(* Title: Knowledge/eqsystem-2.sml

   author: Walther Neuper 050826,

   (c) due to copyright terms

*)

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

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

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

"----------- occur_exactly_in ---------------------------------------------------equsystem-1.sml";

"----------- problems -----------------------------------------------------------equsystem-1.sml";

"----------- rewrite-order ord_simplify_System ----------------------------------equsystem-1.sml";

"----------- rewrite in [EqSystem,normalise,2x2] --------------------------------equsystem-1.sml";

"----------- rewrite example from 2nd [EqSystem,normalise,2x2] ------------------equsystem-1.sml";

"----------- rewrite in [EqSystem,top_down_substitution,2x2] --------------------equsystem-1.sml";

"----------- rewrite in [EqSystem,normalise,4x4] --------------------------------equsystem-1.sml";

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

"----------- refine [linear,system]----------------------------------------------equsystem-1.sml";

"----------- refine [2x2,linear,system] search error-----------------------------equsystem-1.sml";

"----------- me [EqSystem,normalise,2x2], refine Subproblem ---------------------equsystem-1.sml";

"----------- me [EqSystem,normalise,2x2], refine Subproblem, step into istate---equsystem-1a.sml";

"----------- me [linear,system] ..normalise..top_down_sub..----------------------equsystem-2.sml";

"----------- all systems from Biegelinie ----------------------------------------equsystem-2.sml";

"----------- 4x4 systems from Biegelinie ----------------------------------------equsystem-2.sml";

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

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

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

val thy = @{theory "EqSystem"};

val ctxt = Proof_Context.init_global thy;

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

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

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

val fmz = 

    ["equalities\

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

     \                                            - 1 * q_0 / 24 * 0 \<up> 4),\

     \ 0 = c_2 + c * L + 1 / EI * (L * q_0 / 12 * L \<up> 3 +                \

     \                                            - 1 * q_0 / 24 * L \<up> 4)]",

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

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", "normalise", "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 =(*BEFORE "eliminate ThmC.numerals_to_Free"..

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

  "[c_2 = 0, L * c + c_2 = - 1 * q_0 * L \<up> 4 / 24]"

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 (I_Model.to_string (Proof_Context.init_global @{theory Isac_Knowledge}))) probl;

(*[

(1 ,[1] ,true ,#Given ,Cor equalities [c_2 = 0, L * c + c_2 = q_0 * L \<up> 2 / 2] ,(es_, [[c_2 = 0, L * c + c_2 = q_0 * L \<up> 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 =(*BEFORE "eliminate ThmC.numerals_to_Free"..

  "[c = - 1 * q_0 * L \<up> 3 / (24 * EI), c_2 = 0]"*)

  "[c = - 1 * q_0 * L \<up> 3 / 24, 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'";

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

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

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

val thy = @{theory Isac_Knowledge}

val subst = 

  [(TermC.parse_test @{context} "bdv_1", TermC.parse_test @{context} "c"), (TermC.parse_test @{context} "bdv_2", TermC.parse_test @{context} "c_2"),

	(TermC.parse_test @{context} "bdv_3", TermC.parse_test @{context} "c_3"), (TermC.parse_test @{context} "bdv_4", TermC.parse_test @{context} "c_4")]; 

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

States.reset ();

CalcTree [(

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

	  "Randbedingungen [y 0 = (0::real), y L = 0, M_b 0 = 0, M_b L = 0]", "FunktionsVariable x"],

	("Biegelinie", ["Biegelinien"], ["IntegrierenUndKonstanteBestimmen2"]))];

moveActiveRoot 1;

(*

LItool.trace_on := true; autoCalculate 1 CompleteCalc; LItool.trace_on := 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 = TermC.parse_test @{context}

  ("[0 = c_4, " ^

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

  "0 = c_2, " ^

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

val SOME (t, _) = rewrite_set_ ctxt false isolate_bdvs_4x4 t;

if UnparseC.term t =

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

then () else error "Bsp 7.27";

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

val t = TermC.parse_test @{context} "0 = (2 * c_2 + 2 * L * c + - 1 * L \<up> 2 * q_0) / 2";

val NONE = rewrite_set_ ctxt false norm_Rational t;

val SOME (t,_) = 

    rewrite_set_inst_ ctxt false subst simplify_System_parenthesized t;

if UnparseC.term t = "0 = - 1 * q_0 * L \<up> 2 / 2 + (L * c + c_2)"

then () else error "Bsp 7.27 go through the rewrites in met_eqsys_norm_4x4";

"--- isolate_bdvs_4x4";

(*

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

UnparseC.term t;

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

UnparseC.term t;

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

UnparseC.term t;

*)

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

States.reset ();

CalcTree [((*WN130908  <ERROR> error in kernel </ERROR>*)

  ["Traegerlaenge L", "Momentenlinie (-q_0 / L * x \<up> 3 / 6)",

	    "Biegelinie y",

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

	    "FunktionsVariable x"],

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

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

(*

moveActiveRoot 1;

LItool.trace_on := true; autoCalculate 1 CompleteCalc; LItool.trace_on := false;

*)

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

States.reset ();

CalcTree [(

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

	  "Randbedingungen [y 0 = (0::real), y L = 0, y' 0 = 0, y' L = 0]", "FunktionsVariable x"],

	("Biegelinie", ["Biegelinien"], ["IntegrierenUndKonstanteBestimmen2"]))];

moveActiveRoot 1;

(*

LItool.trace_on := true; autoCalculate 1 CompleteCalc; LItool.trace_on := 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 = TermC.parse_test @{context} 

  ("[0 = c_4 + 0 / (- 1 * EI), " ^

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

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

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

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

States.reset ();

CalcTree [(

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

	  "Randbedingungen [Q 0 = q_0 * L, M_b L = 0, y 0 = (0::real), y' 0 = 0]", "FunktionsVariable x"],

	("Biegelinie", ["Biegelinien"], ["IntegrierenUndKonstanteBestimmen2"] ))];

moveActiveRoot 1;

(*

LItool.trace_on := true; autoCalculate 1 CompleteCalc; LItool.trace_on := false;

##7.70##        |subst

c		|

c c_2           |1:c -> 2:c_2

      c_3	|

          c_4   |            STOPPED.WN06? test methods @@@@@@@@@@@@@@@@@@@@@@@*)

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

val t = TermC.parse_test @{context}

  ("[L * q_0 = c, " ^

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

  "0 = c_4, " ^

  "0 = c_3]");

val SOME (t,_) = rewrite_ ctxt Rewrite_Ord.function_empty Rule_Set.empty false @{thm commute_0_equality} t;

val SOME (t,_) = rewrite_ ctxt Rewrite_Ord.function_empty Rule_Set.empty false @{thm commute_0_equality} t;

val SOME (t,_) = rewrite_ ctxt Rewrite_Ord.function_empty Rule_Set.empty false @{thm commute_0_equality} t;

if UnparseC.term t = 

  "[L * q_0 = c, (2 * c_2 + 2 * L * c + - 1 * L \<up> 2 * q_0) / 2 = 0,\n c_4 = 0, c_3 = 0]"

then () else error "7.70 go through the rewrites in met_eqsys_norm_4x4, 1";

val SOME (t,_) = rewrite_set_inst_ ctxt false subst simplify_System_parenthesized t;

if UnparseC.term t = "[L * q_0 = c, - 1 * q_0 * L \<up> 2 / 2 + (L * c + c_2) = 0, c_4 = 0,\n c_3 = 0]"

then () else error "7.70 go through the rewrites in met_eqsys_norm_4x4, 2";

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

if UnparseC.term t =

   "[c = (- 1 * (L * q_0) + 0) / - 1,\n" ^ 

   " L * c + c_2 = - 1 * (- 1 * q_0 * L \<up> 2 / 2) + 0, c_4 = 0, c_3 = 0]"

then () else error "7.70 go through the rewrites in met_eqsys_norm_4x4, 3";

val SOME (t,_) = rewrite_set_inst_ ctxt false subst simplify_System_parenthesized t;

if UnparseC.term t =

  "[c = - 1 * L * q_0 / - 1, L * c + c_2 = q_0 * L \<up> 2 / 2, c_4 = 0,\n c_3 = 0]"

then () else error "7.70 go through the rewrites in met_eqsys_norm_4x4, 4";

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

if UnparseC.term t =

  "[c = - 1 * L * q_0 / - 1, L * c + c_2 = q_0 * L \<up> 2 / 2, c_3 = 0,\n c_4 = 0]"

then () else error "eqsystem.sml: exp 7.70 normalise 4x4 by rewrite changed";

"----- 7.70 with met normalise: ";

val fmz = ["equalities" ^

  "[L * q_0 = c, " ^

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

  "0 = c_4, " ^

  "0 = c_3]", "solveForVars [c, c_2, c_3, c_4]", "solution LL"];

val (dI',pI',mI') = ("Biegelinie",["LINEAR", "system"], ["no_met"]);

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

(*============ inhibit exn WN120314 TODO: investigate type error (same as above)==

  in next but one test below the same type error.

/-------------------------------------------------------\

Type unification failed

Type error in application: incompatible operand type

Operator:  op # c_3 :: 'a list \<Rightarrow> 'a list

Operand:   [c_4] :: 'b list

\-------------------------------------------------------/

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

case nxt of (_,Apply_Method ["EqSystem", "normalise", "4x4"]) => ()

	  | _ => error "eqsystem.sml [EqSystem,normalise,4x4] specify";

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

"----- outcommented before Isabelle2002 --> 2011 -------------------------";

(*-----------------------------------vvvWN080102 Exception- Match raised 

  since associate Rewrite .. Rewrite_Set

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;

if f2str f ="[c = L * q_0, L * c + c_2 = q_0 * L \<up> 2 / 2, c_3 = 0, c_4 = 0]" 

then () else error "eqsystem.sml: exp 7.70 normalise 4x4 by met changed";

--------------------------------------------------------------------------*)

============ inhibit exn WN120314 ==============================================*)

"----- 7.70 with met top_down_: me";

val fmz = [

  "equalities [(c::real) = L * q_0, L * c + (c_2::real) = q_0 * L \<up> 2 / 2, (c_3::real) = 0, (c_4::real) = 0]",

	"solveForVars [(c::real), (c_2::real), (c_3::real), (c_4::real)]", "solution LL"];

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

case nxt of Apply_Method ["EqSystem", "top_down_substitution", "4x4"] => ()

	  | _ => error "eqsystem.sml [EqSystem,top_down_,4x4] specify";

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;

if p = ([], Res) andalso

(*           "[c = L * q_0, c_2 = - 1 * L \<up> 2 * q_0 / 2, c_3 = 0, c_4 = 0]"*)

   f2str f = "[c = L * q_0, c_2 = - 1 * L \<up> 2 * q_0 / 2, c_3 = 0, c_4 = 0]"

then () else error "eqsystem.sml: 7.70 with met top_down_: me";

"------- Bsp 7.71";

States.reset ();

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

	     "Randbedingungen [M_b L = 0, y 0 = (0::real), y L = 0, y' 0 = 0]",

	     "FunktionsVariable x", "GleichungsVariablen [c, c_2, c_3, c_4]",

	     "AbleitungBiegelinie dy"],

	    ("Biegelinie", ["Biegelinien"],

	     ["IntegrierenUndKonstanteBestimmen2"] ))];

moveActiveRoot 1;

(*

LItool.trace_on := true; autoCalculate 1 CompleteCalc; LItool.trace_on := false;

##7.71##       |ordered       |subst.singles (recurs) |2x2       |diagonal

c c_2          |c c_2	      |1'		      |1': c c_2 |

          c_4  |      c_3     |2:c_3 -> 4' :c c_2 c_4 |	         |

c c_2 c_3 c_4  |          c_4 |3'                     |	         |

      c_3      |c c_2 c_3 c_4 |3:c_4 -> 4'':c c_2     |4'':c c_2 |      *)

val t = TermC.parse_test @{context}"[0 = (2 * c_2 + 2 * L * c + - 1 * L \<up> 2 * q_0) / 2, \

\ 0 = c_4 + 0 / (- 1 * EI),                            \

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

\ 0 = c_3 + 0 / (- 1 * EI)]";

"------- Bsp 7.72a ---------------vvvvvvvvvvvvv Momentenlinie postponed";

States.reset ();

CalcTree [(["Traegerlaenge L",

	    "Momentenlinie ((q_0 * L)/ 6 * x - q_0 /(6 * L) * x \<up> ^3)",

	    "Biegelinie y",

	    "Randbedingungen [y 0 = (0::real), y L = 0]",

	    "FunktionsVariable x"],

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

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

moveActiveRoot 1;

(*

LItool.trace_on := true; autoCalculate 1 CompleteCalc; LItool.trace_on := false;

*)

"------- Bsp 7.72b";

States.reset ();

CalcTree [(["Traegerlaenge L", "Streckenlast (q_0 / L * x)", "Biegelinie y",

	    "Randbedingungen [M_b 0 = 0, M_b L = 0, y 0 = (0::real), y L = 0]",

	    "FunktionsVariable x", "GleichungsVariablen [c, c_2, c_3, c_4]",

	    "AbleitungBiegelinie dy"],

	   ("Biegelinie", ["Biegelinien"],

	    ["IntegrierenUndKonstanteBestimmen2"] ))];

moveActiveRoot 1;

(*

LItool.trace_on := true; autoCalculate 1 CompleteCalc; LItool.trace_on := false;

##7.72b##      |ord. |subst.singles         |ord.triang.

  c_2          |     |			    |c_2  

c c_2	       |     |1:c_2 -> 2':c	    |c_2 c

          c_4  |     |			    |

c c_2 c_3 c_4  |     |3:c_4 -> 4':c c_2 c_3 |c_2 c c_3*)

val t = TermC.parse_test @{context}"[0 = c_2,                                            \

\ 0 = (6 * c_2 + 6 * L * c + - 1 * L \<up> 2 * q_0) / 6, \

\ 0 = c_4 + 0 / (- 1 * EI),                            \

\ 0 = c_4 + L * c_3 + (60 * L \<up> 2 * c_2 + 20 * L \<up> 3 * c + - 1 * L \<up> 4 * q_0) / (- 120 * EI)]";

"------- Bsp 7.73 ---------------vvvvvvvvvvvvv Momentenlinie postponed";

States.reset ();

CalcTree [(["Traegerlaenge L", "Momentenlinie ???",(*description unclear*)

	    "Biegelinie y",

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

	    "FunktionsVariable x"],

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

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

moveActiveRoot 1;

(*

LItool.trace_on := true; autoCalculate 1 CompleteCalc; LItool.trace_on := false;

*)

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

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

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

(*STOPPED.WN08?? replace this test with 7.70 *)

"----- Bsp 7.27";

val fmz = ["equalities \

	   \[0 = c_4,                           \

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

	   \ 0 = c_2,                                           \

	   \ 0 = (2 * c_2 + 2 * L * c + - 1 * L \<up> 2 * q_0) / 2]", 

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

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

  ("Biegelinie",["normalise", "4x4", "LINEAR", "system"],

   ["EqSystem", "normalise", "4x4"]);

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

"------------------------------------------- Apply_Method...";

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

"[0 = c_4,                                          \

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

\ 0 = c_2,                                          \

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

(*vvvWN080102 Exception- Match raised 

  since associate Rewrite .. Rewrite_Set

"------------------------------------------- simplify_System_parenthesized...";

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

"[0 = c_4,                                  \

\ 0 = - 1 * q_0 * L \<up> 4 / (- 24 * EI) +     \

\     (4 * L \<up> 3 * c / (- 24 * EI) +       \

\     (12 * L \<up> 2 * c_2 / (- 24 * EI) +    \

\     (L * c_3 + c_4))),                    \

\ 0 = c_2,                                  \

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

(*? "(4 * L \<up> 3 / (- 24 * EI) * c" statt "(4 * L \<up> 3 * c / (- 24 * EI)" ?*)

"------------------------------------------- isolate_bdvs...";

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

"[c_4 = 0,\

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

\ c_2 = 0, \

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

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

---------------------------------------------------------------------*)