8 - 2*x + x^^^2 = 0)) is_expanded_in x";
    70  val t6 = (term_of o the o (parse thy)) "(lhs (-8 - 2*x + x^^^2 = 0)) is_expanded_in x";
    71  val SOME (t,_) = rewrite_set_ PolyEq.thy false PolyEq_prls t6;
    71  val SOME (t,_) = rewrite_set_ PolyEq.thy false PolyEq_prls t6;
    72  if (term2str t) = "True" then ()
    72  if (term2str t) = "True" then ()
    73  else  raise error "polyeq.sml: diff.behav. 5 in is_expended_in";
    73  else  error "polyeq.sml: diff.behav. 5 in is_expended_in";
    74  
    74  
    75  val t3 = (term_of o the o (parse thy))"((-8 - 2*x + x^^^2) has_degree_in x) = 2";
    75  val t3 = (term_of o the o (parse thy))"((-8 - 2*x + x^^^2) has_degree_in x) = 2";
    76  val SOME (t,_) = rewrite_set_ PolyEq.thy false PolyEq_prls t3;
    76  val SOME (t,_) = rewrite_set_ PolyEq.thy false PolyEq_prls t3;
    77  if (term2str t) = "True" then ()
    77  if (term2str t) = "True" then ()
    78  else  raise error "polyeq.sml: diff.behav. in has_degree_in_in";
    78  else  error "polyeq.sml: diff.behav. in has_degree_in_in";
    79 
    79 
    80 
    80 
    81  val t3 = (term_of o the o (parse thy)) "((sqrt(x)) has_degree_in x) = 2";
    81  val t3 = (term_of o the o (parse thy)) "((sqrt(x)) has_degree_in x) = 2";
    82  val SOME (t,_) = rewrite_set_ PolyEq.thy false PolyEq_prls t3;
    82  val SOME (t,_) = rewrite_set_ PolyEq.thy false PolyEq_prls t3;
    83  if (term2str t) = "False" then ()
    83  if (term2str t) = "False" then ()
    84  else  raise error "polyeq.sml: diff.behav. 6 in has_degree_in_in";
    84  else  error "polyeq.sml: diff.behav. 6 in has_degree_in_in";
    85 
    85 
    86  val t4 = (term_of o the o (parse thy)) 
    86  val t4 = (term_of o the o (parse thy)) 
    87 	      "((-8 - 2*x + x^^^2) has_degree_in x) = 1";
    87 	      "((-8 - 2*x + x^^^2) has_degree_in x) = 1";
    88  val SOME (t,_) = rewrite_set_ PolyEq.thy false PolyEq_prls t4;
    88  val SOME (t,_) = rewrite_set_ PolyEq.thy false PolyEq_prls t4;
    89  if (term2str t) = "False" then ()
    89  if (term2str t) = "False" then ()
    90  else  raise error "polyeq.sml: diff.behav. 7 in has_degree_in_in";
    90  else  error "polyeq.sml: diff.behav. 7 in has_degree_in_in";
    91 
    91 
    92 
    92 
    93  val t5 = (term_of o the o (parse thy)) 
    93  val t5 = (term_of o the o (parse thy)) 
    94 	      "((-8 - 2*x + x^^^2) has_degree_in x) = 2";
    94 	      "((-8 - 2*x + x^^^2) has_degree_in x) = 2";
    95  val SOME (t,_) = rewrite_set_ PolyEq.thy false PolyEq_prls t5;
    95  val SOME (t,_) = rewrite_set_ PolyEq.thy false PolyEq_prls t5;
    96  if (term2str t) = "True" then ()
    96  if (term2str t) = "True" then ()
    97  else  raise error "polyeq.sml: diff.behav. 8 in has_degree_in_in";
    97  else  error "polyeq.sml: diff.behav. 8 in has_degree_in_in";
    98 
    98 
    99 
    99 
   100 "----------- test matching problems --------------------------0---";
   100 "----------- test matching problems --------------------------0---";
   101 "----------- test matching problems --------------------------0---";
   101 "----------- test matching problems --------------------------0---";
   102 "----------- test matching problems --------------------------0---";
   102 "----------- test matching problems --------------------------0---";
   136 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   136 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   137 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   137 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   138 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   138 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   139 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   139 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   140 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[]")) => ()
   140 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[]")) => ()
   141 	 | _ => raise error "polyeq.sml: diff.behav. in 1 = 0 -> []";
   141 	 | _ => error "polyeq.sml: diff.behav. in 1 = 0 -> []";
   142 
   142 
   143 "----- d0_true ------";
   143 "----- d0_true ------";
   144 (*EP-7*)
   144 (*EP-7*)
   145 val fmz = ["equality ( 0 = 0)", "solveFor x","solutions L"];
   145 val fmz = ["equality ( 0 = 0)", "solveFor x","solutions L"];
   146 val (dI',pI',mI') = ("PolyEq",["degree_0","polynomial","univariate","equation"],
   146 val (dI',pI',mI') = ("PolyEq",["degree_0","polynomial","univariate","equation"],
   154 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   154 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   155 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   155 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   156 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   156 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   157 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   157 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   158 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"UniversalList")) => ()
   158 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"UniversalList")) => ()
   159 	 | _ => raise error "polyeq.sml: diff.behav. in 0 = 0 -> UniversalList";
   159 	 | _ => error "polyeq.sml: diff.behav. in 0 = 0 -> UniversalList";
   160 
   160 
   161 "-------------------- test thm's degree_2 ------------------------------------------";
   161 "-------------------- test thm's degree_2 ------------------------------------------";
   162 "-------------------- test thm's degree_2 ------------------------------------------";
   162 "-------------------- test thm's degree_2 ------------------------------------------";
   163 
   163 
   164 "-------------------- test thm's d2_pq_formulsxx[_neg]-----";
   164 "-------------------- test thm's d2_pq_formulsxx[_neg]-----";
   187 val (p,_,f,nxt,_,pt) = me nxt p c pt;
   187 val (p,_,f,nxt,_,pt) = me nxt p c pt;
   188 (*### applicable_in Check_elementwise: --> ([x = 2, x = -1], [])
   188 (*### applicable_in Check_elementwise: --> ([x = 2, x = -1], [])
   189   ([5],Res)   "[x = 2, x = -1]"   Check_Postcond*)
   189   ([5],Res)   "[x = 2, x = -1]"   Check_Postcond*)
   190 val (p,_,f,nxt,_,pt) = me nxt p c pt;
   190 val (p,_,f,nxt,_,pt) = me nxt p c pt;
   191 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2, x = -1]")) => ()
   191 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2, x = -1]")) => ()
   192 	 | _ => raise error "polyeq.sml: diff.behav. in -2 + (-1)*x + x^2 = 0 -> [x = 2, x = -1]";
   192 	 | _ => error "polyeq.sml: diff.behav. in -2 + (-1)*x + x^2 = 0 -> [x = 2, x = -1]";
   193 
   193 
   194 "----- d2_pqformula1_neg ------";
   194 "----- d2_pqformula1_neg ------";
   195 (*EP-8*)
   195 (*EP-8*)
   196 val fmz = ["equality ( 2 +(-1)*x + x^^^2 = 0)", "solveFor x","solutions L"];
   196 val fmz = ["equality ( 2 +(-1)*x + x^^^2 = 0)", "solveFor x","solutions L"];
   197 val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"], ["PolyEq","solve_d2_polyeq_pq_equation"]);
   197 val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"], ["PolyEq","solve_d2_polyeq_pq_equation"]);
   211   ([2],Res)  []      Check_elementwise "Assumptions"*)
   211   ([2],Res)  []      Check_elementwise "Assumptions"*)
   212 val (p,_,f,nxt,_,pt) = me nxt p c pt;
   212 val (p,_,f,nxt,_,pt) = me nxt p c pt;
   213 val (p,_,f,nxt,_,pt) = me nxt p c pt;
   213 val (p,_,f,nxt,_,pt) = me nxt p c pt;
   214 val asm = get_assumptions_ pt p;
   214 val asm = get_assumptions_ pt p;
   215 if f = Form' (FormKF (~1,EdUndef,0,Nundef,"[]")) andalso asm = [] then ()
   215 if f = Form' (FormKF (~1,EdUndef,0,Nundef,"[]")) andalso asm = [] then ()
   216 else raise error "polyeq.sml: diff.behav. in 2 +(-1)*x + x^^^2 = 0";
   216 else error "polyeq.sml: diff.behav. in 2 +(-1)*x + x^^^2 = 0";
   217 
   217 
   218 "----- d2_pqformula2 ------";
   218 "----- d2_pqformula2 ------";
   219 val fmz = ["equality (-2 +(-1)*x + 1*x^^^2 = 0)", "solveFor x","solutions L"];
   219 val fmz = ["equality (-2 +(-1)*x + 1*x^^^2 = 0)", "solveFor x","solutions L"];
   220 val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
   220 val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
   221                      ["PolyEq","solve_d2_polyeq_pq_equation"]);
   221                      ["PolyEq","solve_d2_polyeq_pq_equation"]);
   230 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   230 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   231 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   231 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   232 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   232 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   233 val (p,_,f,nxt,_,pt) = me nxt p c pt;
   233 val (p,_,f,nxt,_,pt) = me nxt p c pt;
   234 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2, x = -1]")) => ()
   234 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2, x = -1]")) => ()
   235 	 | _ => raise error "polyeq.sml: diff.behav. in -2 + (-1)*x + x^2 = 0 -> [x = 2, x = -1]";
   235 	 | _ => error "polyeq.sml: diff.behav. in -2 + (-1)*x + x^2 = 0 -> [x = 2, x = -1]";
   236 
   236 
   237 
   237 
   238 "----- d2_pqformula2_neg ------";
   238 "----- d2_pqformula2_neg ------";
   239 val fmz = ["equality ( 2 +(-1)*x + 1*x^^^2 = 0)", "solveFor x","solutions L"];
   239 val fmz = ["equality ( 2 +(-1)*x + 1*x^^^2 = 0)", "solveFor x","solutions L"];
   240 val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
   240 val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
   271 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   271 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   272 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   272 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   273 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   273 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   274 val (p,_,f,nxt,_,pt) = me nxt p c pt; 
   274 val (p,_,f,nxt,_,pt) = me nxt p c pt; 
   275 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 1, x = -2]")) => ()
   275 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 1, x = -2]")) => ()
   276 	 | _ => raise error "polyeq.sml: diff.behav. in  -2 + x + x^2 = 0-> [x = 1, x = -2]";
   276 	 | _ => error "polyeq.sml: diff.behav. in  -2 + x + x^2 = 0-> [x = 1, x = -2]";
   277 
   277 
   278 "----- d2_pqformula3_neg ------";
   278 "----- d2_pqformula3_neg ------";
   279 val fmz = ["equality ( 2 + x + x^^^2 = 0)", "solveFor x","solutions L"];
   279 val fmz = ["equality ( 2 + x + x^^^2 = 0)", "solveFor x","solutions L"];
   280 val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
   280 val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
   281                      ["PolyEq","solve_d2_polyeq_pq_equation"]);
   281                      ["PolyEq","solve_d2_polyeq_pq_equation"]);
   310 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   310 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   311 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   311 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   312 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   312 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   313 val (p,_,f,nxt,_,pt) = me nxt p c pt;
   313 val (p,_,f,nxt,_,pt) = me nxt p c pt;
   314 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 1, x = -2]")) => ()
   314 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 1, x = -2]")) => ()
   315 	 | _ => raise error "polyeq.sml: diff.behav. in  -2 + x + 1*x^^^2 = 0 -> [x = 1, x = -2]";
   315 	 | _ => error "polyeq.sml: diff.behav. in  -2 + x + 1*x^^^2 = 0 -> [x = 1, x = -2]";
   316 
   316 
   317 "----- d2_pqformula4_neg ------";
   317 "----- d2_pqformula4_neg ------";
   318 val fmz = ["equality ( 2 + x + 1*x^^^2 = 0)", "solveFor x","solutions L"];
   318 val fmz = ["equality ( 2 + x + 1*x^^^2 = 0)", "solveFor x","solutions L"];
   319 val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
   319 val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
   320                      ["PolyEq","solve_d2_polyeq_pq_equation"]);
   320                      ["PolyEq","solve_d2_polyeq_pq_equation"]);
   347 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   347 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   348 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   348 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   349 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   349 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   350 val (p,_,f,nxt,_,pt) = me nxt p c pt;
   350 val (p,_,f,nxt,_,pt) = me nxt p c pt;
   351 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 0, x = -1]")) => ()
   351 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 0, x = -1]")) => ()
   352 	 | _ => raise error "polyeq.sml: diff.behav. in  1*x +   x^2 = 0 -> [x = 0, x = -1]";
   352 	 | _ => error "polyeq.sml: diff.behav. in  1*x +   x^2 = 0 -> [x = 0, x = -1]";
   353 
   353 
   354 "----- d2_pqformula6 ------";
   354 "----- d2_pqformula6 ------";
   355 val fmz = ["equality (1*x + 1*x^^^2 = 0)", "solveFor x","solutions L"];
   355 val fmz = ["equality (1*x + 1*x^^^2 = 0)", "solveFor x","solutions L"];
   356 val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
   356 val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
   357                      ["PolyEq","solve_d2_polyeq_pq_equation"]);
   357                      ["PolyEq","solve_d2_polyeq_pq_equation"]);
   366 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   366 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   367 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   367 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   368 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   368 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   369 val (p,_,f,nxt,_,pt) = me nxt p c pt; 
   369 val (p,_,f,nxt,_,pt) = me nxt p c pt; 
   370 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 0, x = -1]")) => ()
   370 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 0, x = -1]")) => ()
   371 	 | _ => raise error "polyeq.sml: diff.behav. in  1*x + 1*x^2 = 0 -> [x = 0, x = -1]";
   371 	 | _ => error "polyeq.sml: diff.behav. in  1*x + 1*x^2 = 0 -> [x = 0, x = -1]";
   372 
   372 
   373 "----- d2_pqformula7 ------";
   373 "----- d2_pqformula7 ------";
   374 (*EP-10*)
   374 (*EP-10*)
   375 val fmz = ["equality (  x +   x^^^2 = 0)", "solveFor x","solutions L"];
   375 val fmz = ["equality (  x +   x^^^2 = 0)", "solveFor x","solutions L"];
   376 val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
   376 val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
   386 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   386 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   387 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   387 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   388 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   388 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   389 val (p,_,f,nxt,_,pt) = me nxt p c pt; 
   389 val (p,_,f,nxt,_,pt) = me nxt p c pt; 
   390 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 0, x = -1]")) => ()
   390 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 0, x = -1]")) => ()
   391 	 | _ => raise error "polyeq.sml: diff.behav. in  x + x^2 = 0 -> [x = 0, x = -1]";
   391 	 | _ => error "polyeq.sml: diff.behav. in  x + x^2 = 0 -> [x = 0, x = -1]";
   392 
   392 
   393 "----- d2_pqformula8 ------";
   393 "----- d2_pqformula8 ------";
   394 val fmz = ["equality (  x + 1*x^^^2 = 0)", "solveFor x","solutions L"];
   394 val fmz = ["equality (  x + 1*x^^^2 = 0)", "solveFor x","solutions L"];
   395 val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
   395 val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
   396                      ["PolyEq","solve_d2_polyeq_pq_equation"]);
   396                      ["PolyEq","solve_d2_polyeq_pq_equation"]);
   406 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   406 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   407 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   407 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   408 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   408 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   409 val (p,_,f,nxt,_,pt) = me nxt p c pt; 
   409 val (p,_,f,nxt,_,pt) = me nxt p c pt; 
   410 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 0, x = -1]")) => ()
   410 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 0, x = -1]")) => ()
   411 	 | _ => raise error "polyeq.sml: diff.behav. in  x + 1*x^2 = 0 -> [x = 0, x = -1]";
   411 	 | _ => error "polyeq.sml: diff.behav. in  x + 1*x^2 = 0 -> [x = 0, x = -1]";
   412 
   412 
   413 "----- d2_pqformula9 ------";
   413 "----- d2_pqformula9 ------";
   414 val fmz = ["equality (-4 + x^^^2 = 0)", "solveFor x","solutions L"];
   414 val fmz = ["equality (-4 + x^^^2 = 0)", "solveFor x","solutions L"];
   415 val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
   415 val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
   416                      ["PolyEq","solve_d2_polyeq_pq_equation"]);
   416                      ["PolyEq","solve_d2_polyeq_pq_equation"]);
   425 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   425 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   426 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   426 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   427 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   427 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   428 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   428 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   429 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2, x = -2]")) => ()
   429 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2, x = -2]")) => ()
   430 	 | _ => raise error "polyeq.sml: diff.behav. in -4 + x^2 = 0 -> [x = 2, x = -2]";
   430 	 | _ => error "polyeq.sml: diff.behav. in -4 + x^2 = 0 -> [x = 2, x = -2]";
   431 
   431 
   432 
   432 
   433 "----- d2_pqformula10_neg ------";
   433 "----- d2_pqformula10_neg ------";
   434 val fmz = ["equality (4 + x^^^2 = 0)", "solveFor x","solutions L"];
   434 val fmz = ["equality (4 + x^^^2 = 0)", "solveFor x","solutions L"];
   435 val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
   435 val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
   465 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   465 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   466 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   466 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   467 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   467 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   468 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   468 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   469 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2, x = -2]")) => ()
   469 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2, x = -2]")) => ()
   470 	 | _ => raise error "polyeq.sml: diff.behav. in -4 + 1*x^2 = 0 -> [x = 2, x = -2]";
   470 	 | _ => error "polyeq.sml: diff.behav. in -4 + 1*x^2 = 0 -> [x = 2, x = -2]";
   471 
   471 
   472 "----- d2_pqformula9_neg ------";
   472 "----- d2_pqformula9_neg ------";
   473 val fmz = ["equality (4 + 1*x^^^2 = 0)", "solveFor x","solutions L"];
   473 val fmz = ["equality (4 + 1*x^^^2 = 0)", "solveFor x","solutions L"];
   474 val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
   474 val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
   475                      ["PolyEq","solve_d2_polyeq_pq_equation"]);
   475                      ["PolyEq","solve_d2_polyeq_pq_equation"]);
   506 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   506 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   507 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   507 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   508 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   508 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   509 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   509 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   510 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 1, x = -1 / 2]")) => ()
   510 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 1, x = -1 / 2]")) => ()
   511 	 | _ => raise error "polyeq.sml: diff.behav. in -1 + (-1)*x + 2*x^2 = 0 -> [x = 1, x = -1/2]";
   511 	 | _ => error "polyeq.sml: diff.behav. in -1 + (-1)*x + 2*x^2 = 0 -> [x = 1, x = -1/2]";
   512 
   512 
   513 val fmz = ["equality ( 1 +(-1)*x + 2*x^^^2 = 0)", "solveFor x","solutions L"];
   513 val fmz = ["equality ( 1 +(-1)*x + 2*x^^^2 = 0)", "solveFor x","solutions L"];
   514 val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
   514 val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
   515                      ["PolyEq","solve_d2_polyeq_abc_equation"]);
   515                      ["PolyEq","solve_d2_polyeq_abc_equation"]);
   516 (*val p = e_pos'; val c = []; 
   516 (*val p = e_pos'; val c = []; 
   543 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   543 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   544 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   544 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   545 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   545 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   546 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   546 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   547 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 1 / 2, x = -1]")) => ()
   547 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 1 / 2, x = -1]")) => ()
   548 	 | _ => raise error "polyeq.sml: diff.behav. in -1 + x + 2*x^2 = 0 -> [x = 1/2, x = -1]";
   548 	 | _ => error "polyeq.sml: diff.behav. in -1 + x + 2*x^2 = 0 -> [x = 1/2, x = -1]";
   549 
   549 
   550 val fmz = ["equality ( 1 + x + 2*x^^^2 = 0)", "solveFor x","solutions L"];
   550 val fmz = ["equality ( 1 + x + 2*x^^^2 = 0)", "solveFor x","solutions L"];
   551 val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
   551 val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
   552                      ["PolyEq","solve_d2_polyeq_abc_equation"]);
   552                      ["PolyEq","solve_d2_polyeq_abc_equation"]);
   553 (*val p = e_pos'; val c = []; 
   553 (*val p = e_pos'; val c = []; 
   580 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   580 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   581 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   581 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   582 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   582 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   583 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   583 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   584 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 1, x = -2]")) => ()
   584 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 1, x = -2]")) => ()
   585 	 | _ => raise error "polyeq.sml: diff.behav. in -2 + 1*x + x^2 = 0 -> [x = 1, x = -2]";
   585 	 | _ => error "polyeq.sml: diff.behav. in -2 + 1*x + x^2 = 0 -> [x = 1, x = -2]";
   586 
   586 
   587 val fmz = ["equality ( 2 + 1*x + x^^^2 = 0)", "solveFor x","solutions L"];
   587 val fmz = ["equality ( 2 + 1*x + x^^^2 = 0)", "solveFor x","solutions L"];
   588 val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
   588 val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
   589                      ["PolyEq","solve_d2_polyeq_abc_equation"]);
   589                      ["PolyEq","solve_d2_polyeq_abc_equation"]);
   590 (*val p = e_pos'; val c = []; 
   590 (*val p = e_pos'; val c = []; 
   618 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   618 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   619 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   619 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   620 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   620 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   621 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   621 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   622 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 1, x = -2]")) => ()
   622 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 1, x = -2]")) => ()
   623 	 | _ => raise error "polyeq.sml: diff.behav. in -2 + x + x^2 = 0 -> [x = 1, x = -2]";
   623 	 | _ => error "polyeq.sml: diff.behav. in -2 + x + x^2 = 0 -> [x = 1, x = -2]";
   624 
   624 
   625 val fmz = ["equality ( 2 + x + x^^^2 = 0)", "solveFor x","solutions L"];
   625 val fmz = ["equality ( 2 + x + x^^^2 = 0)", "solveFor x","solutions L"];
   626 val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
   626 val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
   627                      ["PolyEq","solve_d2_polyeq_abc_equation"]);
   627                      ["PolyEq","solve_d2_polyeq_abc_equation"]);
   628 (*val p = e_pos'; val c = []; 
   628 (*val p = e_pos'; val c = []; 
   656 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   656 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   657 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   657 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   658 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   658 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   659 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   659 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   660 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2, x = -2]")) => ()
   660 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2, x = -2]")) => ()
   661 	 | _ => raise error "polyeq.sml: diff.behav. in -8 + 2*x^2 = 0 -> [x = 2, x = -2]";
   661 	 | _ => error "polyeq.sml: diff.behav. in -8 + 2*x^2 = 0 -> [x = 2, x = -2]";
   662 
   662 
   663 val fmz = ["equality ( 8+ 2*x^^^2 = 0)", "solveFor x","solutions L"];
   663 val fmz = ["equality ( 8+ 2*x^^^2 = 0)", "solveFor x","solutions L"];
   664 val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
   664 val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
   665                      ["PolyEq","solve_d2_polyeq_abc_equation"]);
   665                      ["PolyEq","solve_d2_polyeq_abc_equation"]);
   666 (*val p = e_pos'; val c = []; 
   666 (*val p = e_pos'; val c = []; 
   692 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   692 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   693 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   693 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   694 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   694 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   695 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   695 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   696 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2, x = -2]")) => ()
   696 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2, x = -2]")) => ()
   697 	 | _ => raise error "polyeq.sml: diff.behav. in -4 + x^2 = 0 -> [x = 2, x = -2]";
   697 	 | _ => error "polyeq.sml: diff.behav. in -4 + x^2 = 0 -> [x = 2, x = -2]";
   698 
   698 
   699 
   699 
   700 val fmz = ["equality ( 4+ x^^^2 = 0)", "solveFor x","solutions L"];
   700 val fmz = ["equality ( 4+ x^^^2 = 0)", "solveFor x","solutions L"];
   701 val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"], ["PolyEq","solve_d2_polyeq_abc_equation"]);
   701 val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"], ["PolyEq","solve_d2_polyeq_abc_equation"]);
   702 (*val p = e_pos'; val c = []; 
   702 (*val p = e_pos'; val c = []; 
   729 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   729 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   730 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   730 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   731 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   731 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   732 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   732 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   733 case f of Form' (FormKF (~1,EdUndef,_,Nundef,"[x = 0, x = -1]")) => ()
   733 case f of Form' (FormKF (~1,EdUndef,_,Nundef,"[x = 0, x = -1]")) => ()
   734 	 | _ => raise error "polyeq.sml: diff.behav. in x + x^2 = 0 -> [x = 0, x = -1]";
   734 	 | _ => error "polyeq.sml: diff.behav. in x + x^2 = 0 -> [x = 0, x = -1]";
   735 
   735 
   736 val fmz = ["equality (1*x + x^^^2 = 0)", "solveFor x","solutions L"];
   736 val fmz = ["equality (1*x + x^^^2 = 0)", "solveFor x","solutions L"];
   737 val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
   737 val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
   738                      ["PolyEq","solve_d2_polyeq_abc_equation"]);
   738                      ["PolyEq","solve_d2_polyeq_abc_equation"]);
   739 (*val p = e_pos'; val c = []; 
   739 (*val p = e_pos'; val c = []; 
   747 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   747 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   748 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   748 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   749 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   749 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   750 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   750 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   751 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 0, x = -1]")) => ()
   751 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 0, x = -1]")) => ()
   752 	 | _ => raise error "polyeq.sml: diff.behav. in x + x^2 = 0 -> [x = 0, x = -1]";
   752 	 | _ => error "polyeq.sml: diff.behav. in x + x^2 = 0 -> [x = 0, x = -1]";
   753 
   753 
   754 (*EP-16*)
   754 (*EP-16*)
   755 val fmz = ["equality (x + 2*x^^^2 = 0)", "solveFor x","solutions L"];
   755 val fmz = ["equality (x + 2*x^^^2 = 0)", "solveFor x","solutions L"];
   756 val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
   756 val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
   757                      ["PolyEq","solve_d2_polyeq_abc_equation"]);
   757                      ["PolyEq","solve_d2_polyeq_abc_equation"]);
   766 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   766 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   767 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   767 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   768 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   768 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   769 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   769 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   770 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 0, x = -1 / 2]")) => ()
   770 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 0, x = -1 / 2]")) => ()
   771 	 | _ => raise error "polyeq.sml: diff.behav. in x + x^2 = 0 -> [x = 0, x = -1 / 2]";
   771 	 | _ => error "polyeq.sml: diff.behav. in x + x^2 = 0 -> [x = 0, x = -1 / 2]";
   772 
   772 
   773 (*EP-//*)
   773 (*EP-//*)
   774 val fmz = ["equality (x + x^^^2 = 0)", "solveFor x","solutions L"];
   774 val fmz = ["equality (x + x^^^2 = 0)", "solveFor x","solutions L"];
   775 val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
   775 val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
   776                      ["PolyEq","solve_d2_polyeq_abc_equation"]);
   776                      ["PolyEq","solve_d2_polyeq_abc_equation"]);
   785 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   785 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   786 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   786 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   787 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   787 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   788 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   788 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   789 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 0, x = -1]")) => ()
   789 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 0, x = -1]")) => ()
   790 	 | _ => raise error "polyeq.sml: diff.behav. in x + x^2 = 0 -> [x = 0, x = -1]";
   790 	 | _ => error "polyeq.sml: diff.behav. in x + x^2 = 0 -> [x = 0, x = -1]";
   791 
   791 
   792 "----------- (-8 - 2*x + x^^^2 = 0),  (*Schalk 2, S.67 Nr.31.b----";
   792 "----------- (-8 - 2*x + x^^^2 = 0),  (*Schalk 2, S.67 Nr.31.b----";
   793 "----------- (-8 - 2*x + x^^^2 = 0),  (*Schalk 2, S.67 Nr.31.b----";
   793 "----------- (-8 - 2*x + x^^^2 = 0),  (*Schalk 2, S.67 Nr.31.b----";
   794 "----------- (-8 - 2*x + x^^^2 = 0),  (*Schalk 2, S.67 Nr.31.b----";
   794 "----------- (-8 - 2*x + x^^^2 = 0),  (*Schalk 2, S.67 Nr.31.b----";
   795  val fmz = ["equality (-8 - 2*x + x^^^2 = 0)", (*Schalk 2, S.67 Nr.31.b*)
   795  val fmz = ["equality (-8 - 2*x + x^^^2 = 0)", (*Schalk 2, S.67 Nr.31.b*)
   833  val (p,_,f,nxt,_,pt) = me nxt p c pt;
   833  val (p,_,f,nxt,_,pt) = me nxt p c pt;
   834  (*"[x = -2, x = 4]" nxt = Check_Postcond*)
   834  (*"[x = -2, x = 4]" nxt = Check_Postcond*)
   835  val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;
   835  val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;
   836 (* FIXXXME 
   836 (* FIXXXME 
   837  case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = -2, x = 4]")) => () TODO
   837  case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = -2, x = 4]")) => () TODO
   838 	 | _ => raise error "polyeq.sml: diff.behav. in [x = -2, x = 4]";
   838 	 | _ => error "polyeq.sml: diff.behav. in [x = -2, x = 4]";
   839 *)
   839 *)
   840 if f2str f = "[x = -1 * -1 + -1 * sqrt (1 ^^^ 2 - -8),\n x = -1 * -1 + -1 * (-1 * sqrt (1 ^^^ 2 - -8))]" then ()
   840 if f2str f = "[x = -1 * -1 + -1 * sqrt (1 ^^^ 2 - -8),\n x = -1 * -1 + -1 * (-1 * sqrt (1 ^^^ 2 - -8))]" then ()
   841 else raise error "polyeq.sml corrected?behav. in [x = -2, x = 4]";
   841 else error "polyeq.sml corrected?behav. in [x = -2, x = 4]";
   842 
   842 
   843 
   843 
   844 "-------------------- (3 - 10*x + 3*x^^^2 = 0), ----------------------";
   844 "-------------------- (3 - 10*x + 3*x^^^2 = 0), ----------------------";
   845 "-------------------- (3 - 10*x + 3*x^^^2 = 0), ----------------------";
   845 "-------------------- (3 - 10*x + 3*x^^^2 = 0), ----------------------";
   846 "-------------------- (3 - 10*x + 3*x^^^2 = 0), ----------------------";
   846 "-------------------- (3 - 10*x + 3*x^^^2 = 0), ----------------------";
   847 "---- test the erls ----";
   847 "---- test the erls ----";
   848  val t1 = (term_of o the o (parse thy)) "0 <= (10/3/2)^^^2 - 1";
   848  val t1 = (term_of o the o (parse thy)) "0 <= (10/3/2)^^^2 - 1";
   849  val SOME (t,_) = rewrite_set_ PolyEq.thy false PolyEq_erls t1;
   849  val SOME (t,_) = rewrite_set_ PolyEq.thy false PolyEq_erls t1;
   850  val t' = term2str t;
   850  val t' = term2str t;
   851  (*if t'= "True" then ()
   851  (*if t'= "True" then ()
   852  else raise error "polyeq.sml: diff.behav. in 'rewrite_set_.. PolyEq_erls";*)
   852  else error "polyeq.sml: diff.behav. in 'rewrite_set_.. PolyEq_erls";*)
   853 (* *)
   853 (* *)
   854  val fmz = ["equality (3 - 10*x + 3*x^^^2 = 0)",
   854  val fmz = ["equality (3 - 10*x + 3*x^^^2 = 0)",
   855  	    "solveFor x","solutions L"];
   855  	    "solveFor x","solutions L"];
   856  val (dI',pI',mI') =
   856  val (dI',pI',mI') =
   857      ("PolyEq",["degree_2","expanded","univariate","equation"],
   857      ("PolyEq",["degree_2","expanded","univariate","equation"],
   902  val (p,_,f,nxt,_,pt) = me nxt p c pt;
   902  val (p,_,f,nxt,_,pt) = me nxt p c pt;
   903  val (p,_,f,nxt,_,pt) = me nxt p c pt;
   903  val (p,_,f,nxt,_,pt) = me nxt p c pt;
   904  val (p,_,f,nxt,_,pt) = me nxt p c pt;
   904  val (p,_,f,nxt,_,pt) = me nxt p c pt;
   905 (* FIXXXXME n1.,
   905 (* FIXXXXME n1.,
   906  case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2, x = -4]")) => () TODO
   906  case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2, x = -4]")) => () TODO
   907 	 | _ => raise error "polyeq.sml: diff.behav. in [x = 2, x = -4]";
   907 	 | _ => error "polyeq.sml: diff.behav. in [x = 2, x = -4]";
   908 *)
   908 *)
   909 
   909 
   910 "----------- (a*b - (a+b)*x + x^^^2 = 0), (*Schalk 2,S.68Nr.44.a*)";
   910 "----------- (a*b - (a+b)*x + x^^^2 = 0), (*Schalk 2,S.68Nr.44.a*)";
   911 "----------- (a*b - (a+b)*x + x^^^2 = 0), (*Schalk 2,S.68Nr.44.a*)";
   911 "----------- (a*b - (a+b)*x + x^^^2 = 0), (*Schalk 2,S.68Nr.44.a*)";
   912 "----------- (a*b - (a+b)*x + x^^^2 = 0), (*Schalk 2,S.68Nr.44.a*)";
   912 "----------- (a*b - (a+b)*x + x^^^2 = 0), (*Schalk 2,S.68Nr.44.a*)";
   944      Form' 
   944      Form' 
   945 	 (FormKF 
   945 	 (FormKF 
   946 	      (~1,EdUndef,0,Nundef,
   946 	      (~1,EdUndef,0,Nundef,
   947 	       "[x = (a + b) / 2 + -1 * sqrt ((a + b) ^^^ 2 / 2 ^^^ 2 - a * b),\n x = (a + b) / 2 + sqrt ((a + b) ^^^ 2 / 2 ^^^ 2 - a * b)]")) 
   947 	       "[x = (a + b) / 2 + -1 * sqrt ((a + b) ^^^ 2 / 2 ^^^ 2 - a * b),\n x = (a + b) / 2 + sqrt ((a + b) ^^^ 2 / 2 ^^^ 2 - a * b)]")) 
   948 	 => ()
   948 	 => ()
   949    | _ => raise error "polyeq.sml: diff.behav. in a*b - (a+b)*x + x^^^2 = 0";
   949    | _ => error "polyeq.sml: diff.behav. in a*b - (a+b)*x + x^^^2 = 0";
   950  this will be simplified [x = a, x = b] to by Factor.ML*)
   950  this will be simplified [x = a, x = b] to by Factor.ML*)
   951 
   951 
   952 
   952 
   953 "----------- (-64 + x^^^2 = 0), (*Schalk 2, S.66 Nr.1.a~--------*)";
   953 "----------- (-64 + x^^^2 = 0), (*Schalk 2, S.66 Nr.1.a~--------*)";
   954 "----------- (-64 + x^^^2 = 0), (*Schalk 2, S.66 Nr.1.a~--------*)";
   954 "----------- (-64 + x^^^2 = 0), (*Schalk 2, S.66 Nr.1.a~--------*)";
   976  val (p,_,f,nxt,_,pt) = me nxt p c pt;
   976  val (p,_,f,nxt,_,pt) = me nxt p c pt;
   977  val (p,_,f,nxt,_,pt) = me nxt p c pt;
   977  val (p,_,f,nxt,_,pt) = me nxt p c pt;
   978  val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;
   978  val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;
   979 (*WN.2.5.03 TODO "[x = sqrt (0 - -64), x = -1 * sqrt (0 - -64)]"
   979 (*WN.2.5.03 TODO "[x = sqrt (0 - -64), x = -1 * sqrt (0 - -64)]"
   980  case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 8, x = -8]")) => ()
   980  case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 8, x = -8]")) => ()
   981 	 | _ => raise error "polyeq.sml: diff.behav. in [x = 8, x = -8]";
   981 	 | _ => error "polyeq.sml: diff.behav. in [x = 8, x = -8]";
   982 *)
   982 *)
   983 
   983 
   984 "----------- (-147 + 3*x^^^2 = 0), (*Schalk 2, S.66 Nr.1.b------*)";
   984 "----------- (-147 + 3*x^^^2 = 0), (*Schalk 2, S.66 Nr.1.b------*)";
   985 "----------- (-147 + 3*x^^^2 = 0), (*Schalk 2, S.66 Nr.1.b------*)";
   985 "----------- (-147 + 3*x^^^2 = 0), (*Schalk 2, S.66 Nr.1.b------*)";
   986 "----------- (-147 + 3*x^^^2 = 0), (*Schalk 2, S.66 Nr.1.b------*)";
   986 "----------- (-147 + 3*x^^^2 = 0), (*Schalk 2, S.66 Nr.1.b------*)";
  1002  val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
  1002  val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
  1003  val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
  1003  val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
  1004  val (p,_,f,nxt,_,pt) = me nxt p c pt;
  1004  val (p,_,f,nxt,_,pt) = me nxt p c pt;
  1005 (*WN.2.5.03 TODO "[x = sqrt (0 - -49), x = -1 * sqrt (0 - -49)]"
  1005 (*WN.2.5.03 TODO "[x = sqrt (0 - -49), x = -1 * sqrt (0 - -49)]"
  1006  case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 7, x = -7]")) => ()
  1006  case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 7, x = -7]")) => ()
  1007 	 | _ => raise error "polyeq.sml: diff.behav. in [x = 7, x = -7]";
  1007 	 | _ => error "polyeq.sml: diff.behav. in [x = 7, x = -7]";
  1008 *)
  1008 *)
  1009 if f2str f = "[x = sqrt (0 - -49), x = -1 * sqrt (0 - -49)]" then ()
  1009 if f2str f = "[x = sqrt (0 - -49), x = -1 * sqrt (0 - -49)]" then ()
  1010 else raise error "polyeq.sml CORRECTED?behav. in [x = 7, x = -7]";
  1010 else error "polyeq.sml CORRECTED?behav. in [x = 7, x = -7]";
  1011 
  1011 
  1012 
  1012 
  1013 "----------- (3*x - 1 - (5*x - (2 - 4*x)) = -11),(*Schalk Is86Bsp5";
  1013 "----------- (3*x - 1 - (5*x - (2 - 4*x)) = -11),(*Schalk Is86Bsp5";
  1014 "----------- (3*x - 1 - (5*x - (2 - 4*x)) = -11),(*Schalk Is86Bsp5";
  1014 "----------- (3*x - 1 - (5*x - (2 - 4*x)) = -11),(*Schalk Is86Bsp5";
  1015 "----------- (3*x - 1 - (5*x - (2 - 4*x)) = -11),(*Schalk Is86Bsp5";
  1015 "----------- (3*x - 1 - (5*x - (2 - 4*x)) = -11),(*Schalk Is86Bsp5";
  1050 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1050 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1051 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1051 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1052 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1052 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1053 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1053 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1054 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2]")) => ()
  1054 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2]")) => ()
  1055 	 | _ => raise error "polyeq.sml: diff.behav. in [x = 2]";
  1055 	 | _ => error "polyeq.sml: diff.behav. in [x = 2]";
  1056 
  1056 
  1057 
  1057 
  1058 "----------- ((x+1)*(x+2) - (3*x - 2)^^^2=.. Schalk II s.68 Bsp 37";
  1058 "----------- ((x+1)*(x+2) - (3*x - 2)^^^2=.. Schalk II s.68 Bsp 37";
  1059 "----------- ((x+1)*(x+2) - (3*x - 2)^^^2=.. Schalk II s.68 Bsp 37";
  1059 "----------- ((x+1)*(x+2) - (3*x - 2)^^^2=.. Schalk II s.68 Bsp 37";
  1060 "----------- ((x+1)*(x+2) - (3*x - 2)^^^2=.. Schalk II s.68 Bsp 37";
  1060 "----------- ((x+1)*(x+2) - (3*x - 2)^^^2=.. Schalk II s.68 Bsp 37";
  1095 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1095 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1096 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1096 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1097 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1097 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1098 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1098 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1099 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2 / 15, x = 1]")) => ()
  1099 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2 / 15, x = 1]")) => ()
  1100 	 | _ => raise error "polyeq.sml: diff.behav. in [x = 2 / 15, x = 1]";
  1100 	 | _ => error "polyeq.sml: diff.behav. in [x = 2 / 15, x = 1]";
  1101 
  1101 
  1102 
  1102 
  1103 "    -4 + x^^^2 =0     ";
  1103 "    -4 + x^^^2 =0     ";
  1104 "    -4 + x^^^2 =0     ";
  1104 "    -4 + x^^^2 =0     ";
  1105 "    -4 + x^^^2 =0     ";
  1105 "    -4 + x^^^2 =0     ";
  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;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1121 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1122 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1122 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
  1123 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2, x = -2]")) => ()
  1123 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2, x = -2]")) => ()
  1124 	 | _ => raise error "polyeq.sml: diff.behav. in [x = 2, x = -2]";
  1124 	 | _ => error "polyeq.sml: diff.behav. in [x = 2, x = -2]";
  1125 
  1125 
  1126 "----------------- polyeq.sml end ------------------";
  1126 "----------------- polyeq.sml end ------------------";
  1127 
  1127 
  1128 (*Punkte aus dem TestBericht, die ich in rlang.sml nicht zuordnen konnte:*)
  1128 (*Punkte aus dem TestBericht, die ich in rlang.sml nicht zuordnen konnte:*)
  1129 (*WN.19.3.03 ---v-*)
  1129 (*WN.19.3.03 ---v-*)