(* tests on systems of equations

   author: Walther Neuper

   050826,

   (c) due to copyright terms

use"../smltest/IsacKnowledge/eqsystem.sml";

use"eqsystem.sml";

*)

"-----------------------------------------------------------------";

"table of contents -----------------------------------------------";

"-----------------------------------------------------------------";

"----------- occur_exactly_in ------------------------------------";

"----------- problems --------------------------------------------";

"----------- rewrite-order ord_simplify_System -------------------";

"----------- rewrite in [EqSystem,normalize,2x2] -----------------";

"----------- rewrite example from 2nd [EqSystem,normalize,2x2] ---";

"----------- rewrite in [EqSystem,top_down_substitution,2x2] -----";

"----------- rewrite in [EqSystem,normalize,4x4] -----------------";

"----------- script [EqSystem,normalize,2x2] ---------------------";

"----------- script [EqSystem,top_down_substitution,2x2] Vers.1 --";

"----------- script [EqSystem,top_down_substitution,2x2] Vers.2 --";

"----------- refine [linear,system]-------------------------------";

"----------- refine [2x2,linear,system] search error--------------";

"----------- me [EqSystem,normalize,2x2] -------------------------";

"----------- me [linear,system] ..normalize..top_down_sub..-------";

"----------- all systems from Biegelinie -------------------------";

"----------- 4x4 systems from Biegelinie -------------------------";

"-----------------------------------------------------------------";

"-----------------------------------------------------------------";

"-----------------------------------------------------------------";

val thy = @{theory "EqSystem"};

"----------- occur_exactly_in ------------------------------------";

"----------- occur_exactly_in ------------------------------------";

"----------- occur_exactly_in ------------------------------------";

val all = [str2term"c", str2term"c_2", str2term"c_3"];

val t = str2term"0 = -1 * q_0 * L ^^^ 2 / 2 + L * c + c_2";

if occur_exactly_in [str2term"c", str2term"c_2"] all t

then () else error "eqsystem.sml occur_exactly_in 1";

if not (occur_exactly_in [str2term"c", str2term"c_2", str2term"c_3"] all t)

then () else error "eqsystem.sml occur_exactly_in 2";

if not (occur_exactly_in [str2term"c_2"] all t)

then () else error "eqsystem.sml occur_exactly_in 3";

(*=== inhibit exn 110722=============================================================

val t = str2term"[c,c_2] from [c,c_2,c_3] occur_exactly_in \

		\-1 * q_0 * L ^^^ 2 / 2 + L * c + c_2";

val SOME (str, t') = eval_occur_exactly_in 0 "EqSystem.occur'_exactly'_in" t 0;

if str = "[c, c_2] from [c, c_2,\n                c_3] occur_exactly_in -1 * q_0 * L ^^^ 2 / 2 + L * c + c_2 = True" then ()

else error "eval_occur_exactly_in [c, c_2]";

val t = str2term"[c,c_2,c_3] from [c,c_2,c_3] occur_exactly_in \

		\-1 * q_0 * L ^^^ 2 / 2 + L * c + c_2";

val SOME (str, t') = eval_occur_exactly_in 0 "EqSystem.occur'_exactly'_in" t 0;

if str = "[c, c_2,\n c_3] from_ [c, c_2,\n             c_3] occur_exactly_in -1 * q_0 * L ^^^ 2 / 2 + L * c + c_2 = False" then ()

else error "eval_occur_exactly_in [c, c_2, c_3]";

val t = str2term"[c_2] from [c,c_2,c_3] occur_exactly_in \

		\-1 * q_0 * L ^^^ 2 / 2 + L * c + c_2";

val SOME (str, t') = eval_occur_exactly_in 0 "EqSystem.occur'_exactly'_in" t 0;

if str = "[c_2] from_ [c, c_2,\n             c_3] occur_exactly_in -1 * q_0 * L ^^^ 2 / 2 + L * c + c_2 = False" then ()

else error "eval_occur_exactly_in [c, c_2, c_3]";

val t = str2term"[] from [c,c_2,c_3] occur_exactly_in 0";

val SOME (str, t') = eval_occur_exactly_in 0 "EqSystem.occur'_exactly'_in" t 0;

if str = "[] from_ [c, c_2, c_3] occur_exactly_in 0 = True" then ()

else error "eval_occur_exactly_in [c, c_2, c_3]";

val t = 

    str2term

	"[] from [c, c_2, c_3, c_4] occur_exactly_in -1 * (q_0 * L ^^^ 2) /2";

val SOME (str, t') = eval_occur_exactly_in 0 "EqSystem.occur'_exactly'_in" t 0;

if str = "[] from_ [c, c_2, c_3, c_4] occur_exactly_in \

	 \-1 * (q_0 * L ^^^ 2) / 2 = True" then ()

else error "eval_occur_exactly_in [c, c_2, c_3, c_4]";

"----------- problems --------------------------------------------";

"----------- problems --------------------------------------------";

"----------- problems --------------------------------------------";

val t = str2term "LENGTH [x+y=1,y=2] = 2";

atomty t;

val testrls = append_rls "testrls" e_rls 

			 [(Thm ("length_Nil_",num_str @{thm length_Nil_})),

			  (Thm ("length_Cons_",num_str @{thm length_Cons_})),

			  Calc ("Groups.plus_class.plus", eval_binop "#add_"),

			  Calc ("HOL.eq",eval_equal "#equal_")

			  ];

val SOME (t',_) = rewrite_set_ thy false testrls t;

if term2str t' = "HOL.True" then () 

else error "eqsystem.sml: length_ [x+y=1,y=2] = 2";

val SOME t = parse EqSystem.thy "solution L";

atomty (term_of t);

val SOME t = parse Biegelinie.thy "solution L";

atomty (term_of t);

val t = str2term 

"(tl (tl (tl v_s))) from_ v_s occur_exactly_in (nth_ 1 (es_::bool list))";

atomty t;

val t = str2term 

"(tl (tl (tl [c,c_2,c_3,c_4]))) from_ [c,c_2,c_3,c_4] occur_exactly_in \

\(nth_ 1 [c_4 = 1, 2=2,3=3,4=4])";

val SOME (t,_) = 

    rewrite_set_ thy true 

		 (append_rls "prls_" e_rls 

			     [Thm ("nth_Cons_",num_str @{thm nth_Cons_}),

			      Thm ("nth_Nil_",num_str @{thm nth_Nil_}),

			      Thm ("tl_Cons",num_str @{thm tl_Cons}),

			      Thm ("tl_Nil",num_str @{thm tl_Nil}),

			      Calc ("EqSystem.occur'_exactly'_in", 

				    eval_occur_exactly_in 

					"#eval_occur_exactly_in_")

			      ]) t;

if t = HOLogic.true_const then () 

else error "eqsystem.sml ..occur_exactly_in (nth_ 1 [c_4..";

=== inhibit exn 110722=============================================================*)

"----------- rewrite-order ord_simplify_System -------------------";

"----------- rewrite-order ord_simplify_System -------------------";

"----------- rewrite-order ord_simplify_System -------------------";

"M_b x = c * x + -1 * q_0 * (x ^^^ 2 / 2) + c_2";

"--- add_commute ---";

if ord_simplify_System false thy [] (str2term"-1 * q_0 * (x ^^^ 2 / 2)", 

				       str2term"c * x") then ()

else error "integrate.sml, (-1 * q_0 * (x ^^^ 2 / 2)) < (c * x) not#1";

if ord_simplify_System false thy [] (str2term"-1 * q_0 * (x ^^^ 2 / 2)", 

				       str2term"c_2") then ()

else error "integrate.sml, (-1 * q_0 * (x ^^^ 2 / 2)) < (c_2) not#2";

if ord_simplify_System false thy [] (str2term"c * x", 

				       str2term"c_2") then ()

else error "integrate.sml, (c * x) < (c_2) not#3";

"--- mult_commute ---";

if ord_simplify_System false thy [] (str2term"x * c", 

				       str2term"c * x") then ()

else error "integrate.sml, (x * c) < (c * x) not#4";

if ord_simplify_System false thy [] (str2term"-1 * q_0 * (x ^^^ 2 / 2) * c", 

				       str2term"-1 * q_0 * c * (x ^^^ 2 / 2)") 

then () else error "integrate.sml, (. * .) < (. * .) not#5";

if ord_simplify_System false thy [] (str2term"-1 * q_0 * (x ^^^ 2 / 2) * c", 

				       str2term"c * -1 * q_0 * (x ^^^ 2 / 2)") 

then () else error "integrate.sml, (. * .) < (. * .) not#6";

"----------- rewrite in [EqSystem,normalize,2x2] -----------------";

"----------- rewrite in [EqSystem,normalize,2x2] -----------------";

"----------- rewrite in [EqSystem,normalize,2x2] -----------------";

val t = str2term"[0 = -1 * q_0 * L ^^^ 2 / 2 + L * c + c_2,\

	        \0 = -1 * q_0 * 0 ^^^ 2 / 2 + 0 * c + c_2]";

val bdvs = [(str2term"bdv_1",str2term"c"),

	    (str2term"bdv_2",str2term"c_2")];

val SOME(t,_)= rewrite_set_inst_ thy true bdvs simplify_System_parenthesized t;

if term2str t = "[0 = -1 * q_0 * L ^^^ 2 / 2 + (L * c + c_2), 0 = c_2]"

then () else error "eqsystem.sml rewrite in 2x2 simplify_System_par.1";

val SOME (t,_) = rewrite_set_inst_ thy true bdvs isolate_bdvs t;

if term2str t = "[L * c + c_2 = 0 + -1 * (-1 * q_0 * L ^^^ 2 / 2), c_2 = 0]"then () else error "eqsystem.sml rewrite in 2x2 isolate_bdvs";

val SOME(t,_)= rewrite_set_inst_ thy true bdvs simplify_System t;

if term2str t = "[L * c + c_2 = q_0 * L ^^^ 2 / 2, c_2 = 0]"

then () else error "eqsystem.sml rewrite in 2x2 simplify_System_par.2";

"--- 3--- see EqSystem.thy (*..if replaced by 'and' ...";

val SOME (t,_) = rewrite_set_ thy true order_system t;

if term2str t = "[c_2 = 0, L * c + c_2 = q_0 * L ^^^ 2 / 2]"

then () else error "eqsystem.sml rewrite in 2x2 simplify_System_par.3";

"--- 4---";

"----------- rewrite example from 2nd [EqSystem,normalize,2x2] ---";

"----------- rewrite example from 2nd [EqSystem,normalize,2x2] ---";

"----------- rewrite example from 2nd [EqSystem,normalize,2x2] ---";

val thy = @{theory "Isac"} (*because of Undeclared constant "Biegelinie.EI*);

val t = 

    str2term"[0 = c_2 + c * 0 + 1 / EI * (L * q_0 / 12 * 0 ^^^ 3 +         \

	    \                                     -1 * q_0 / 24 * 0 ^^^ 4),\

	    \ 0 = c_2 + c * L + 1 / EI * (L * q_0 / 12 * L ^^^ 3 +         \

	    \                                     -1 * q_0 / 24 * L ^^^ 4)]";

val SOME (t,_) = rewrite_set_ thy true norm_Rational t;

if term2str t="[0 = c_2, 0 = c_2 + L * c + L ^^^ 4 * q_0 / (EI * 24)]"

then () else error "eqsystem.sml rewrite in 2x2 simplify_System_par.0b";

val SOME(t,_)= rewrite_set_inst_ thy true bdvs simplify_System_parenthesized t;

if term2str t = "[0 = c_2, 0 = q_0 * L ^^^ 4 / (24 * EI) + (L * c + c_2)]"

then () else error "eqsystem.sml rewrite in 2x2 simplify_System_par.1b";

val SOME (t,_) = rewrite_set_inst_ thy true bdvs isolate_bdvs t;

if term2str t = "[c_2 = 0, L * c + c_2 = 0 + -1 * (q_0 * L ^^^ 4 / (24 * EI))]"

then () else error "eqsystem.sml rewrite in 2x2 isolate_bdvs b";

val SOME(t,_)= rewrite_set_inst_ thy true bdvs simplify_System t;

if term2str t = "[c_2 = 0, L * c + c_2 = -1 * q_0 * L ^^^ 4 / (24 * EI)]"

then () else error "eqsystem.sml rewrite in 2x2 simplify_System.2b";

val xxx = rewrite_set_ thy true order_system t;

if is_none xxx

then () else error "eqsystem.sml rewrite in 2x2 simplify_System.3b";

"----------- rewrite in [EqSystem,top_down_substitution,2x2] -----";

"----------- rewrite in [EqSystem,top_down_substitution,2x2] -----";

"----------- rewrite in [EqSystem,top_down_substitution,2x2] -----";

val e1__ = str2term "c_2 = 77";

val e2__ = str2term "L * c + c_2 = q_0 * L ^^^ 2 / 2";

val bdvs = [(str2term"bdv_1",str2term"c"),

	    (str2term"bdv_2",str2term"c_2")];

val SOME (e2__,_) = rewrite_terms_ thy dummy_ord Erls [e1__] e2__;

if term2str e2__ = "L * c + 77 = q_0 * L ^^^ 2 / 2" then ()

else error "eqsystem.sml top_down_substitution,2x2] subst";

val SOME (e2__,_) = 

    rewrite_set_inst_ thy true bdvs simplify_System_parenthesized e2__;

if term2str e2__ = "77 + L * c = q_0 * L ^^^ 2 / 2" then ()

else error "eqsystem.sml top_down_substitution,2x2] simpl_par";

val SOME (e2__,_) = rewrite_set_inst_ thy true bdvs isolate_bdvs e2__;

if term2str e2__ = "c = (q_0 * L ^^^ 2 / 2 + -1 * 77) / L" then ()

else error "eqsystem.sml top_down_substitution,2x2] isolate";

val t = str2term "[c_2 = 77, c = (q_0 * L ^^^ 2 / 2 + -1 * 77) / L]";

val SOME (t,_) = rewrite_set_ thy true order_system t;

if term2str t = "[c = (q_0 * L ^^^ 2 / 2 + -1 * 77) / L, c_2 = 77]" then ()

else error "eqsystem.sml top_down_substitution,2x2] order_system";

if not (ord_simplify_System

	    false thy [] 

	    (str2term"[c_2 = 77, c = (q_0 * L ^^^ 2 / 2 + -1 * 77) / L]", 

	     str2term"[c = (q_0 * L ^^^ 2 / 2 + -1 * 77) / L, c_2 = 77]")) 

then () else error "eqsystem.sml, order_result rew_ord";

trace_rewrite:=true;

trace_rewrite:=false;

"----------- rewrite in [EqSystem,normalize,4x4] -----------------";

"----------- rewrite in [EqSystem,normalize,4x4] -----------------";

"----------- rewrite in [EqSystem,normalize,4x4] -----------------";

(*STOPPED.WN06?: revise rewrite in [EqSystem,normalize,4x4] from before 0609*)

val t = str2term"[0 = -1 * q_0 * 0 ^^^ 2 / 2 + 0 * c_3 + c_4,\

	        \0 = -1 * q_0 * L ^^^ 2 / 2 + L * c_3 + c_4,\

		\c + c_2 + c_3 + c_4 = 0,\

		\c_2 + c_3 + c_4 = 0]";

val bdvs = [(str2term"bdv_1",str2term"c"),

	    (str2term"bdv_2",str2term"c_2"),

	    (str2term"bdv_3",str2term"c_3"),

	    (str2term"bdv_4",str2term"c_4")];

val SOME (t,_) = 

    rewrite_set_inst_ thy true bdvs simplify_System_parenthesized t;

if term2str t = "[0 = c_4, 0 = -1 * q_0 * L ^^^ 2 / 2 + (L * c_3 + c_4),\n\

	        \ c + (c_2 + (c_3 + c_4)) = 0, c_2 + (c_3 + c_4) = 0]"

then () else error "eqsystem.sml rewrite in 4x4 simplify_System_paren";

val SOME (t,_) = rewrite_set_inst_ thy true bdvs isolate_bdvs t;

if term2str t = "[c_4 = 0, \

	        \L * c_3 + c_4 = 0 + -1 * (-1 * q_0 * L ^^^ 2 / 2),\n \

		\c + (c_2 + (c_3 + c_4)) = 0, c_2 + (c_3 + c_4) = 0]"

then () else error "eqsystem.sml rewrite in 4x4 isolate_bdvs";

val SOME(t,_)= rewrite_set_inst_ thy true bdvs simplify_System_parenthesized t;

if term2str t = "[c_4 = 0,\

		\ L * c_3 + c_4 = q_0 * L ^^^ 2 / 2,\

		\ c + (c_2 + (c_3 + c_4)) = 0,\n\

		\ c_2 + (c_3 + c_4) = 0]"

then () else error "eqsystem.sml rewrite in 4x4 simplify_System_p..2";

val SOME (t,_) = rewrite_set_ thy true order_system t;

if term2str t = "[c_4 = 0,\

		\ L * c_3 + c_4 = q_0 * L ^^^ 2 / 2,\

		\ c_2 + (c_3 + c_4) = 0,\n\

		\ c + (c_2 + (c_3 + c_4)) = 0]"

then () else error "eqsystem.sml rewrite in 4x4 order_system";

(*=== inhibit exn 110722=============================================================

"----------- script [EqSystem,normalize,2x2] ---------------------";

"----------- script [EqSystem,normalize,2x2] ---------------------";

"----------- script [EqSystem,normalize,2x2] ---------------------";

val str = 

"Script SolveSystemScript (es_::bool list) (v_s::real list) = \

\  (let es__ = (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                simplify_System_parenthesized False) es_  \

\   in ([]))";

val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;

val str = 

"Script SolveSystemScript (es_::bool list) (v_s::real list) = \

\  (let es__ = (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                 simplify_System_parenthesized False) es_  \

\   in (SubProblem (Biegelinie_,[linear,system],[no_met])\

\                  []))";

val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;

val str = 

"Script SolveSystemScript (es_::bool list) (v_s::real list) = \

\  (let es__ = (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                 simplify_System_parenthesized False) es_  \

\   in (SubProblem (Biegelinie_,[linear,system],[no_met])\

\                  [BOOL_LIST es__, REAL_LIST v_s]))"

;

val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;

val str = 

"Script SolveSystemScript (es_::bool list) (v_s::real list) = \

\  (let es__ = Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                 simplify_System_parenthesized False) es_  \

\   in (SubProblem (Biegelinie_,[linear,system],[no_met])\

\                  [BOOL_LIST es__, REAL_LIST v_s]))"

;

val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;

val str = 

"Script SolveSystemScript (es_::bool list) (v_s::real list) = \

\  (let es__ = (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                 simplify_System_parenthesized False)) es_  \

\   in (SubProblem (Biegelinie_,[linear,system],[no_met])\

\                  [BOOL_LIST es__, REAL_LIST v_s]))"

;

val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;

val str = 

"Script SolveSystemScript (es_::bool list) (v_s::real list) = \

\  (let es__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                 simplify_System_parenthesized False)) @@\

\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                 simplify_System_parenthesized False))) es_\

\   in (SubProblem (Biegelinie_,[linear,system],[no_met])\

\                  [BOOL_LIST es__, REAL_LIST v_s]))"

;

val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;

val str = 

"Script SolveSystemScript (es_::bool list) (v_s::real list) = \

\  (let es__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                 simplify_System_parenthesized False)) @@\

\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                 simplify_System_parenthesized False)) @@\

\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                 simplify_System_parenthesized False))) es_\

\   in (SubProblem (Biegelinie_,[linear,system],[no_met])\

\                  [BOOL_LIST es__, REAL_LIST v_s]))"

;

val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;

val str = 

"Script SolveSystemScript (es_::bool list) (v_s::real list) = \

\  (let es__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                 simplify_System_parenthesized False)) @@\

\               (Try (Rewrite_Set_Inst [] isolate_bdvs False)) @@\

\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                 simplify_System_parenthesized False)) @@\

\               (Try (Rewrite_Set order_system False))) es_\

\   in (SubProblem (Biegelinie_,[linear,system],[no_met])\

\                  [BOOL_LIST es__, REAL_LIST v_s]))"

;

val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;

val str = 

"Script SolveSystemScript (es_::bool list) (v_s::real list) = \

\  (let es__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                 simplify_System_parenthesized False)) @@\

\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s)]\

\                                                    isolate_bdvs False)) @@\

\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                 simplify_System_parenthesized False)) @@\

\               (Try (Rewrite_Set order_system False))) es_\

\   in (SubProblem (Biegelinie_,[linear,system],[no_met])\

\                  [BOOL_LIST es__, REAL_LIST v_s]))"

;

val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;

val str = 

"Script SolveSystemScript (es_::bool list) (v_s::real list) = \

\  (let es__ = ((Try (Rewrite_Set simplify_System_parenthesized False)) @@\

\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                                    isolate_bdvs False)) @@\

\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                 simplify_System_parenthesized False)) @@\

\               (Try (Rewrite_Set order_system False))) es_\

\   in (SubProblem (Biegelinie_,[linear,system],[no_met])\

\                  [BOOL_LIST es__, REAL_LIST v_s]))"

;

val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;

"----------- script [EqSystem,top_down_substitution,2x2] Vers.1 --";

"----------- script [EqSystem,top_down_substitution,2x2] Vers.1 --";

"----------- script [EqSystem,top_down_substitution,2x2] Vers.1 --";

val str = 

"Script SolveSystemScript (es_::bool list) (v_s::real list) = \

\  (let es__ = (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                 simplify_System_parenthesized False) es_  \

\   in ([]))";

val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;

val str = 

"Script SolveSystemScript (es_::bool list) (v_s::real list) = \

\  (let e1__ = Take (hd es_)                \

\   in ([]))";

val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;

val str = 

"Script SolveSystemScript (es_::bool list) (v_s::real list) = \

\  (let e1__ = Take (hd es_);               \

\       e1__ = Take (hd es_)                \

\   in ([]))";

val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;

val str = 

"Script SolveSystemScript (es_::bool list) (v_s::real list) = \

\  (let e1__ = Take (hd es_);               \

\       e1__ = (Take (hd es_))\

\   in ([]))";

val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;

val str = 

"Script SolveSystemScript (es_::bool list) (v_s::real list) = \

\  (let e1__ = Take (hd es_);               \

\       e1__ = ((Rewrite_Set order_system False)) e1__\

\   in ([]))";

val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;

val str = 

"(Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                           isolate_bdvs False) (e1__::bool)";

val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;

val str = 

"Script SolveSystemScript (es_::bool list) (v_s::real list) = \

\  (let e1__ = Take (hd es_);               \

\       e1__ = ((Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                           isolate_bdvs False)) e1__\

\   in ([]))";

val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;

val str = 

"Script SolveSystemScript (es_::bool list) (v_s::real list) = \

\  (let e1__ = Take (hd es_);               \

\       e1__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                           isolate_bdvs False)) @@\

\               (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                 simplify_System False)) e1__\

\   in ([]))";

val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;

val str = 

"Script SolveSystemScript (es_::bool list) (v_s::real list) = \

\  (let e1__ = Take (hd es_);               \

\       e1__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                           isolate_bdvs False)) @@\

\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                 simplify_System False))) e1__\

\   in ([]))";

val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;

val str = 

"Script SolveSystemScript (es_::bool list) (v_s::real list) =                \

\  (let e1__ = Take (hd es_);                                                \

\       e1__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                           isolate_bdvs False)) @@          \

\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                 simplify_System False))) e1__;           \

\       e2__ = Take (hd (tl es_))                                            \

\   in ([]))";

val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;

val str = 

"Script SolveSystemScript (es_::bool list) (v_s::real list) =                \

\  (let e1__ = Take (hd es_);                                                \

\       e1__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                           isolate_bdvs False)) @@          \

\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                 simplify_System False))) e1__;           \

\       e2__ = Take (hd (tl es_));                                           \

\       e2__ = Substitute [e1__] e2__                                       \

\   in ([]))";

val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;

val str = 

"Script SolveSystemScript (es_::bool list) (v_s::real list) =                \

\  (let e1__ = Take (hd es_);                                                \

\       e1__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                           isolate_bdvs False)) @@          \

\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                 simplify_System False))) e1__;           \

\       e2__ = Take (hd (tl es_));                                           \

\       e2__ = ((Substitute [e1__])) e2__                                  \

\   in ([]))";

val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;

val str = 

"Script SolveSystemScript (es_::bool list) (v_s::real list) =                \

\  (let e1__ = Take (hd es_);                                                \

\       e1__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                      isolate_bdvs False)) @@               \

\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                 simplify_System False))) e1__;           \

\       e2__ = Take (hd (tl es_));                                           \

\       e2__ = ((Substitute [e1__]) @@                                       \

\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                      isolate_bdvs False)) @@               \

\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                 simplify_System False))) e2__            \

\   in [e1__, e2__])"

;

val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;

val str = 

"Script SolveSystemScript (es_::bool list) (v_s::real list) =                \

\  (let e1__ = Take (hd es_);                                                \

\       e1__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                      isolate_bdvs False)) @@               \

\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                 simplify_System False))) e1__;           \

\       e2__ = Take (hd (tl es_));                                           \

\       e2__ = ((Substitute [e1__]) @@                                       \

\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                 simplify_System_parenthesized False)) @@ \

\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                      isolate_bdvs False)) @@               \

\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                 simplify_System False)) @@               \

\               (Try (Rewrite_Set order_system False))) e2__                 \

\   in [e1__, e2__])"

;

val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;

=== inhibit exn 110722=============================================================*)

val str = 

"Script SolveSystemScript (es_::bool list) (v_s::real list) =                \

\  (let e1__ = Take (hd es_);                                                \

\       e1__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                      isolate_bdvs False)) @@               \

\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                 simplify_System False))) e1__;           \

\       e2__ = Take (hd (tl es_));                                           \

\       e2__ = ((Substitute [e1__]) @@                                       \

\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                 simplify_System_parenthesized False)) @@ \

\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                      isolate_bdvs False)) @@               \

\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                 simplify_System False))) e2__;           \

\       es__ = Take [e1__, e2__]\

\   in (Try (Rewrite_Set order_system False)) es__)"

;

(*=== inhibit exn 110722=============================================================

val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;

atomty sc;

=== inhibit exn 110722=============================================================*)

"----------- script [EqSystem,top_down_substitution,2x2] Vers.2 --";

"----------- script [EqSystem,top_down_substitution,2x2] Vers.2 --";

"----------- script [EqSystem,top_down_substitution,2x2] Vers.2 --";

val str = 

"Script SolveSystemScript (es_s::bool list) (v_s::real list) = \

\  (let es__s = Take es_s;   \

\       e1__1 = hd es__e\

\   in ([]))"

;

val str = 

"Script SolveSystemScript (es_::bool list) (v_s::real list) =         \

\  (let es__ = Take es_;                                              \

\       e1__ = hd es__;                                               \

\       e2__ = hd (tl es__);                                          \

\       es__ = [e1__, Substitute [e1__] e2__]                         "^

(* this        ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ is a script-'Expr'

   which is not yet searched for 'STac's; thus this script does not yet work*)

"   in ((Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                 simplify_System_parenthesized False)) @@   \

\       (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))] \

\                              isolate_bdvs False))              @@   \

\       (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\

\                                 simplify_System False))) es__)"

;

(*=== inhibit exn 110722=============================================================

val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;

atomty sc;

=== inhibit exn 110722=============================================================*)

"----------- refine [linear,system]-------------------------------";

"----------- refine [linear,system]-------------------------------";

"----------- refine [linear,system]-------------------------------";

val fmz = ["equalities [0 = -1 * q_0 * 0 ^^^ 2 / 2 + 0 * c + c_2,\

	               \0 = -1 * q_0 * L ^^^ 2 / 2 + L * c + c_2]", 

	   "solveForVars [c, c_2]", "solution L"];

(*=== inhibit exn 110722=============================================================

val matches = refine fmz ["linear","system"];

case matches of [_,_,_,

		 Matches (["normalize", "2x2", "linear", "system"],

			  {Find = [Correct "solution L"],

			   With = [],

			   Given =

			   [Correct

				"equalities\n [0 = -1 * q_0 * 0 ^^^ 2 / 2 + 0 * c + c_2,\n  0 = -1 * q_0 * L ^^^ 2 / 2 + L * c + c_2]",

				Correct "solveForVars [c, c_2]"],

			   Where = [],

			   Relate = []})] => ()

	      | _ => error "eqsystem.sml refine ['normalize','2x2'...]";

=== inhibit exn 110722=============================================================*)

val fmz = ["equalities [c_2 = 0, L * c + c_2 = q_0 * L ^^^ 2 / 2]", 

	   "solveForVars [c, c_2]", "solution L"];

(*=== inhibit exn 110722=============================================================

val matches = refine fmz ["linear","system"];

case matches of [_,_,

		 Matches

		     (["triangular", "2x2", "linear", "system"],

		      {Find = [Correct "solution L"],

		       With = [],

		       Given =

		       [Correct

			    "equalities [c_2 = 0, L * c + c_2 = q_0 * L ^^^ 2 / 2]",

			    Correct "solveForVars [c, c_2]"],

		       Where =

		       [Correct

			    "tl [c, c_2] from_ [c, c_2] occur_exactly_in nth_ 1\n       [c_2 = 0, L * c + c_2 = q_0 * L ^^^ 2 / 2]",

			    Correct

				"[c, c_2] from_ [c, c_2] occur_exactly_in nth_ 2\n    [c_2 = 0, L * c + c_2 = q_0 * L ^^^ 2 / 2]"],

		       Relate = []})] => ()

	      | _ => error "eqsystem.sml refine ['triangular','2x2'...]";

=== inhibit exn 110722=============================================================*)

(*=== inhibit exn 110722=============================================================

(*WN051014---------------------------------------------------------------- 

  the above 'val matches = refine fmz ["linear","system"]'

  didn't work anymore; we investigated in these steps:*)

val fmz = ["equalities [c_2 = 0, L * c + c_2 = q_0 * L ^^^ 2 / 2]", 

	   "solveForVars [c, c_2]", "solution L"];

val matches = refine fmz ["triangular", "2x2", "linear","system"];

(*... resulted in 

   False "[c, c_2] from_ [c, c_2] occur_exactly_in nth_ 2\n    

          [c_2 = 0, L * c + c_2 = q_0 * L ^^^ 2 / 2]"]*)

val t = str2term"[c, c_2] from_ [c, c_2] occur_exactly_in nth_ 2\   

		\[c_2 = 0, L * c + c_2 = q_0 * L ^^^ 2 / 2]";

trace_rewrite:=true;

val SOME (t',_) = rewrite_set_ thy false prls_triangular t;

(*found:...

##  try thm: nth_Cons_

###  eval asms: 1 < 2 + - 1

==> nth_ (2 + - 1) [L * c + c_2 = q_0 * L ^^^ 2 / 2] =

    nth_ (2 + - 1 + - 1) []

####  rls: erls_prls_triangular on: 1 < 2 + - 1

#####  try calc: op <'

###  asms accepted: ["1 < 2 + - 1"]   stored: ["1 < 2 + -1"]

... i.e Calc ("Groups.plus_class.plus", eval_binop "#add_") was missing in erls_prls_triangular*)

trace_rewrite:=false;

"----- relaxed preconditions for triangular system";

val fmz = ["equalities [L * q_0 = c,                                       \

	   \            0 = (2 * c_2 + 2 * L * c + -1 * L ^^^ 2 * q_0) / 2,\

	   \            0 = c_4,                           \

	   \            0 = c_3]", 

	   "solveForVars [c, c_2, c_3, c_4]", "solution L"];

val matches = refine fmz ["linear","system"];

(* trace_rewrite := true;

   trace_rewrite := false;

   *)

(*print_depth 6; matches; print_depth 3;*)

case matches of 

    [Matches (["linear", "system"], _),

     NoMatch (["2x2", "linear", "system"], _),

     NoMatch (["3x3", "linear", "system"], _),

     Matches (["4x4", "linear", "system"], _),

     NoMatch (["triangular", "4x4", "linear", "system"], _),

     Matches (["normalize", "4x4", "linear", "system"], _)] => ()

  | _ => error "eqsystem.sml: refine relaxed triangular sys NoMatch";

(*WN060914 does NOT match, because 3rd and 4th equ are not ordered*)

val fmz = ["equalities [L * q_0 = c,                                       \

	   \            0 = (2 * c_2 + 2 * L * c + -1 * L ^^^ 2 * q_0) / 2,\

	   \            0 = c_3,                           \

	   \            0 = c_4]", 

	   "solveForVars [c, c_2, c_3, c_4]", "solution L"];

val matches = refine fmz ["triangular", "4x4", "linear","system"];

(* print_depth 11; matches; print_depth 3;

   *)

case matches of 

    [Matches (["triangular", "4x4", "linear", "system"], _)] => ()

  | _ => error "eqsystem.sml: refine relaxed triangular sys Matches";

val matches = refine fmz ["linear","system"];

"----------- refine [2x2,linear,system] search error--------------";

"----------- refine [2x2,linear,system] search error--------------";

"----------- refine [2x2,linear,system] search error--------------";

(*didn't go into ["2x2", "linear", "system"]; 

  we investigated in these steps:*)

val fmz = ["equalities [0 = -1 * q_0 * 0 ^^^ 2 / 2 + 0 * c + c_2,\

	               \0 = -1 * q_0 * L ^^^ 2 / 2 + L * c + c_2]", 

	   "solveForVars [c, c_2]", "solution L"];

trace_rewrite:=true;

val matches = refine fmz ["2x2", "linear","system"];

trace_rewrite:=false;

print_depth 11; matches; print_depth 3;

(*brought: 'False "length_ es_ = 2"'*)

(*-----fun refin' (pblRD:pblRD) fmz pbls ((Ptyp (pI,[py],[])):pbt ptyp) =

(* val ((pblRD:pblRD), fmz, pbls, ((Ptyp (pI,[py],[])):pbt ptyp)) =

       (rev ["linear","system"], fmz, [(*match list*)],

	((Ptyp ("2x2",[get_pbt ["2x2","linear","system"]],[])):pbt ptyp));

   *)

> show_types:=true; term2str (hd where_); show_types:=false;

val it = "length_ (es_::real list) = (2::real)" : string

=========================================================================\

-------fun prep_pbt

(* val (thy, (pblID, dsc_dats: (string * (string list)) list, 

		  ev:rls, ca: string option, metIDs:metID list)) =

       (EqSystem.thy, (["system"],

		       [("#Given" ,["equalities es_", "solveForVars v_s"]),

			("#Find"  ,["solution ss___"](*___ is copy-named*))

			],

		       append_rls "e_rls" e_rls [(*for preds in where_*)], 

		       SOME "solveSystem es_ v_s", 

		       []));

   *)

> val [("#Given", [equalities_es_, "solveForVars v_s"])] = gi;

val equalities_es_ = "equalities es_" : string

> val (dd, ii) = (split_did o term_of o the o (parse thy)) equalities_es_;

> show_types:=true; term2str ii; show_types:=false;

val it = "es_::bool list" : string

~~~~~~~~~~~~~~~^^^^^^^^^ OK~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

> val {where_,...} = get_pbt ["2x2", "linear","system"];

> show_types:=true; term2str (hd where_); show_types:=false;

=========================================================================/

-----fun refin' ff:

> (writeln o (itms2str_ (thy2ctxt "Isac"))) itms;

[

(1 ,[1] ,true ,#Given ,Cor equalities

 [0 = -1 * q_0 * 0 ^^^ 2 / 2 + 0 * c + c_2,

  0 = -1 * q_0 * L ^^^ 2 / 2 + L * c + c_2] ,(es_, [[0 = -1 * q_0 * 0 ^^^ 2 / 2 + 0 * c + c_2,

 0 = -1 * q_0 * L ^^^ 2 / 2 + L * c + c_2]])),

(2 ,[1] ,true ,#Given ,Cor solveForVars [c, c_2] ,(v_s, [[c, c_2]])),

(3 ,[1] ,true ,#Find ,Cor solution L ,(ss___, [L]))]

> (writeln o pres2str) pre';

[

(false, length_ es_ = 2),

(true, length_ [c, c_2] = 2)]

----- fun match_oris':

> (writeln o (itms2str_ (thy2ctxt "Isac"))) itms;

> (writeln o pres2str) pre';

..as in refin'

----- fun check_preconds'

> (writeln o env2str) env;

["

(es_, [0 = -1 * q_0 * 0 ^^^ 2 / 2 + 0 * c + c_2,

 0 = -1 * q_0 * L ^^^ 2 / 2 + L * c + c_2])","

(v_s, [c, c_2])","

(ss___, L)"]

> val es_ = (fst o hd) env;

val es_ = Free ("es_", "bool List.list") : Term.term

> val pre1 = hd pres;

atomty pre1;

***

*** Const (op =, [real, real] => bool)

*** . Const (ListG.length_, real list => real)

*** . . Free (es_, real list)

~~~~~~~~~~~~~~~~~~~^^^^^^^^^ should be bool list~~~~~~~~~~~~~~~~~~~

*** . Free (2, real)

***

THE REASON WAS A non-type-constrained variable IN #WHERE OF PROBLEM

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

*)

"----------- me [EqSystem,normalize,2x2] -------------------------";

"----------- me [EqSystem,normalize,2x2] -------------------------";

"----------- me [EqSystem,normalize,2x2] -------------------------";

val fmz = ["equalities [0 = -1 * q_0 * 0 ^^^ 2 / 2 + 0 * c + c_2,\

	               \0 = -1 * q_0 * L ^^^ 2 / 2 + L * c + c_2]", 

	   "solveForVars [c, c_2]", "solution L"];

val (dI',pI',mI') =

  ("Biegelinie",["normalize", "2x2", "linear", "system"],

   ["EqSystem","normalize","2x2"]);

val p = e_pos'; val c = []; 

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

val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;

val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;

val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;

val (p,_,f,nxt,_,pt) = me nxt p c pt;

case nxt of ("Specify_Method",_) => ()

	  | _ => error "eqsystem.sml [EqSystem,normalize,2x2] specify";

val (p,_,f,nxt,_,pt) = me nxt p c pt;

val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;

val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f(*["(bdv_1, c)", "(bdv_2, hd (tl [c, c_2] ... corrected srls; ran only AFTER use"RCODE-root.sml", store_met was NOT SUFFICIENT*);

val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;

val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;

val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;

case nxt of

    (_, Subproblem ("Biegelinie", ["triangular", "2x2", "linear",_])) => ()

  | _ => error "eqsystem.sml me [EqSystem,normalize,2x2] SubProblem";

val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;

val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;

val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;

val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;

case nxt of

    (_, Specify_Method ["EqSystem", "top_down_substitution", "2x2"]) => ()

  | _ => error "eqsystem.sml me [EqSys...2x2] top_down_substitution";

val (p,_,f,nxt,_,pt) = me nxt p c pt;

val PblObj {probl,...} = get_obj I pt [5];

    (writeln o (itms2str_ (thy2ctxt "Isac"))) probl;

(*[

(1 ,[1] ,true ,#Given ,Cor equalities [c_2 = 0, L * c + c_2 = q_0 * L ^^^ 2 / 2] ,(es_, [[c_2 = 0, L * c + c_2 = q_0 * L ^^^ 2 / 2]])),

(2 ,[1] ,true ,#Given ,Cor solveForVars [c, c_2] ,(v_s, [[c, c_2]])),

(3 ,[1] ,true ,#Find ,Cor solution ss___ ,(ss___, [ss___]))]

*)

val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;

val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;

val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;

val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;

val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;

val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;

val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;

val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;

case nxt of

    (_, Check_Postcond ["triangular", "2x2", "linear", "system"]) => ()

  | _ => error "eqsystem.sml me Subpbl .[EqSys...2x2] finished";

val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;

val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;

if f2str f = "[c = L * q_0 / 2, c_2 = 0]" then ()

else error "eqsystem.sml me [EqSys...2x2] finished f2str f";

case nxt of

    (_, End_Proof') => ()

  | _ => error "eqsystem.sml me [EqSys...2x2] finished End_Proof'";

"----------- me [linear,system] ..normalize..top_down_sub..-------";

"----------- me [linear,system] ..normalize..top_down_sub..-------";

"----------- me [linear,system] ..normalize..top_down_sub..-------";

val fmz = 

    ["equalities\

     \[0 = c_2 + c * 0 + 1 / EI * (L * q_0 / 12 * 0 ^^^ 3 +                \

     \                                            -1 * q_0 / 24 * 0 ^^^ 4),\

     \ 0 = c_2 + c * L + 1 / EI * (L * q_0 / 12 * L ^^^ 3 +                \

     \                                            -1 * q_0 / 24 * L ^^^ 4)]",

     "solveForVars [c, c_2]", "solution L"];

val (dI',pI',mI') =

  ("Biegelinie",["linear", "system"], ["no_met"]);

val p = e_pos'; val c = []; 

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

val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;

val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;

val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;

val (p,_,f,nxt,_,pt) = me nxt p c pt;

case nxt of (_,Specify_Method ["EqSystem", "normalize", "2x2"]) => ()

	  | _ => error "eqsystem.sml [linear,system] specify b";

val (p,_,f,nxt,_,pt) = me nxt p c pt;

val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;

val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;

val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;

val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;

val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;

if f2str f = 

"[c_2 = 0, L * c + c_2 = -1 * q_0 * L ^^^ 4 / (24 * EI)]"

then () else error "eqsystem.sml me simpl. before SubProblem b";

case nxt of

    (_, Subproblem ("Biegelinie", ["triangular", "2x2", "linear",_])) => ()

  | _ => error "eqsystem.sml me [linear,system] SubProblem b";

val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;

val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;

val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;

val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;

case nxt of

    (_, Specify_Method ["EqSystem", "top_down_substitution", "2x2"]) => ()

  | _ => error "eqsystem.sml me [EqSys...2x2] top_down_substitution b";

val (p,_,f,nxt,_,pt) = me nxt p c pt;

val PblObj {probl,...} = get_obj I pt [5];

    (writeln o (itms2str_ (thy2ctxt "Isac"))) probl;

(*[

(1 ,[1] ,true ,#Given ,Cor equalities [c_2 = 0, L * c + c_2 = q_0 * L ^^^ 2 / 2] ,(es_, [[c_2 = 0, L * c + c_2 = q_0 * L ^^^ 2 / 2]])),

(2 ,[1] ,true ,#Given ,Cor solveForVars [c, c_2] ,(v_s, [[c, c_2]])),

(3 ,[1] ,true ,#Find ,Cor solution ss___ ,(ss___, [ss___]))]

*)

val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;

val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;

val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;

val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;

val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;

val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;

val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;

val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;

case nxt of

    (_, Check_Postcond ["triangular", "2x2", "linear", "system"]) => ()

  | _ => error "eqsystem.sml me Subpbl .[EqSys...2x2] finished b";

val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;

val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;

if f2str f = 

"[c = -1 * q_0 * L ^^^ 4 / (24 * EI * L), c_2 = 0]"

then () else error "eqsystem.sml me [EqSys...2x2] finished f2str f b";

case nxt of

    (_, End_Proof') => ()

  | _ => error "eqsystem.sml me [EqSys...2x2] finished End_Proof'" b;

"----------- all systems from Biegelinie -------------------------";

"----------- all systems from Biegelinie -------------------------";

"----------- all systems from Biegelinie -------------------------";

val subst = [(str2term "bdv_1", str2term "c"),

	     (str2term "bdv_2", str2term "c_2"),

	     (str2term "bdv_3", str2term "c_3"),

	     (str2term "bdv_4", str2term "c_4")]; 

"------- Bsp 7.27";

states:=[];

CalcTree [(["Traegerlaenge L","Streckenlast q_0","Biegelinie y",

	     "Randbedingungen [y 0 = 0, y L = 0, M_b 0 = 0, M_b L = 0]",

	     "FunktionsVariable x"],

	    ("Biegelinie", ["Biegelinien"],

		     ["IntegrierenUndKonstanteBestimmen2"]))];

moveActiveRoot 1;

(*

trace_script := true; autoCalculate 1 CompleteCalc; trace_script := false;

##7.27##          ordered           substs

          c_4       c_2           

c c_2 c_3 c_4     c c_2             1->2: c

  c_2                       c_4	  

c c_2             c c_2 c_3 c_4     [2':c, 1:c_2, 3:c_4] -> 4:c_3*)

val t = str2term"[0 = c_4,                           \

\ 0 = c_4 + L * c_3 +(12 * L ^^^ 2 * c_2 + 4 * L ^^^ 3 * c + -1 * L ^^^ 4 * q_0) / (-24 * EI),                                       \

\ 0 = c_2,                                           \

\ 0 = (2 * c_2 + 2 * L * c + -1 * L ^^^ 2 * q_0) / 2]";

val SOME (t',_) = rewrite_set_ thy false isolate_bdvs_4x4 t;

term2str t';

"[c_4 = 0,\n (12 * L ^^^ 2 * c_2 + 4 * L ^^^ 3 * c + -1 * L ^^^ 4 * q_0) / (-24 * EI) =\n 0 + -1 * (c_4 + L * c_3),\n c_2 = 0, (2 * c_2 + 2 * L * c + -1 * L ^^^ 2 * q_0) / 2 = 0]";

"----- 7.27 go through the rewrites in met_eqsys_norm_4x4";

val t = str2term "0 = (2 * c_2 + 2 * L * c + -1 * L ^^^ 2 * q_0) / 2";

val NONE = rewrite_set_ thy false norm_Rational t;

val SOME (t,_) = 

    rewrite_set_inst_ thy false subst simplify_System_parenthesized t;

term2str t = "0 = -1 * q_0 * L ^^^ 2 / 2 + (L * c + c_2)";

"--- isolate_bdvs_4x4";

(*

val SOME (t,_) = rewrite_set_inst_ thy false subst isolate_bdvs_4x4 t;

term2str t;

val SOME (t,_) = rewrite_set_inst_ thy false subst simplify_System t;

term2str t;

val SOME (t,_) = rewrite_set_ thy false order_system t;

term2str t;

*)

"------- Bsp 7.28 ---------------vvvvvvvvvvvvv Momentenlinie postponed";

states:=[];

CalcTree [(["Traegerlaenge L","Momentenlinie (-q_0 / L * x^3 / 6)",

	    "Biegelinie y",

	    "Randbedingungen [y L = 0, y' L = 0]",

	    "FunktionsVariable x"],

	   ("Biegelinie", ["vonMomentenlinieZu","Biegelinien"],

	    ["Biegelinien", "AusMomentenlinie"]))];

moveActiveRoot 1;

(*

trace_script := true; autoCalculate 1 CompleteCalc; trace_script := false;

*)

"------- Bsp 7.69";

states:=[];

CalcTree [(["Traegerlaenge L","Streckenlast q_0","Biegelinie y",

	     "Randbedingungen [y 0 = 0, y L = 0, y' 0 = 0, y' L = 0]",

	     "FunktionsVariable x"],

	    ("Biegelinie", ["Biegelinien"],

	     ["IntegrierenUndKonstanteBestimmen2"] ))];

moveActiveRoot 1;

(*

trace_script := true; autoCalculate 1 CompleteCalc; trace_script := false;

##7.69##          ordered           subst                   2x2

          c_4           c_3         

c c_2 c_3 c_4     c c_2 c_3	    1:c_3 -> 2:c c_2        2:         c c_2

      c_3                   c_4	 			   

c c_2 c_3         c c_2 c_3 c_4     3:c_4 -> 4:c c_2 c_3    1:c_3 -> 4:c c_2*)

val t = str2term"[0 = c_4 + 0 / (-1 * EI),                                   \

\ 0 = c_4 + L * c_3 + (12 * L ^^^ 2 * c_2 + 4 * L ^^^ 3 * c + -1 * L ^^^ 4 * q_0) / (-24 * EI),                                                              \

\ 0 = c_3 + 0 / (-1 * EI),                                                   \

\ 0 = c_3 + (6 * L * c_2 + 3 * L ^^^ 2 * c + -1 * L ^^^ 3 * q_0) / (-6 * EI)]";

"------- Bsp 7.70";

states:=[];

CalcTree [(["Traegerlaenge L","Streckenlast q_0","Biegelinie y",

	     "Randbedingungen [Q 0 = q_0 * L, M_b L = 0, y 0 = 0, y' 0 = 0]",

	     "FunktionsVariable x"],