1 (* Title: Knowledge/eqsystem-2.sml
2 author: Walther Neuper 050826,
3 (c) due to copyright terms
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 "-----------------------------------------------------------------";
29 val thy = @{theory "EqSystem"};
30 val ctxt = Proof_Context.init_global thy;
32 "----------- me [linear,system] ..normalise..top_down_sub..-------";
33 "----------- me [linear,system] ..normalise..top_down_sub..-------";
34 "----------- me [linear,system] ..normalise..top_down_sub..-------";
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"];
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";
63 (Subproblem ("Biegelinie", ["triangular", "2x2", "LINEAR",_])) => ()
64 | _ => error "eqsystem.sml me [linear,system] SubProblem b";
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;
71 (Specify_Method ["EqSystem", "top_down_substitution", "2x2"]) => ()
72 | _ => error "eqsystem.sml me [EqSys...2x2] top_down_substitution b";
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;
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___]))]
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;
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;
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";
102 | _ => error "eqsystem.sml me [EqSys...2x2] finished End_Proof'";
105 "----------- all systems from Biegelinie -------------------------";
106 "----------- all systems from Biegelinie -------------------------";
107 "----------- all systems from Biegelinie -------------------------";
108 val thy = @{theory Isac_Knowledge}
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")];
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"]))];
121 LItool.trace_on := true; autoCalculate 1 CompleteCalc; LItool.trace_on := false;
122 ##7.27## ordered substs
124 c c_2 c_3 c_4 c c_2 1->2: c
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
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), " ^
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;
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";
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;
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";
145 "--- isolate_bdvs_4x4";
147 val SOME (t,_) = rewrite_set_inst_ ctxt false subst isolate_bdvs_4x4 t;
149 val SOME (t,_) = rewrite_set_inst_ ctxt false subst simplify_System t;
151 val SOME (t,_) = rewrite_set_ ctxt false order_system t;
155 "------- Bsp 7.28 ---------------vvvvvvvvvvvvv Momentenlinie postponed";
157 CalcTree [((*WN130908 <ERROR> error in kernel </ERROR>*)
158 ["Traegerlaenge L", "Momentenlinie (-q_0 / L * x \<up> 3 / 6)",
160 "Randbedingungen [y L = 0, y' L = 0]",
161 "FunktionsVariable x"],
162 ("Biegelinie", ["vonMomentenlinieZu", "Biegelinien"],
163 ["Biegelinien", "AusMomentenlinie"]))];
166 LItool.trace_on := true; autoCalculate 1 CompleteCalc; LItool.trace_on := false;
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"]))];
177 LItool.trace_on := true; autoCalculate 1 CompleteCalc; LItool.trace_on := false;
178 ##7.69## ordered subst 2x2
180 c c_2 c_3 c_4 c c_2 c_3 1:c_3 -> 2:c c_2 2: c c_2
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)]");
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"] ))];
197 LItool.trace_on := true; autoCalculate 1 CompleteCalc; LItool.trace_on := false;
202 c_4 | STOPPED.WN06? test methods @@@@@@@@@@@@@@@@@@@@@@@*)
204 "----- 7.70 go through the rewrites in met_eqsys_norm_4x4";
205 val t = TermC.str2term
207 "0 = (2 * c_2 + 2 * L * c + - 1 * L \<up> 2 * q_0) / 2, " ^
210 val SOME (t,_) = rewrite_ ctxt e_rew_ord Rule_Set.empty false @{thm commute_0_equality} t;
211 val SOME (t,_) = rewrite_ ctxt e_rew_ord Rule_Set.empty false @{thm commute_0_equality} t;
212 val SOME (t,_) = rewrite_ ctxt e_rew_ord Rule_Set.empty false @{thm commute_0_equality} 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";
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";
221 val SOME (t,_) = rewrite_set_inst_ ctxt false subst isolate_bdvs_4x4 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";
227 val SOME (t,_) = rewrite_set_inst_ ctxt false subst simplify_System_parenthesized 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";
232 val SOME (t, _) = rewrite_set_ ctxt false order_system 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";
237 "----- 7.70 with met normalise: ";
238 val fmz = ["equalities" ^
240 "0 = (2 * c_2 + 2 * L * c + - 1 * L \<up> 2 * q_0) / 2, " ^
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 = [];
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
252 Operator: op # c_3 :: 'a list \<Rightarrow> 'a list
253 Operand: [c_4] :: 'b list
254 \-------------------------------------------------------/
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;
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;
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;
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 ==============================================*)
282 "----- 7.70 with met top_down_: me";
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"];
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";
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"] ))];
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)]";
328 "------- Bsp 7.72a ---------------vvvvvvvvvvvvv Momentenlinie postponed";
330 CalcTree [(["Traegerlaenge L",
331 "Momentenlinie ((q_0 * L)/ 6 * x - q_0 /(6 * L) * x \<up> ^3)",
333 "Randbedingungen [y 0 = (0::real), y L = 0]",
334 "FunktionsVariable x"],
335 ("Biegelinie", ["vonMomentenlinieZu", "Biegelinien"],
336 ["Biegelinien", "AusMomentenlinie"]))];
339 LItool.trace_on := true; autoCalculate 1 CompleteCalc; LItool.trace_on := false;
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"] ))];
352 LItool.trace_on := true; autoCalculate 1 CompleteCalc; LItool.trace_on := false;
353 ##7.72b## |ord. |subst.singles |ord.triang.
355 c c_2 | |1:c_2 -> 2':c |c_2 c
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)]";
363 "------- Bsp 7.73 ---------------vvvvvvvvvvvvv Momentenlinie postponed";
365 CalcTree [(["Traegerlaenge L", "Momentenlinie ???",(*description unclear*)
367 "Randbedingungen [y L = 0, y' L = 0]",
368 "FunktionsVariable x"],
369 ("Biegelinie", ["vonMomentenlinieZu", "Biegelinien"],
370 ["Biegelinien", "AusMomentenlinie"]))];
373 LItool.trace_on := true; autoCalculate 1 CompleteCalc; LItool.trace_on := false;
376 "----------- 4x4 systems from Biegelinie -------------------------";
377 "----------- 4x4 systems from Biegelinie -------------------------";
378 "----------- 4x4 systems from Biegelinie -------------------------";
379 (*STOPPED.WN08?? replace this test with 7.70 *)
381 val fmz = ["equalities \
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), \
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"];
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;
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), \
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;
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))), \
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;
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),\
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;
422 ---------------------------------------------------------------------*)