1 (* chapter 'Biegelinie' from the textbook:
2 Timischl, Kaiser. Ingenieur-Mathematik 3. Wien 1999. p.268-271.
3 author: Walther Neuper 050826,
4 (c) due to copyright terms
7 theory Biegelinie imports Integrate Equation EqSystem Atools begin
11 qq :: "real => real" (* Streckenlast *)
12 Q :: "real => real" (* Querkraft *)
13 Q' :: "real => real" (* Ableitung der Querkraft *)
14 M'_b :: "real => real" ("M'_b") (* Biegemoment *)
15 M'_b' :: "real => real" ("M'_b'") (* Ableitung des Biegemoments *)
16 y'' :: "real => real" (* 2.Ableitung der Biegeline *)
17 y' :: "real => real" (* Neigung der Biegeline *)
18 (*y :: "real => real" (* Biegeline *)*)
19 EI :: "real" (* Biegesteifigkeit *)
21 (*new Descriptions in the related problems*)
22 Traegerlaenge :: "real => una"
23 Streckenlast :: "real => una"
24 BiegemomentVerlauf :: "bool => una"
25 Biegelinie :: "(real => real) => una"
26 Randbedingungen :: "bool list => una"
27 RandbedingungenBiegung :: "bool list => una"
28 RandbedingungenNeigung :: "bool list => una"
29 RandbedingungenMoment :: "bool list => una"
30 RandbedingungenQuerkraft :: "bool list => una"
31 FunktionsVariable :: "real => una"
32 Funktionen :: "bool list => una"
33 Gleichungen :: "bool list => una"
36 Biegelinie2Script :: "[real,real,real,real=>real,bool list,
38 ("((Script Biegelinie2Script (_ _ _ _ _ =))// (_))" 9)
39 BiegelinieScript :: "[real,real,real,real=>real,bool list,bool list,
41 ("((Script BiegelinieScript (_ _ _ _ _ _ =))// (_))" 9)
42 Biege2xIntegrierenScript :: "[real,real,real,bool,real=>real,bool list,
44 ("((Script Biege2xIntegrierenScript (_ _ _ _ _ _ =))// (_))" 9)
45 Biege4x4SystemScript :: "[real,real,real,real=>real,bool list,
47 ("((Script Biege4x4SystemScript (_ _ _ _ _ =))// (_))" 9)
48 Biege1xIntegrierenScript ::
49 "[real,real,real,real=>real,bool list,bool list,bool list,
51 ("((Script Biege1xIntegrierenScript (_ _ _ _ _ _ _ =))// (_))" 9)
52 Belastung2BiegelScript :: "[real,real,
53 bool list] => bool list"
54 ("((Script Belastung2BiegelScript (_ _ =))// (_))" 9)
55 SetzeRandbedScript :: "[bool list,bool list,
56 bool list] => bool list"
57 ("((Script SetzeRandbedScript (_ _ =))// (_))" 9)
59 axioms(*axiomatization where*)
61 Querkraft_Belastung: "Q' x = -qq x" (*and*)
62 Belastung_Querkraft: "-qq x = Q' x" (*and*)
64 Moment_Querkraft: "M_b' x = Q x" (*and*)
65 Querkraft_Moment: "Q x = M_b' x" (*and*)
67 Neigung_Moment: "y'' x = -M_b x/ EI" (*and*)
68 Moment_Neigung: "M_b x = -EI * y'' x" (*and*)
70 (*according to rls 'simplify_Integral': .. = 1/a * .. instead .. = ../ a*)
71 make_fun_explicit: "Not (a =!= 0) ==> (a * (f x) = b) = (f x = 1/a * b)"
76 (** theory elements for transfer into html **)
78 store_isa ["IsacKnowledge"] [];
80 ["Walther Neuper 2005 supported by a grant from NMI Austria"];
81 store_isa ["IsacKnowledge", theory2thyID thy, "Theorems"]
82 ["Walther Neuper 2005 supported by a grant from NMI Austria"];
83 store_thm thy "IsacKnowledge" ("Belastung_Querkraft", prop_of @{thm Belastung_Querkraft})
84 ["Walther Neuper 2005 supported by a grant from NMI Austria"];
85 store_thm thy "IsacKnowledge" ("Moment_Neigung", prop_of @{thm Moment_Neigung})
86 ["Walther Neuper 2005 supported by a grant from NMI Austria"];
87 store_thm thy "IsacKnowledge" ("Moment_Querkraft", prop_of @{thm Moment_Querkraft})
88 ["Walther Neuper 2005 supported by a grant from NMI Austria"];
89 store_thm thy "IsacKnowledge" ("Neigung_Moment", prop_of @{thm Neigung_Moment})
90 ["Walther Neuper 2005 supported by a grant from NMI Austria"];
91 store_thm thy "IsacKnowledge" ("Querkraft_Belastung", prop_of @{thm Querkraft_Belastung})
92 ["Walther Neuper 2005 supported by a grant from NMI Austria"];
93 store_thm thy "IsacKnowledge" ("Querkraft_Moment", prop_of @{thm Querkraft_Moment})
94 ["Walther Neuper 2005 supported by a grant from NMI Austria"];
95 store_thm thy "IsacKnowledge" ("make_fun_explicit", prop_of @{thm make_fun_explicit})
96 ["Walther Neuper 2005 supported by a grant from NMI Austria"];
103 (prep_pbt thy "pbl_bieg" [] e_pblID
105 [("#Given" ,["Traegerlaenge l_l", "Streckenlast q_q"]),
106 (*("#Where",["0 < l_l"]), ...wait for < and handling Arbfix*)
107 ("#Find" ,["Biegelinie b_b"]),
108 ("#Relate",["Randbedingungen r_b"])
110 append_rls "e_rls" e_rls [],
112 [["IntegrierenUndKonstanteBestimmen2"]]));
115 (prep_pbt thy "pbl_bieg_mom" [] e_pblID
116 (["MomentBestimmte","Biegelinien"],
117 [("#Given" ,["Traegerlaenge l_l", "Streckenlast q_q"]),
118 (*("#Where",["0 < l_l"]), ...wait for < and handling Arbfix*)
119 ("#Find" ,["Biegelinie b_b"]),
120 ("#Relate",["RandbedingungenBiegung r_b","RandbedingungenMoment r_m"])
122 append_rls "e_rls" e_rls [],
124 [["IntegrierenUndKonstanteBestimmen"]]));
127 (prep_pbt thy "pbl_bieg_momg" [] e_pblID
128 (["MomentGegebene","Biegelinien"],
130 append_rls "e_rls" e_rls [],
132 [["IntegrierenUndKonstanteBestimmen","2xIntegrieren"]]));
135 (prep_pbt thy "pbl_bieg_einf" [] e_pblID
136 (["einfache","Biegelinien"],
138 append_rls "e_rls" e_rls [],
140 [["IntegrierenUndKonstanteBestimmen","4x4System"]]));
143 (prep_pbt thy "pbl_bieg_momquer" [] e_pblID
144 (["QuerkraftUndMomentBestimmte","Biegelinien"],
146 append_rls "e_rls" e_rls [],
148 [["IntegrierenUndKonstanteBestimmen","1xIntegrieren"]]));
151 (prep_pbt thy "pbl_bieg_vonq" [] e_pblID
152 (["vonBelastungZu","Biegelinien"],
153 [("#Given" ,["Streckenlast q_q","FunktionsVariable v_v"]),
154 ("#Find" ,["Funktionen funs'''"])],
155 append_rls "e_rls" e_rls [],
157 [["Biegelinien","ausBelastung"]]));
160 (prep_pbt thy "pbl_bieg_randbed" [] e_pblID
161 (["setzeRandbedingungen","Biegelinien"],
162 [("#Given" ,["Funktionen fun_s","Randbedingungen r_b"]),
163 ("#Find" ,["Gleichungen equs'''"])],
164 append_rls "e_rls" e_rls [],
166 [["Biegelinien","setzeRandbedingungenEin"]]));
169 (prep_pbt thy "pbl_equ_fromfun" [] e_pblID
170 (["makeFunctionTo","equation"],
171 [("#Given" ,["functionEq fu_n","substitution su_b"]),
172 ("#Find" ,["equality equ'''"])],
173 append_rls "e_rls" e_rls [],
175 [["Equation","fromFunction"]]));
181 val srls = Rls {id="srls_IntegrierenUnd..",
183 rew_ord = ("termlessI",termlessI),
184 erls = append_rls "erls_in_srls_IntegrierenUnd.." e_rls
185 [(*for asm in NTH_CONS ...*)
186 Calc ("Orderings.ord_class.less",eval_equ "#less_"),
187 (*2nd NTH_CONS pushes n+-1 into asms*)
188 Calc("Groups.plus_class.plus", eval_binop "#add_")
190 srls = Erls, calc = [], errpatts = [],
191 rules = [Thm ("NTH_CONS",num_str @{thm NTH_CONS}),
192 Calc("Groups.plus_class.plus", eval_binop "#add_"),
193 Thm ("NTH_NIL",num_str @{thm NTH_NIL}),
194 Calc("Tools.lhs", eval_lhs"eval_lhs_"),
195 Calc("Tools.rhs", eval_rhs"eval_rhs_"),
196 Calc("Atools.argument'_in",
197 eval_argument_in "Atools.argument'_in")
202 Rls {id="srls_IntegrierenUnd..",
204 rew_ord = ("termlessI",termlessI),
205 erls = append_rls "erls_in_srls_IntegrierenUnd.." e_rls
206 [(*for asm in NTH_CONS ...*)
207 Calc ("Orderings.ord_class.less",eval_equ "#less_"),
208 (*2nd NTH_CONS pushes n+-1 into asms*)
209 Calc("Groups.plus_class.plus", eval_binop "#add_")
211 srls = Erls, calc = [], errpatts = [],
212 rules = [Thm ("NTH_CONS",num_str @{thm NTH_CONS}),
213 Calc("Groups.plus_class.plus", eval_binop "#add_"),
214 Thm ("NTH_NIL", num_str @{thm NTH_NIL}),
215 Calc("Tools.lhs", eval_lhs "eval_lhs_"),
216 Calc("Atools.filter'_sameFunId",
217 eval_filter_sameFunId "Atools.filter'_sameFunId"),
218 (*WN070514 just for smltest/../biegelinie.sml ...*)
219 Calc("Atools.sameFunId", eval_sameFunId "Atools.sameFunId"),
220 Thm ("filter_Cons", num_str @{thm filter_Cons}),
221 Thm ("filter_Nil", num_str @{thm filter_Nil}),
222 Thm ("if_True", num_str @{thm if_True}),
223 Thm ("if_False", num_str @{thm if_False}),
224 Thm ("hd_thm", num_str @{thm hd_thm})
231 (prep_met thy "met_biege" [] e_metID
232 (["IntegrierenUndKonstanteBestimmen"],
233 [("#Given" ,["Traegerlaenge l_l", "Streckenlast q__q", "FunktionsVariable v_v"]),
234 (*("#Where",["0 < l_l"]), ...wait for < and handling Arbfix*)
235 ("#Find" ,["Biegelinie b_b"]),
236 ("#Relate",["RandbedingungenBiegung r_b", "RandbedingungenMoment r_m"])],
237 {rew_ord'="tless_true",
238 rls' = append_rls "erls_IntegrierenUndK.." e_rls
239 [Calc ("Atools.ident",eval_ident "#ident_"),
240 Thm ("not_true",num_str @{thm not_true}),
241 Thm ("not_false",num_str @{thm not_false})],
242 calc = [], srls = srls, prls = Erls, crls = Atools_erls, errpats = [], nrls = Erls},
243 "Script BiegelinieScript " ^
244 "(l_l::real) (q__q::real) (v_v::real) (b_b::real=>real) " ^
245 "(r_b::bool list) (r_m::bool list) = " ^
246 " (let q___q = Take (qq v_v = q__q); " ^
247 " q___q = ((Rewrite sym_neg_equal_iff_equal True) @@ " ^
248 " (Rewrite Belastung_Querkraft True)) q___q; " ^
249 " (Q__Q:: bool) = " ^
250 " (SubProblem (Biegelinie',[named,integrate,function], " ^
251 " [diff,integration,named]) " ^
252 " [REAL (rhs q___q), REAL v_v, REAL_REAL Q]); " ^
253 " Q__Q = Rewrite Querkraft_Moment True Q__Q; " ^
255 " (SubProblem (Biegelinie',[named,integrate,function], " ^
256 " [diff,integration,named]) " ^
257 " [REAL (rhs Q__Q), REAL v_v, REAL_REAL M_b]); " ^
258 (*([5], Res), M_b x = c_2 + c * x + -1 * q_0 / 2 * x ^^^ 2*)
259 " e__1 = NTH 1 r_m; " ^
260 " (x__1::real) = argument_in (lhs e__1); " ^
261 " (M__1::bool) = (Substitute [v_v = x__1]) M__M; " ^
262 (*([6], Res), M_b 0 = c_2 + c * 0 + -1 * q_0 / 2 * 0 ^^^ 2*)
263 " M__1 = (Substitute [e__1]) M__1; " ^
264 (*([7], Res), 0 = c_2 + c * 0 + -1 * q_0 / 2 * 0 ^^^ 2*)
265 " M__2 = Take M__M; " ^
266 (*([8], Frm), M_b x = c_2 + c * x + -1 * q_0 / 2 * x ^^^ 2*)
267 (*without above Take 'Substitute [v_v = x__2]' takes _last formula from ctree_*)
268 " e__2 = NTH 2 r_m; " ^
269 " (x__2::real) = argument_in (lhs e__2); " ^
270 " (M__2::bool) = (Substitute [v_v = x__2]) M__M; " ^
271 (*([8], Res), M_b L = c_2 + c * L + -1 * q_0 / 2 * L ^^^ 2*)
272 " M__2 = (Substitute [e__2]) M__2; " ^
274 " (c_1_2::bool list) = " ^
275 " (SubProblem (Biegelinie',[linear,system],[no_met]) " ^
276 " [BOOL_LIST [M__1, M__2], REAL_LIST [c,c_2]]); " ^
277 " M__M = Take M__M; " ^
278 " M__M = ((Substitute c_1_2) @@ " ^
279 " (Try (Rewrite_Set_Inst [(bdv_1, c),(bdv_2, c_2)] " ^
280 " simplify_System False)) @@ " ^
281 " (Rewrite Moment_Neigung False) @@ " ^
282 " (Rewrite make_fun_explicit False)) M__M; " ^
283 (*----------------------- and the same once more ------------------------*)
284 " (N__N:: bool) = " ^
285 " (SubProblem (Biegelinie',[named,integrate,function], " ^
286 " [diff,integration,named]) " ^
287 " [REAL (rhs M__M), REAL v_v, REAL_REAL y']); " ^
288 " (B__B:: bool) = " ^
289 " (SubProblem (Biegelinie',[named,integrate,function], " ^
290 " [diff,integration,named]) " ^
291 " [REAL (rhs N__N), REAL v_v, REAL_REAL y]); " ^
292 " e__1 = NTH 1 r_b; " ^
293 " (x__1::real) = argument_in (lhs e__1); " ^
294 " (B__1::bool) = (Substitute [v_v = x__1]) B__B; " ^
295 " B__1 = (Substitute [e__1]) B__1 ; " ^
296 " B__2 = Take B__B; " ^
297 " e__2 = NTH 2 r_b; " ^
298 " (x__2::real) = argument_in (lhs e__2); " ^
299 " (B__2::bool) = (Substitute [v_v = x__2]) B__B; " ^
300 " B__2 = (Substitute [e__2]) B__2 ; " ^
301 " (c_1_2::bool list) = " ^
302 " (SubProblem (Biegelinie',[linear,system],[no_met]) " ^
303 " [BOOL_LIST [B__1, B__2], REAL_LIST [c,c_2]]); " ^
304 " B__B = Take B__B; " ^
305 " B__B = ((Substitute c_1_2) @@ " ^
306 " (Rewrite_Set_Inst [(bdv, x)] make_ratpoly_in False)) B__B " ^
312 (prep_met thy "met_biege_2" [] e_metID
313 (["IntegrierenUndKonstanteBestimmen2"],
314 [("#Given" ,["Traegerlaenge l_l", "Streckenlast q__q", "FunktionsVariable v_v"]),
315 (*("#Where",["0 < l_l"]), ...wait for < and handling Arbfix*)
316 ("#Find" ,["Biegelinie b_b"]),
317 ("#Relate",["Randbedingungen r_b"])],
318 {rew_ord'="tless_true",
319 rls' = append_rls "erls_IntegrierenUndK.." e_rls
320 [Calc ("Atools.ident",eval_ident "#ident_"),
321 Thm ("not_true",num_str @{thm not_true}),
322 Thm ("not_false",num_str @{thm not_false})],
324 srls = append_rls "erls_IntegrierenUndK.." e_rls
325 [Calc("Tools.rhs", eval_rhs"eval_rhs_"),
326 Calc ("Atools.ident",eval_ident "#ident_"),
327 Thm ("last_thmI",num_str @{thm last_thmI}),
328 Thm ("if_True",num_str @{thm if_True}),
329 Thm ("if_False",num_str @{thm if_False})],
330 prls = Erls, crls = Atools_erls, errpats = [], nrls = Erls},
331 "Script Biegelinie2Script " ^
332 "(l_l::real) (q__q::real) (v_v::real) (b_b::real=>real) (r_b::bool list) = " ^
334 " (fun_s:: bool list) = " ^
335 " (SubProblem (Biegelinie',[vonBelastungZu,Biegelinien], " ^
336 " [Biegelinien,ausBelastung]) " ^
337 " [REAL q__q, REAL v_v]); " ^
338 " (equ_s::bool list) = " ^
339 " (SubProblem (Biegelinie',[setzeRandbedingungen,Biegelinien], " ^
340 " [Biegelinien,setzeRandbedingungenEin]) " ^
341 " [BOOL_LIST fun_s, BOOL_LIST r_b]); " ^
342 " (con_s::bool list) = " ^
343 " (SubProblem (Biegelinie',[linear,system],[no_met]) " ^
344 " [BOOL_LIST equ_s, REAL_LIST [c,c_2,c_3,c_4]]); " ^
345 " B_B = Take (lastI fun_s); " ^
346 " B_B = ((Substitute con_s) @@ " ^
347 " (Rewrite_Set_Inst [(bdv, v_v)] make_ratpoly_in False)) B_B " ^
354 (prep_met thy "met_biege_intconst_2" [] e_metID
355 (["IntegrierenUndKonstanteBestimmen","2xIntegrieren"],
357 {rew_ord'="tless_true", rls'=Erls, calc = [],
360 crls = Atools_erls, errpats = [], nrls = e_rls},
365 (prep_met thy "met_biege_intconst_4" [] e_metID
366 (["IntegrierenUndKonstanteBestimmen","4x4System"],
368 {rew_ord'="tless_true", rls'=Erls, calc = [],
371 crls = Atools_erls, errpats = [], nrls = e_rls},
376 (prep_met thy "met_biege_intconst_1" [] e_metID
377 (["IntegrierenUndKonstanteBestimmen","1xIntegrieren"],
379 {rew_ord'="tless_true", rls'=Erls, calc = [],
382 crls = Atools_erls, errpats = [], nrls = e_rls},
387 (prep_met thy "met_biege2" [] e_metID
390 {rew_ord'="tless_true", rls'=Erls, calc = [],
393 crls = Atools_erls, errpats = [], nrls = e_rls},
400 (prep_met thy "met_biege_ausbelast" [] e_metID
401 (["Biegelinien", "ausBelastung"],
402 [("#Given" ,["Streckenlast q__q", "FunktionsVariable v_v"]),
403 ("#Find" ,["Funktionen fun_s"])],
404 {rew_ord'="tless_true",
405 rls' = append_rls "erls_ausBelastung" e_rls
406 [Calc ("Atools.ident", eval_ident "#ident_"),
407 Thm ("not_true", num_str @{thm not_true}),
408 Thm ("not_false", num_str @{thm not_false})],
410 srls = append_rls "srls_ausBelastung" e_rls
411 [Calc ("Tools.rhs", eval_rhs "eval_rhs_")],
412 prls = e_rls, crls = Atools_erls, errpats = [], nrls = e_rls},
413 "Script Belastung2BiegelScript (q__q::real) (v_v::real) = " ^
414 " (let q___q = Take (qq v_v = q__q); " ^
415 " q___q = ((Rewrite sym_neg_equal_iff_equal True) @@ " ^
416 " (Rewrite Belastung_Querkraft True)) q___q; " ^
417 " (Q__Q:: bool) = " ^
418 " (SubProblem (Biegelinie',[named,integrate,function], " ^
419 " [diff,integration,named]) " ^
420 " [REAL (rhs q___q), REAL v_v, REAL_REAL Q]); " ^
421 " M__M = Rewrite Querkraft_Moment True Q__Q; " ^
423 " (SubProblem (Biegelinie',[named,integrate,function], " ^
424 " [diff,integration,named]) " ^
425 " [REAL (rhs M__M), REAL v_v, REAL_REAL M_b]); " ^
426 " N__N = ((Rewrite Moment_Neigung False) @@ " ^
427 " (Rewrite make_fun_explicit False)) M__M; " ^
428 " (N__N:: bool) = " ^
429 " (SubProblem (Biegelinie',[named,integrate,function], " ^
430 " [diff,integration,named]) " ^
431 " [REAL (rhs N__N), REAL v_v, REAL_REAL y']); " ^
432 " (B__B:: bool) = " ^
433 " (SubProblem (Biegelinie',[named,integrate,function], " ^
434 " [diff,integration,named]) " ^
435 " [REAL (rhs N__N), REAL v_v, REAL_REAL y]) " ^
436 " in [Q__Q, M__M, N__N, B__B])"
442 (prep_met thy "met_biege_setzrand" [] e_metID
443 (["Biegelinien", "setzeRandbedingungenEin"],
444 [("#Given" , ["Funktionen fun_s", "Randbedingungen r_b"]),
445 ("#Find" , ["Gleichungen equs'''"])],
446 {rew_ord'="tless_true", rls'=Erls, calc = [],
449 crls = Atools_erls, errpats = [], nrls = e_rls},
450 "Script SetzeRandbedScript (fun_s::bool list) (r_b::bool list) = " ^
451 " (let b_1 = NTH 1 r_b; " ^
452 " f_s = filter_sameFunId (lhs b_1) fun_s; " ^
454 " (SubProblem (Biegelinie',[makeFunctionTo,equation]," ^
455 " [Equation,fromFunction]) " ^
456 " [BOOL (hd f_s), BOOL b_1]); " ^
457 " b_2 = NTH 2 r_b; " ^
458 " f_s = filter_sameFunId (lhs b_2) fun_s; " ^
460 " (SubProblem (Biegelinie',[makeFunctionTo,equation]," ^
461 " [Equation,fromFunction]) " ^
462 " [BOOL (hd f_s), BOOL b_2]); " ^
463 " b_3 = NTH 3 r_b; " ^
464 " f_s = filter_sameFunId (lhs b_3) fun_s; " ^
466 " (SubProblem (Biegelinie',[makeFunctionTo,equation]," ^
467 " [Equation,fromFunction]) " ^
468 " [BOOL (hd f_s), BOOL b_3]); " ^
469 " b_4 = NTH 4 r_b; " ^
470 " f_s = filter_sameFunId (lhs b_4) fun_s; " ^
472 " (SubProblem (Biegelinie',[makeFunctionTo,equation]," ^
473 " [Equation,fromFunction]) " ^
474 " [BOOL (hd f_s), BOOL b_4]) " ^
475 " in [e_1, e_2, e_3, e_4])"
476 (* filter requires more than 1 sec !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
477 "Script SetzeRandbedScript (fun_s::bool list) (r_b::bool list) = " ^
478 " (let b_1 = NTH 1 r_b; " ^
479 " f_s = filter (sameFunId (lhs b_1)) fun_s; " ^
481 " (SubProblem (Biegelinie',[makeFunctionTo,equation]," ^
482 " [Equation,fromFunction]) " ^
483 " [BOOL (hd f_s), BOOL b_1]); " ^
484 " b_2 = NTH 2 r_b; " ^
485 " f_s = filter (sameFunId (lhs b_2)) fun_s; " ^
487 " (SubProblem (Biegelinie',[makeFunctionTo,equation]," ^
488 " [Equation,fromFunction]) " ^
489 " [BOOL (hd f_s), BOOL b_2]); " ^
490 " b_3 = NTH 3 r_b; " ^
491 " f_s = filter (sameFunId (lhs b_3)) fun_s; " ^
493 " (SubProblem (Biegelinie',[makeFunctionTo,equation]," ^
494 " [Equation,fromFunction]) " ^
495 " [BOOL (hd f_s), BOOL b_3]); " ^
496 " b_4 = NTH 4 r_b; " ^
497 " f_s = filter (sameFunId (lhs b_4)) fun_s; " ^
499 " (SubProblem (Biegelinie',[makeFunctionTo,equation]," ^
500 " [Equation,fromFunction]) " ^
501 " [BOOL (hd f_s), BOOL b_4]) " ^
502 " in [e_1,e_2,e_3,e_4])"*)
508 (prep_met thy "met_equ_fromfun" [] e_metID
509 (["Equation","fromFunction"],
510 [("#Given" ,["functionEq fu_n","substitution su_b"]),
511 ("#Find" ,["equality equ'''"])],
512 {rew_ord'="tless_true", rls'=Erls, calc = [],
513 srls = append_rls "srls_in_EquationfromFunc" e_rls
514 [Calc("Tools.lhs", eval_lhs"eval_lhs_"),
515 Calc("Atools.argument'_in", eval_argument_in "Atools.argument'_in")],
516 prls=e_rls, crls = Atools_erls, errpats = [], nrls = e_rls},
517 (*(M_b x = c_2 + c * x + -1 * q_0 / 2 * x ^^^ 2) (M_b L = 0) -->
518 0 = c_2 + c * L + -1 * q_0 / 2 * L ^^^ 2*)
519 "Script Function2Equality (fu_n::bool) (su_b::bool) =" ^
520 " (let fu_n = Take fu_n; " ^
521 " bd_v = argument_in (lhs fu_n); " ^
522 " va_l = argument_in (lhs su_b); " ^
523 " eq_u = (Substitute [bd_v = va_l]) fu_n; " ^
524 (*([1], Res), M_b L = c_2 + c * L + -1 * q_0 / 2 * L ^^^ 2*)
525 " eq_u = (Substitute [su_b]) eq_u " ^
526 " in (Rewrite_Set norm_Rational False) eq_u) "