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test/Tools/isac/Knowledge/eqsystem-2.sml
author wneuper <Walther.Neuper@jku.at>
Thu, 04 Aug 2022 12:48:37 +0200
changeset 60509 2e0b7ca391dc
parent 60500 59a3af532717
child 60549 c0a775618258
permissions -rw-r--r--
polish naming in Rewrite_Order 
     1 (* Title: Knowledge/eqsystem-2.sml

     2    author: Walther Neuper 050826,

     3    (c) due to copyright terms

     4 *)

     5 

     6 "-----------------------------------------------------------------";

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

     8 "-----------------------------------------------------------------";

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

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

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

    12 "----------- rewrite in [EqSystem,normalise,2x2] -----------------";

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

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

    15 "----------- rewrite in [EqSystem,normalise,4x4] -----------------";

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

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

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

    19 "----------- me [EqSystem,normalise,2x2] -------------------------";

    20 (*^^^--- eqsystem-1.sml ######### together exceed resources here, but not in Test_Isac.thy #####

    21   vvv--- eqsystem-2.sml ######### together exceed resources here, but not in Test_Isac.thy #####*)

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

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

    24 "----------- 4x4 systems from Biegelinie -------------------------";

    25 "-----------------------------------------------------------------";

    26 "-----------------------------------------------------------------";

    27 "-----------------------------------------------------------------";

    28 

    29 val thy = @{theory "EqSystem"};

    30 val ctxt = Proof_Context.init_global thy;

    31 

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

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

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

    35 val fmz = 

    36     ["equalities\

    37      \[0 = c_2 + c * 0 + 1 / EI * (L * q_0 / 12 * 0 \<up> 3 +                \

    38      \                                            - 1 * q_0 / 24 * 0 \<up> 4),\

    39      \ 0 = c_2 + c * L + 1 / EI * (L * q_0 / 12 * L \<up> 3 +                \

    40      \                                            - 1 * q_0 / 24 * L \<up> 4)]",

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

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

    43   ("Biegelinie",["LINEAR", "system"], ["no_met"]);

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

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

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

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

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

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

    50 case nxt of (Specify_Method ["EqSystem", "normalise", "2x2"]) => ()

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

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

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

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

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

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

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

    58 if f2str f =(*BEFORE "eliminate ThmC.numerals_to_Free"..

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

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

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

    62 case nxt of

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

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

    65 

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

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

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

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

    70 case nxt of

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

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

    73 

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

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

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

    77 (*[

    78 (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]])),

    79 (2 ,[1] ,true ,#Given ,Cor solveForVars [c, c_2] ,(v_s, [[c, c_2]])),

    80 (3 ,[1] ,true ,#Find ,Cor solution ss___ ,(ss___, [ss___]))]

    81 *)

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

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

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

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

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

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

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

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

    90 case nxt of

    91     (Check_Postcond ["triangular", "2x2", "LINEAR", "system"]) => ()

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

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

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

    95 

    96 if f2str f =(*BEFORE "eliminate ThmC.numerals_to_Free"..

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

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

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

   100 case nxt of

   101     (End_Proof') => ()

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

   103 

   104 

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

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

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

   108 val thy = @{theory Isac_Knowledge}

   109 val subst = 

   110   [(TermC.str2term "bdv_1", TermC.str2term "c"), (TermC.str2term "bdv_2", TermC.str2term "c_2"),

   111 	(TermC.str2term "bdv_3", TermC.str2term "c_3"), (TermC.str2term "bdv_4", TermC.str2term "c_4")]; 

   112 

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

   114 reset_states ();

   115 CalcTree [(

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

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

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

   119 moveActiveRoot 1;

   120 (*

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

   122 ##7.27##          ordered           substs

   123           c_4       c_2           

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

   125   c_2                       c_4	  

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

   127 val t = TermC.str2term

   128   ("[0 = c_4, " ^

   129   "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), " ^

   130   "0 = c_2, " ^

   131   "0 = (2 * c_2 + 2 * L * c + - 1 * L \<up> 2 * q_0) / 2]");

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

   133 if UnparseC.term t =

   134 "[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]"

   135 then () else error "Bsp 7.27";

   136 

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

   138 val t = TermC.str2term "0 = (2 * c_2 + 2 * L * c + - 1 * L \<up> 2 * q_0) / 2";

   139 val NONE = rewrite_set_ ctxt false norm_Rational t;

   140 val SOME (t,_) = 

   141     rewrite_set_inst_ ctxt false subst simplify_System_parenthesized t;

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

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

   144 

   145 "--- isolate_bdvs_4x4";

   146 (*

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

   148 UnparseC.term t;

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

   150 UnparseC.term t;

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

   152 UnparseC.term t;

   153 *)

   154 

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

   156 reset_states ();

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

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

   159 	    "Biegelinie y",

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

   161 	    "FunktionsVariable x"],

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

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

   164 (*

   165 moveActiveRoot 1;

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

   167 *)

   168 

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

   170 reset_states ();

   171 CalcTree [(

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

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

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

   175 moveActiveRoot 1;

   176 (*

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

   178 ##7.69##          ordered           subst                   2x2

   179           c_4           c_3         

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

   181       c_3                   c_4	 			   

   182 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*)

   183 val t = TermC.str2term 

   184   ("[0 = c_4 + 0 / (- 1 * EI), " ^

   185   "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), " ^

   186   "0 = c_3 + 0 / (- 1 * EI), " ^

   187   "0 = c_3 + (6 * L * c_2 + 3 * L \<up> 2 * c + - 1 * L \<up> 3 * q_0) / (-6 * EI)]");

   188 

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

   190 reset_states ();

   191 CalcTree [(

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

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

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

   195 moveActiveRoot 1;

   196 (*

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

   198 ##7.70##        |subst

   199 c		|

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

   201       c_3	|

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

   203 

   204 "----- 7.70 go through the rewrites in met_eqsys_norm_4x4";

   205 val t = TermC.str2term

   206   ("[L * q_0 = c, " ^

   207   "0 = (2 * c_2 + 2 * L * c + - 1 * L \<up> 2 * q_0) / 2, " ^

   208   "0 = c_4, " ^

   209   "0 = c_3]");

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

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

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

   213 if UnparseC.term t = 

   214   "[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]"

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

   216 

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

   218 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]"

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

   220 

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

   222 if UnparseC.term t =

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

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

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

   226 

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

   228 if UnparseC.term t =

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

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

   231 

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

   233 if UnparseC.term t =

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

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

   236 

   237 "----- 7.70 with met normalise: ";

   238 val fmz = ["equalities" ^

   239   "[L * q_0 = c, " ^

   240   "0 = (2 * c_2 + 2 * L * c + - 1 * L \<up> 2 * q_0) / 2, " ^

   241   "0 = c_4, " ^

   242   "0 = c_3]", "solveForVars [c, c_2, c_3, c_4]", "solution LL"];

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

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

   245 

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

   247   in next but one test below the same type error.

   248 /-------------------------------------------------------\

   249 Type unification failed

   250 Type error in application: incompatible operand type

   251 

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

   253 Operand:   [c_4] :: 'b list

   254 \-------------------------------------------------------/

   255 

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

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

   258 val (p,_,f,nxt,_,pt) = me nxt p c pt;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 case nxt of (_,Apply_Method ["EqSystem", "normalise", "4x4"]) => ()

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

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

   264 

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

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

   267   since associate Rewrite .. Rewrite_Set

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

   269 

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

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

   272 

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

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

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

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

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

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

   279 --------------------------------------------------------------------------*)

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

   281 

   282 "----- 7.70 with met top_down_: me";

   283 val fmz = [

   284   "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]",

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

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

   287   ("Biegelinie",["LINEAR", "system"],["no_met"]);

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

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

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

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

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

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

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

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

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

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

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

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

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

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

   302 if p = ([], Res) andalso

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

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

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

   306 

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

   308 reset_states ();

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

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

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

   312 	     "AbleitungBiegelinie dy"],

   313 	    ("Biegelinie", ["Biegelinien"],

   314 	     ["IntegrierenUndKonstanteBestimmen2"] ))];

   315 moveActiveRoot 1;

   316 (*

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

   318 ##7.71##       |ordered       |subst.singles (recurs) |2x2       |diagonal

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

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

   321 c c_2 c_3 c_4  |          c_4 |3'                     |	         |

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

   323 val t = TermC.str2term"[0 = (2 * c_2 + 2 * L * c + - 1 * L \<up> 2 * q_0) / 2, \

   324 \ 0 = c_4 + 0 / (- 1 * EI),                            \

   325 \ 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),\

   326 \ 0 = c_3 + 0 / (- 1 * EI)]";

   327 

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

   329 reset_states ();

   330 CalcTree [(["Traegerlaenge L",

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

   332 	    "Biegelinie y",

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

   334 	    "FunktionsVariable x"],

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

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

   337 moveActiveRoot 1;

   338 (*

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

   340 *)

   341 

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

   343 reset_states ();

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

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

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

   347 	    "AbleitungBiegelinie dy"],

   348 	   ("Biegelinie", ["Biegelinien"],

   349 	    ["IntegrierenUndKonstanteBestimmen2"] ))];

   350 moveActiveRoot 1;

   351 (*

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

   353 ##7.72b##      |ord. |subst.singles         |ord.triang.

   354   c_2          |     |			    |c_2  

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

   356           c_4  |     |			    |

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

   358 val t = TermC.str2term"[0 = c_2,                                            \

   359 \ 0 = (6 * c_2 + 6 * L * c + - 1 * L \<up> 2 * q_0) / 6, \

   360 \ 0 = c_4 + 0 / (- 1 * EI),                            \

   361 \ 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)]";

   362 

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

   364 reset_states ();

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

   366 	    "Biegelinie y",

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

   368 	    "FunktionsVariable x"],

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

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

   371 moveActiveRoot 1;

   372 (*

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

   374 *)

   375 

   376 "----------- 4x4 systems from Biegelinie -------------------------";

   377 "----------- 4x4 systems from Biegelinie -------------------------";

   378 "----------- 4x4 systems from Biegelinie -------------------------";

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

   380 "----- Bsp 7.27";

   381 val fmz = ["equalities \

   382 	   \[0 = c_4,                           \

   383 	   \ 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),                                       \

   384 	   \ 0 = c_2,                                           \

   385 	   \ 0 = (2 * c_2 + 2 * L * c + - 1 * L \<up> 2 * q_0) / 2]", 

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

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

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

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

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

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

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

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

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

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

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

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

   398 "[0 = c_4,                                          \

   399 \ 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),                                   \

   400 \ 0 = c_2,                                          \

   401 \ 0 = (2 * c_2 + 2 * L * c + - 1 * L \<up> 2 * q_0) / 2]";

   402 (*vvvWN080102 Exception- Match raised 

   403   since associate Rewrite .. Rewrite_Set

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

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

   406 "[0 = c_4,                                  \

   407 \ 0 = - 1 * q_0 * L \<up> 4 / (- 24 * EI) +     \

   408 \     (4 * L \<up> 3 * c / (- 24 * EI) +       \

   409 \     (12 * L \<up> 2 * c_2 / (- 24 * EI) +    \

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

   411 \ 0 = c_2,                                  \

   412 \ 0 = - 1 * q_0 * L \<up> 2 / 2 + (L * c + c_2)]";

   413 (*? "(4 * L \<up> 3 / (- 24 * EI) * c" statt "(4 * L \<up> 3 * c / (- 24 * EI)" ?*)

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

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

   416 "[c_4 = 0,\

   417 \ 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),\

   418 \ c_2 = 0, \

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

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

   421 

   422 ---------------------------------------------------------------------*)
wneuper/isa