test/Tools/isac/Knowledge/rootrateq.sml
author wneuper <Walther.Neuper@jku.at>
Mon, 01 Jan 2024 11:31:16 +0100
changeset 60789 8fa678b678e8
parent 60675 d841c720d288
permissions -rw-r--r--
Doc/Specify_Phase 4: start use antiquotations from isar-ref
     1 (* testexamples for RootratEq, equations mixing fractions and roots
     2    WN120314 some complicated equations still are outcommented.
     3    *)
     4 
     5 "-----------------------------------------------------------------";
     6 "table of contents -----------------------------------------------";
     7 "-----------------------------------------------------------------";
     8 "------------ tests on predicates  -------------------------------";
     9 "------------ test thm rootrat_equation_left_1 -------------------";
    10 "------------ test thm rootrat_equation_left_2 -------------------";
    11 "------------ test thm rootrat_equation_right_1 ------------------";
    12 "------------ test thm rootrat_equation_right_2 ------------------";
    13 "-----------------------------------------------------------------";
    14 "-----------------------------------------------------------------";
    15 (* Note on ERROR "check_elementwise: no set 1 + sqrt x = 3".
    16   this error popped up with this harmless changeset, which
    17 (1) triggered ["RootEq", "solve_sq_root_equation"] first time, because wrong '' in
    18     (Try (Repeat (Rewrite_Set ''make_rooteq ''))) was found
    19 (2) correction ''make_rooteq'' led further to "check_elementwise: no set 1 + sqrt x = 3"
    20   Since the changeset seems have nothing todo with these errors, this indicates that
    21 (a) either method ["RootEq", "solve_sq_root_equation"] & Co are somewhat indeterministic
    22 (b) of this is a case of indeterminism due to something elementary.
    23 
    24 *)                               
    25 val thy = @{theory "RootRatEq"};
    26 val ctxt = Proof_Context.init_global thy;
    27 
    28 "------------ tests on predicates  -------------------------------";
    29 "------------ tests on predicates  -------------------------------";
    30 "------------ tests on predicates  -------------------------------";
    31 val t1 = ParseC.parse_test ctxt "(-8 - sqrt(x) + x \<up> 2) is_rootRatAddTerm_in x";
    32 val SOME (t,_) = rewrite_set_ ctxt  false RootRatEq_prls t1;
    33 if (UnparseC.term @{context} t) = "False" then ()
    34  else  error "rootrateq.sml: diff.behav. 1 in is_rootRatAddTerm_in";
    35 
    36 val t1 = ParseC.parse_test ctxt "(1/x) is_rootRatAddTerm_in x";
    37 val SOME (t,_) = rewrite_set_ ctxt false RootRatEq_prls t1;
    38 if (UnparseC.term @{context} t) = "False" then ()
    39  else  error "rootrateq.sml: diff.behav. 2 in is_rootRatAddTerm_in";
    40 
    41 val t1 = ParseC.parse_test ctxt "(1/sqrt(x)) is_rootRatAddTerm_in x";
    42 val SOME (t,_) = rewrite_set_ ctxt false RootRatEq_prls t1;
    43 if (UnparseC.term @{context} t) = "False" then ()
    44  else  error "rootrateq.sml: diff.behav. 3 in is_rootRatAddTerm_in";
    45 
    46 val t1 = ParseC.parse_test ctxt "(1/(sqrt(x)+1)) is_rootRatAddTerm_in x";
    47 val SOME (t,_) = rewrite_set_ ctxt false RootRatEq_prls t1;
    48 if (UnparseC.term @{context} t) = "True" then ()
    49  else  error "rootrateq.sml: diff.behav. 4 in is_rootRatAddTerm_in";
    50 
    51 val t1 = ParseC.parse_test ctxt "(3 + 1/(1+sqrt(x))) is_rootRatAddTerm_in x";
    52 val SOME (t,_) = rewrite_set_ ctxt false RootRatEq_prls t1;
    53 if (UnparseC.term @{context} t) = "True" then ()
    54  else  error "rootrateq.sml: diff.behav. 5 in is_rootRatAddTerm_in";
    55 
    56 val t1 = ParseC.parse_test ctxt "(1/(1+sqrt(y)) + 3 + 1/(1+sqrt(x))) is_rootRatAddTerm_in x";
    57 val SOME (t,_) = rewrite_set_ ctxt false RootRatEq_prls t1;
    58 if (UnparseC.term @{context} t) = "True" then ()
    59  else  error "rootrateq.sml: diff.behav. 6 in is_rootRatAddTerm_in";
    60 
    61 val t1 = ParseC.parse_test ctxt "(1/(1+sqrt(x)) + 3 + 1/(1+sqrt(y))) is_rootRatAddTerm_in x";
    62 val SOME (t,_) = rewrite_set_ ctxt false RootRatEq_prls t1;
    63 if (UnparseC.term @{context} t) = "True" then ()
    64  else  error "rootrateq.sml: diff.behav. 7 in is_rootRatAddTerm_in";
    65 
    66 "------------ test thm rootrat_equation_left_1 -------------------";
    67 "------------ test thm rootrat_equation_left_1 -------------------";
    68 "------------ test thm rootrat_equation_left_1 -------------------";
    69 val c = [];
    70 val fmz = ["equality ( - 2 + 1/(1 - sqrt(x))= (0::real))", "solveFor x", "solutions L"];
    71 val (dI',pI',mI') = ("RootRatEq",["univariate", "equation"],["no_met"]);
    72 val (p,_,f,nxt,_,pt) = Test_Code.init_calc @{context} [(fmz, (dI',pI',mI'))];
    73 val (p,_,f,nxt,_,pt) = me nxt p c pt;
    74 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
    75 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
    76 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
    77 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
    78 val (p,_,f,nxt,_,pt) = me nxt p c pt;
    79 (*============ inhibit exn WN120319 ==============================================
    80 (*From final Test_Isac.thy we suddenly have
    81 
    82           nxt = ("Model_Problem", Model_Problem)
    83 
    84 which we did not investigate further due to the decision to drop the whole type of equation.
    85 *)
    86 if f2str f = "1 = (0 - - 2) * (1 + - 1 * sqrt x)" then ()
    87 else error "rootrateq.sml: diff.behav. in rootrat_equation_left_1 a";
    88 (*-> Subproblem ("RootRatEq", ["sq", "rootX", "univariate", "equation"])*)
    89 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
    90 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
    91 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
    92 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
    93 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p''',_,f,nxt,_,pt''') = me nxt p c pt;
    94 
    95 (*we investigate, why the next step results in Empty_Tac*)
    96 f2str f = "1 = 2 * (1 + - 1 * sqrt x)";
    97 nxt = ("Rewrite_Set", Rewrite_Set "make_rooteq");
    98 (*... these ar the step's arguments; from these we do directly ...*)
    99 val SOME t = ParseC.term_opt ctxt "1 = 2 * (1 + - 1 * sqrt x)"
   100 val SOME (t, _) = rewrite_set_ thy true make_rooteq t;
   101 UnparseC.term @{context} t = "1 = 2 + - 2 * sqrt x";
   102 (*... which works; thus error must be in script interpretation*)
   103 
   104 "~~~~~ fun me, args:"; val (tac, (p:pos'), _, (pt:ctree)) = (nxt, p, c, pt);
   105 val (pt, p) = case Step.by_tactic tac (pt,p) of
   106 	("ok", (_, _, ptp))  => ptp;
   107 "~~~~~ fun Step.do_next, args:"; val (ip as (_,p_), (ptp as (pt,p), tacis)) = (p, ((pt, e_pos'), []))
   108 val pIopt = get_pblID (pt,ip);
   109 ip;    (*= ([3, 2], Res)*)
   110 tacis; (*= []*)
   111 pIopt; (*= SOME ["sq", "rootX", "univariate", "equation"]*)
   112 member op = [Pbl,Met] p_; (*= false*)
   113 "~~~~~ fun do_next, args:"; (*stopped due to strange exn
   114   "check_elementwise: no set 1 = 2 + - 2 * sqrt x"*)
   115 
   116 (*---- 2nd try: we investigate the script ["RootEq", "solve_sq_root_equation"] found via pbl*)
   117 val t = ParseC.parse_test @{context} "((lhs e_e) is_sqrtTerm_in v_v) | ((rhs e_e) is_sqrtTerm_in v_v)";
   118 val t = ParseC.parse_test @{context} ("((lhs (1 = 2 * (1 + - 1 * sqrt x))) is_sqrtTerm_in x) |" ^
   119                  " ((rhs (1 = 2 * (1 + - 1 * sqrt x))) is_sqrtTerm_in x)");
   120 val SOME (t, _) = rewrite_set_ thy true rooteq_srls t;
   121 UnparseC.term @{context} t = "True | True"; (*...was same in 2002 (NOT "True"); so program seems to take 
   122   [univariate,equation] and to refine to ["sq", "rootX", "univariate", "equation"] in 2002*)
   123 
   124 (*(*these are the errors during stepping into the code:*)
   125 Step_Solve.do_next (pt,ip); (*check_elementwise: no set 1 = 2 + - 2 * sqrt x: fun mk_set raises
   126   this exn in Check_elementwise ONLY ?!?*)
   127 Step.do_next p ((pt, e_pos'),[]); (* = ("helpless",*)
   128 *)
   129 
   130 val (p,_,f,nxt,_,pt) = me nxt p''' c pt''';
   131 f2str f = "1 = 2 + - 2 * sqrt x)"; (* <<<-------------- this should be*)
   132 fst nxt = "Empty_Tac"; (* <<<-------------- this we have*)
   133 (*============ inhibit exn WN120314: stopped due to effort; continue with equ-solver
   134 The equation is strange: it calls script ["RootEq", "solve_sq_root_equation"] twice
   135 and works differently due to an "if" in that script.
   136 
   137 if f2str f = "1 = 2 + - 2 * sqrt x" then ()
   138 else error "rootrateq.sml: diff.behav. in rootrat_equation_left_1 b";
   139 (*-> Subproblem ("RootRatEq", ["sq", "rootX", "univariate", "equation"]) ?!? the SAME as above*)
   140 val (p,_,f,nxt,_,pt) = me nxt p c pt; 
   141 val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;
   142 val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f; 
   143 val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;
   144 val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f; 
   145 val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;
   146 val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f; 
   147 val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;
   148 val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;
   149 val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;
   150 val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;
   151 if f2str f = "1 = 4 * x" then ()
   152 else error "rootrateq.sml: diff.behav. in rootrat_equation_left_1 c";
   153 (*-> Subproblem ("PolyEq", ["normalise", "polynomial", "univariate", "equation"])*)
   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;
   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;
   158 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   159 val (p,_,f,nxt,_,pt) = me nxt p c pt; 
   160 if f2str f = "1 + -4 * x = 0" then ()
   161 else error "rootrateq.sml: diff.behav. in rootrat_equation_left_1";
   162 (*-> Subproblem ("PolyEq", ["degree_1", "polynomial", "univariate", "equation"])*)
   163 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   164 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   165 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   166 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   167 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   168 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   169 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   170 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   171 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   172 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   173 case f of Form' (Test_Out.FormKF (~1,EdUndef,0,Nundef,"[x = 1 / 4]")) => ()
   174 	 | _ => error "rootrateq.sml: diff.behav. in  - 2 + 1/(1 - sqrt(x))= 0 -> [x = 1/4]";
   175 ============ inhibit exn WN120314 ==============================================*)
   176 ============ inhibit exn WN120319 ==============================================*)
   177 
   178 "------------ test thm rootrat_equation_left_2 -------------------";
   179 "------------ test thm rootrat_equation_left_2 -------------------";
   180 "------------ test thm rootrat_equation_left_2 -------------------";
   181 val fmz = ["equality (3/(1+sqrt(x))= 1)", "solveFor x", "solutions L"];
   182 val (dI',pI',mI') = ("RootRatEq",["univariate", "equation"],["no_met"]);
   183 
   184 val (p,_,f,nxt,_,pt) = Test_Code.init_calc @{context} [(fmz, (dI',pI',mI'))];
   185 val (p,_,f,nxt,_,pt) = me nxt p c pt;
   186 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   187 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   188 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   189 (* \<up>  10 *)
   190 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   191 (*-> Subproblem ("RootEq", ["univariate", ...])*)
   192 val (p,_,f,nxt,_,pt) = me nxt p c pt;
   193 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   194 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   195 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   196 (* \<up>  20 *)
   197 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   198 
   199 (*//------------------ ERROR check_elementwise: no set 1 + sqrt x = 3 -----------------------\\* )
   200 val (p,_,f,nxt,_,pt) = me nxt p c pt; 
   201 (*-> Subproblem ("RootEq", ["univariate", ...])*)
   202 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   203 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   204 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   205 (* \<up>  30 *)
   206 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   207 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   208 val (p,_,f,nxt,_,pt) = me nxt p c pt; 
   209 (*-> Subproblem ("RootEq", ["univariate", ...])*)
   210 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   211 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   212 (* \<up>  40 *)
   213 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   214 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   215 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   216 val (p,_,f,nxt,_,pt) = me nxt p c pt; 
   217 ( *\\------------------ ERROR check_elementwise: no set 1 + sqrt x = 3 -----------------------//*)
   218 
   219 (*============ inhibit exn WN120314 ==============================================
   220 if f = Form' (Test_Out.FormKF (~1, EdUndef, 0, Nundef, "4 + - 1 * x = 0")) then ()
   221 else error "rootrateq.sml: diff.behav. in rootrat_equation_left_2";
   222 (*-> Subproblem ("PolyEq", ["polynomial", ...])*)
   223 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   224 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   225 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   226 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   227 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   228 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   229 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;
   232 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   233 case f of Form' (Test_Out.FormKF (~1,EdUndef,0,Nundef,"[x = 4]")) => ()
   234 	 | _ => error "rootrateq.sml: diff.behav. in  3/(1+sqrt(x))= 1 -> [x = 4]";
   235 ============ inhibit exn WN120314 ==============================================*)
   236 
   237 "------------ test thm rootrat_equation_right_1 ------------------";
   238 "------------ test thm rootrat_equation_right_1 ------------------";
   239 "------------ test thm rootrat_equation_right_1 ------------------";
   240 val fmz = ["equality ( 0= - 2 + 1/(1 - sqrt(x)))", "solveFor x", "solutions L"];
   241 val (dI',pI',mI') = ("RootRatEq",["univariate", "equation"],["no_met"]);
   242 
   243 val (p,_,f,nxt,_,pt) = Test_Code.init_calc @{context} [(fmz, (dI',pI',mI'))];
   244 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   245 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   246 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   247 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   248 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   249 (* \<up>  10 *)
   250 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   251 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   252 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   253 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   254 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   255 (* \<up>  20 *)
   256 (*//------------------ ERROR check_elementwise: no set 1 + sqrt x = 3 -----------------------\\* )
   257 val (p,_,f,nxt,_,pt) = me nxt p c pt;
   258 val (p,_,f,nxt,_,pt) = me nxt p c pt;
   259 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   260 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   261 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   262 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   263 (* \<up>  30 *)
   264 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   265 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   266 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   267 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   268 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   269 (* \<up>  40 *)
   270 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; 
   272 ( *\\------------------ ERROR check_elementwise: no set 1 + sqrt x = 3 -----------------------//*)
   273 
   274 (*============ inhibit exn WN120314: similar complicated equation, dropped.
   275 if f = Form' (Test_Out.FormKF (~1, EdUndef, 0, Nundef, "- 1 + 4 * x = 0")) then ()
   276 else error "rootrateq.sml: diff.behav.ppoly in rootrat_equation_right_1";
   277 val (p,_,f,nxt,_,pt) = me nxt p c pt;
   278 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   279 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   280 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   281 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   282 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   283 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   284 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   285 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   286 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   287 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   288 case f of Form' (Test_Out.FormKF (~1,EdUndef,0,Nundef,"[x = 1 / 4]")) => ()
   289 	 | _ => error "rootrateq.sml: diff.behav. in  - 2 + 1/(1 - sqrt(x))= 0 -> [x = 1/4]";
   290 ============ inhibit exn WN120314 ==============================================*)
   291 
   292 "------------ test thm rootrat_equation_right_2 ------------------";
   293 "------------ test thm rootrat_equation_right_2 ------------------";
   294 "------------ test thm rootrat_equation_right_2 ------------------";
   295 val fmz = ["equality (1 = 3/(1+sqrt(x)))", "solveFor x", "solutions L"];
   296 val (dI',pI',mI') = ("RootRatEq",["univariate", "equation"],["no_met"]);
   297 
   298 val (p,_,f,nxt,_,pt) = Test_Code.init_calc @{context} [(fmz, (dI',pI',mI'))];
   299 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   300 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   301 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   302 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   303 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   304 (* \<up>  10 *)
   305 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   306 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   307 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   308 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   309 
   310 (*//------------------ ERROR rls "make_rooteq " missing in Know_Store.
   311     after repair (Try (Repeat (Rewrite_Set ''make_rooteq ''))) 
   312     ------------------ ERROR check_elementwise: no set 1 + sqrt x = 3 -----------------------\\* )
   313 (*val (p,_,f,nxt,_,pt) =*) me nxt p c pt;
   314 "~~~~~ fun me , args:"; val (tac, p, _(*NEW remove*), pt) = (nxt, p, c, pt);
   315       val (pt, p) = 
   316   	    (*Step.by_tactic is here for testing by me; do_next would suffice in me*)
   317   	    case Step.by_tactic tac (pt, p) of
   318   		    ("ok", (_, _, ptp)) => ptp
   319   	    | ("unsafe-ok", (_, _, ptp)) => ptp
   320   	    | ("not-applicable",_) => (pt, p)
   321   	    | ("end-of-calculation", (_, _, ptp)) => ptp
   322   	    | ("failure", _) => error "sys-error"
   323   	    | _ => error "me: uncovered case Step.by_tactic"
   324 
   325     (*case*)
   326       Step.do_next p ((pt, Pos.e_pos'), []) (*of*);
   327 "~~~~~ fun do_next , args:"; val ((ip as (_, p_)), (ptp as (pt, p), tacis))
   328   = (p, ((pt, Pos.e_pos'), []));
   329  val pIopt = Ctree.get_pblID (pt, ip);
   330     (*if*) ip = ([], Pos.Res) (*else*);
   331       val _ = (*case*) tacis (*of*);
   332         val SOME _ = (*case*) pIopt (*of*);
   333 
   334   	       switch_specify_solve p_ (pt, ip);
   335 "~~~~~ fun switch_specify_solve , args:"; val (state_pos, (pt, input_pos)) = (p_, (pt, ip));
   336       (*if*) member op = [Pos.Pbl, Pos.Met] state_pos (*else*);
   337 
   338         LI.do_next (pt, input_pos);
   339 "~~~~~ and do_next , args:"; val (ptp as (pt, pos as (p, p_))) = (pt, input_pos);
   340     (*if*) MethodC.id_empty = get_obj g_metID pt (par_pblobj pt p) (*else*);
   341         val thy' = get_obj g_domID pt (par_pblobj pt p);
   342 
   343 	      val (_, (ist, ctxt), sc) =
   344     LItool.resume_prog (p,p_) pt;
   345 "~~~~~ fun resume_prog , args:"; val (thy, (p, p_), pt) = (thy', (p,p_), pt);
   346   (*if*) Pos.on_specification (p, p_) (*else*);
   347     val (pbl, p', rls') = parent_node pt pos
   348     (*if*) pbl (*then*);
   349 	         val metID = get_obj g_metID pt p'
   350 (*["RootEq", "solve_sq_root_equation"] found for correction, which caused ERROR 2*)
   351 
   352 (*\\------------------ end ERROR check ------------------------------------------------------//*)
   353 
   354 val (p,_,f,nxt,_,pt) = me nxt p c pt;
   355 (* \<up>  20 *)
   356 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   357 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   358 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   359 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   360 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   361 (* \<up>  30 *)
   362 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   363 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   364 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   365 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 (* \<up>  40 *)
   368 val (p,_,f,nxt,_,pt) = me nxt p c pt; 
   369 ( *\\------------------ ERROR WN200211 1, 2 -------------------------------------------------//*)
   370 
   371 (*============ inhibit exn WN120314 ==============================================
   372 if f = Form' (Test_Out.FormKF (~1, EdUndef, 0, Nundef, "-4 + x = 0")) then ()
   373 else error "rootrateq.sml: diff.behav. in rootrat_equation_right_2";
   374 val (p,_,f,nxt,_,pt) = me nxt p c pt;
   375 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   376 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   377 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   378 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   379 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   380 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   381 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   382 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   383 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   384 val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
   385 case f of Form' (Test_Out.FormKF (~1,EdUndef,0,Nundef,"[x = 4]")) => ()
   386 	 | _ => error "rootrateq.sml: diff.behav. in  3/(1+sqrt(x))= 1 -> [x = 4]";
   387 ============ inhibit exn WN120314 ==============================================*)
   388