|
neuper@37906
|
1 |
(* chapter 'Biegelinie' from the textbook:
|
|
neuper@37906
|
2 |
Timischl, Kaiser. Ingenieur-Mathematik 3. Wien 1999. p.268-271.
|
|
neuper@37999
|
3 |
author: Walther Neuper 050826,
|
|
neuper@37906
|
4 |
(c) due to copyright terms
|
|
neuper@37906
|
5 |
*)
|
|
neuper@37906
|
6 |
|
|
bonzai@41919
|
7 |
theory Biegelinie imports Integrate Equation EqSystem Atools begin
|
|
neuper@37906
|
8 |
|
|
neuper@37906
|
9 |
consts
|
|
neuper@37906
|
10 |
|
|
neuper@42385
|
11 |
qq :: "real => real" (* Streckenlast *)
|
|
neuper@37999
|
12 |
Q :: "real => real" (* Querkraft *)
|
|
neuper@37999
|
13 |
Q' :: "real => real" (* Ableitung der Querkraft *)
|
|
neuper@37999
|
14 |
M'_b :: "real => real" ("M'_b") (* Biegemoment *)
|
|
neuper@37999
|
15 |
M'_b' :: "real => real" ("M'_b'") (* Ableitung des Biegemoments *)
|
|
neuper@37999
|
16 |
y'' :: "real => real" (* 2.Ableitung der Biegeline *)
|
|
neuper@37999
|
17 |
y' :: "real => real" (* Neigung der Biegeline *)
|
|
neuper@37999
|
18 |
(*y :: "real => real" (* Biegeline *)*)
|
|
neuper@37999
|
19 |
EI :: "real" (* Biegesteifigkeit *)
|
|
neuper@37906
|
20 |
|
|
neuper@37906
|
21 |
(*new Descriptions in the related problems*)
|
|
neuper@37999
|
22 |
Traegerlaenge :: "real => una"
|
|
neuper@37999
|
23 |
Streckenlast :: "real => una"
|
|
neuper@37999
|
24 |
BiegemomentVerlauf :: "bool => una"
|
|
neuper@37999
|
25 |
Biegelinie :: "(real => real) => una"
|
|
neuper@37999
|
26 |
Randbedingungen :: "bool list => una"
|
|
neuper@37999
|
27 |
RandbedingungenBiegung :: "bool list => una"
|
|
neuper@37999
|
28 |
RandbedingungenNeigung :: "bool list => una"
|
|
neuper@37999
|
29 |
RandbedingungenMoment :: "bool list => una"
|
|
neuper@37999
|
30 |
RandbedingungenQuerkraft :: "bool list => una"
|
|
neuper@37999
|
31 |
FunktionsVariable :: "real => una"
|
|
neuper@37999
|
32 |
Funktionen :: "bool list => una"
|
|
neuper@37999
|
33 |
Gleichungen :: "bool list => una"
|
|
neuper@37906
|
34 |
|
|
neuper@37906
|
35 |
(*Script-names*)
|
|
neuper@37906
|
36 |
Biegelinie2Script :: "[real,real,real,real=>real,bool list,
|
|
neuper@37906
|
37 |
bool] => bool"
|
|
neuper@37906
|
38 |
("((Script Biegelinie2Script (_ _ _ _ _ =))// (_))" 9)
|
|
neuper@37906
|
39 |
BiegelinieScript :: "[real,real,real,real=>real,bool list,bool list,
|
|
neuper@37906
|
40 |
bool] => bool"
|
|
neuper@37906
|
41 |
("((Script BiegelinieScript (_ _ _ _ _ _ =))// (_))" 9)
|
|
neuper@37906
|
42 |
Biege2xIntegrierenScript :: "[real,real,real,bool,real=>real,bool list,
|
|
neuper@37906
|
43 |
bool] => bool"
|
|
neuper@37906
|
44 |
("((Script Biege2xIntegrierenScript (_ _ _ _ _ _ =))// (_))" 9)
|
|
neuper@37906
|
45 |
Biege4x4SystemScript :: "[real,real,real,real=>real,bool list,
|
|
neuper@37906
|
46 |
bool] => bool"
|
|
neuper@37906
|
47 |
("((Script Biege4x4SystemScript (_ _ _ _ _ =))// (_))" 9)
|
|
neuper@37906
|
48 |
Biege1xIntegrierenScript ::
|
|
neuper@37906
|
49 |
"[real,real,real,real=>real,bool list,bool list,bool list,
|
|
neuper@37906
|
50 |
bool] => bool"
|
|
neuper@37906
|
51 |
("((Script Biege1xIntegrierenScript (_ _ _ _ _ _ _ =))// (_))" 9)
|
|
neuper@37906
|
52 |
Belastung2BiegelScript :: "[real,real,
|
|
neuper@37906
|
53 |
bool list] => bool list"
|
|
neuper@37906
|
54 |
("((Script Belastung2BiegelScript (_ _ =))// (_))" 9)
|
|
neuper@37906
|
55 |
SetzeRandbedScript :: "[bool list,bool list,
|
|
neuper@37906
|
56 |
bool list] => bool list"
|
|
neuper@37906
|
57 |
("((Script SetzeRandbedScript (_ _ =))// (_))" 9)
|
|
neuper@37906
|
58 |
|
|
neuper@52148
|
59 |
axiomatization where
|
|
neuper@37906
|
60 |
|
|
neuper@52148
|
61 |
Querkraft_Belastung: "Q' x = -qq x" and
|
|
neuper@52148
|
62 |
Belastung_Querkraft: "-qq x = Q' x" and
|
|
neuper@37906
|
63 |
|
|
neuper@52148
|
64 |
Moment_Querkraft: "M_b' x = Q x" and
|
|
neuper@52148
|
65 |
Querkraft_Moment: "Q x = M_b' x" and
|
|
neuper@37906
|
66 |
|
|
neuper@52148
|
67 |
Neigung_Moment: "y'' x = -M_b x/ EI" and
|
|
neuper@52148
|
68 |
Moment_Neigung: "M_b x = -EI * y'' x" and
|
|
neuper@37906
|
69 |
|
|
neuper@37906
|
70 |
(*according to rls 'simplify_Integral': .. = 1/a * .. instead .. = ../ a*)
|
|
neuper@37983
|
71 |
make_fun_explicit: "Not (a =!= 0) ==> (a * (f x) = b) = (f x = 1/a * b)"
|
|
neuper@37906
|
72 |
|
|
neuper@37954
|
73 |
ML {*
|
|
neuper@37972
|
74 |
val thy = @{theory};
|
|
neuper@37972
|
75 |
|
|
neuper@37954
|
76 |
(** theory elements for transfer into html **)
|
|
neuper@37954
|
77 |
|
|
neuper@37954
|
78 |
store_isa ["IsacKnowledge"] [];
|
|
neuper@37972
|
79 |
store_thy thy
|
|
neuper@37954
|
80 |
["Walther Neuper 2005 supported by a grant from NMI Austria"];
|
|
neuper@37972
|
81 |
store_isa ["IsacKnowledge", theory2thyID thy, "Theorems"]
|
|
neuper@37954
|
82 |
["Walther Neuper 2005 supported by a grant from NMI Austria"];
|
|
neuper@42411
|
83 |
store_thm thy "IsacKnowledge" ("Belastung_Querkraft", prop_of @{thm Belastung_Querkraft})
|
|
neuper@37954
|
84 |
["Walther Neuper 2005 supported by a grant from NMI Austria"];
|
|
neuper@42411
|
85 |
store_thm thy "IsacKnowledge" ("Moment_Neigung", prop_of @{thm Moment_Neigung})
|
|
neuper@37954
|
86 |
["Walther Neuper 2005 supported by a grant from NMI Austria"];
|
|
neuper@42411
|
87 |
store_thm thy "IsacKnowledge" ("Moment_Querkraft", prop_of @{thm Moment_Querkraft})
|
|
neuper@37954
|
88 |
["Walther Neuper 2005 supported by a grant from NMI Austria"];
|
|
neuper@42411
|
89 |
store_thm thy "IsacKnowledge" ("Neigung_Moment", prop_of @{thm Neigung_Moment})
|
|
neuper@37954
|
90 |
["Walther Neuper 2005 supported by a grant from NMI Austria"];
|
|
neuper@42411
|
91 |
store_thm thy "IsacKnowledge" ("Querkraft_Belastung", prop_of @{thm Querkraft_Belastung})
|
|
neuper@37954
|
92 |
["Walther Neuper 2005 supported by a grant from NMI Austria"];
|
|
neuper@42411
|
93 |
store_thm thy "IsacKnowledge" ("Querkraft_Moment", prop_of @{thm Querkraft_Moment})
|
|
neuper@37954
|
94 |
["Walther Neuper 2005 supported by a grant from NMI Austria"];
|
|
neuper@42411
|
95 |
store_thm thy "IsacKnowledge" ("make_fun_explicit", prop_of @{thm make_fun_explicit})
|
|
neuper@37954
|
96 |
["Walther Neuper 2005 supported by a grant from NMI Austria"];
|
|
neuper@37954
|
97 |
|
|
neuper@37999
|
98 |
*}
|
|
neuper@37999
|
99 |
ML {*
|
|
neuper@37954
|
100 |
(** problems **)
|
|
neuper@37954
|
101 |
|
|
neuper@37954
|
102 |
store_pbt
|
|
neuper@37972
|
103 |
(prep_pbt thy "pbl_bieg" [] e_pblID
|
|
neuper@37954
|
104 |
(["Biegelinien"],
|
|
neuper@37999
|
105 |
[("#Given" ,["Traegerlaenge l_l", "Streckenlast q_q"]),
|
|
neuper@37999
|
106 |
(*("#Where",["0 < l_l"]), ...wait for < and handling Arbfix*)
|
|
neuper@37999
|
107 |
("#Find" ,["Biegelinie b_b"]),
|
|
neuper@37999
|
108 |
("#Relate",["Randbedingungen r_b"])
|
|
neuper@37954
|
109 |
],
|
|
neuper@37954
|
110 |
append_rls "e_rls" e_rls [],
|
|
neuper@37954
|
111 |
NONE,
|
|
neuper@37954
|
112 |
[["IntegrierenUndKonstanteBestimmen2"]]));
|
|
neuper@37954
|
113 |
|
|
neuper@37954
|
114 |
store_pbt
|
|
neuper@37972
|
115 |
(prep_pbt thy "pbl_bieg_mom" [] e_pblID
|
|
neuper@37954
|
116 |
(["MomentBestimmte","Biegelinien"],
|
|
neuper@37999
|
117 |
[("#Given" ,["Traegerlaenge l_l", "Streckenlast q_q"]),
|
|
neuper@37999
|
118 |
(*("#Where",["0 < l_l"]), ...wait for < and handling Arbfix*)
|
|
neuper@37999
|
119 |
("#Find" ,["Biegelinie b_b"]),
|
|
neuper@37999
|
120 |
("#Relate",["RandbedingungenBiegung r_b","RandbedingungenMoment r_m"])
|
|
neuper@37954
|
121 |
],
|
|
neuper@37954
|
122 |
append_rls "e_rls" e_rls [],
|
|
neuper@37954
|
123 |
NONE,
|
|
neuper@37954
|
124 |
[["IntegrierenUndKonstanteBestimmen"]]));
|
|
neuper@37954
|
125 |
|
|
neuper@37954
|
126 |
store_pbt
|
|
neuper@37972
|
127 |
(prep_pbt thy "pbl_bieg_momg" [] e_pblID
|
|
neuper@37954
|
128 |
(["MomentGegebene","Biegelinien"],
|
|
neuper@37954
|
129 |
[],
|
|
neuper@37954
|
130 |
append_rls "e_rls" e_rls [],
|
|
neuper@37954
|
131 |
NONE,
|
|
neuper@37954
|
132 |
[["IntegrierenUndKonstanteBestimmen","2xIntegrieren"]]));
|
|
neuper@37954
|
133 |
|
|
neuper@37954
|
134 |
store_pbt
|
|
neuper@37972
|
135 |
(prep_pbt thy "pbl_bieg_einf" [] e_pblID
|
|
neuper@37954
|
136 |
(["einfache","Biegelinien"],
|
|
neuper@37954
|
137 |
[],
|
|
neuper@37954
|
138 |
append_rls "e_rls" e_rls [],
|
|
neuper@37954
|
139 |
NONE,
|
|
neuper@37954
|
140 |
[["IntegrierenUndKonstanteBestimmen","4x4System"]]));
|
|
neuper@37954
|
141 |
|
|
neuper@37954
|
142 |
store_pbt
|
|
neuper@37972
|
143 |
(prep_pbt thy "pbl_bieg_momquer" [] e_pblID
|
|
neuper@37954
|
144 |
(["QuerkraftUndMomentBestimmte","Biegelinien"],
|
|
neuper@37954
|
145 |
[],
|
|
neuper@37954
|
146 |
append_rls "e_rls" e_rls [],
|
|
neuper@37954
|
147 |
NONE,
|
|
neuper@37954
|
148 |
[["IntegrierenUndKonstanteBestimmen","1xIntegrieren"]]));
|
|
neuper@37954
|
149 |
|
|
neuper@37954
|
150 |
store_pbt
|
|
neuper@37972
|
151 |
(prep_pbt thy "pbl_bieg_vonq" [] e_pblID
|
|
neuper@37954
|
152 |
(["vonBelastungZu","Biegelinien"],
|
|
neuper@37999
|
153 |
[("#Given" ,["Streckenlast q_q","FunktionsVariable v_v"]),
|
|
neuper@37999
|
154 |
("#Find" ,["Funktionen funs'''"])],
|
|
neuper@37954
|
155 |
append_rls "e_rls" e_rls [],
|
|
neuper@37954
|
156 |
NONE,
|
|
neuper@37954
|
157 |
[["Biegelinien","ausBelastung"]]));
|
|
neuper@37954
|
158 |
|
|
neuper@37954
|
159 |
store_pbt
|
|
neuper@37972
|
160 |
(prep_pbt thy "pbl_bieg_randbed" [] e_pblID
|
|
neuper@37954
|
161 |
(["setzeRandbedingungen","Biegelinien"],
|
|
neuper@37999
|
162 |
[("#Given" ,["Funktionen fun_s","Randbedingungen r_b"]),
|
|
neuper@37999
|
163 |
("#Find" ,["Gleichungen equs'''"])],
|
|
neuper@37954
|
164 |
append_rls "e_rls" e_rls [],
|
|
neuper@37954
|
165 |
NONE,
|
|
neuper@37954
|
166 |
[["Biegelinien","setzeRandbedingungenEin"]]));
|
|
neuper@37954
|
167 |
|
|
neuper@37954
|
168 |
store_pbt
|
|
neuper@37972
|
169 |
(prep_pbt thy "pbl_equ_fromfun" [] e_pblID
|
|
neuper@37954
|
170 |
(["makeFunctionTo","equation"],
|
|
neuper@37999
|
171 |
[("#Given" ,["functionEq fu_n","substitution su_b"]),
|
|
neuper@37999
|
172 |
("#Find" ,["equality equ'''"])],
|
|
neuper@37954
|
173 |
append_rls "e_rls" e_rls [],
|
|
neuper@37954
|
174 |
NONE,
|
|
neuper@37954
|
175 |
[["Equation","fromFunction"]]));
|
|
neuper@37954
|
176 |
|
|
neuper@37999
|
177 |
*}
|
|
neuper@37999
|
178 |
ML {*
|
|
neuper@37954
|
179 |
(** methods **)
|
|
neuper@37954
|
180 |
|
|
neuper@37954
|
181 |
val srls = Rls {id="srls_IntegrierenUnd..",
|
|
neuper@37954
|
182 |
preconds = [],
|
|
neuper@37954
|
183 |
rew_ord = ("termlessI",termlessI),
|
|
neuper@37954
|
184 |
erls = append_rls "erls_in_srls_IntegrierenUnd.." e_rls
|
|
neuper@37999
|
185 |
[(*for asm in NTH_CONS ...*)
|
|
neuper@38045
|
186 |
Calc ("Orderings.ord_class.less",eval_equ "#less_"),
|
|
neuper@37999
|
187 |
(*2nd NTH_CONS pushes n+-1 into asms*)
|
|
neuper@38014
|
188 |
Calc("Groups.plus_class.plus", eval_binop "#add_")
|
|
neuper@37954
|
189 |
],
|
|
neuper@42451
|
190 |
srls = Erls, calc = [], errpatts = [],
|
|
neuper@37999
|
191 |
rules = [Thm ("NTH_CONS",num_str @{thm NTH_CONS}),
|
|
neuper@38014
|
192 |
Calc("Groups.plus_class.plus", eval_binop "#add_"),
|
|
neuper@37999
|
193 |
Thm ("NTH_NIL",num_str @{thm NTH_NIL}),
|
|
neuper@37954
|
194 |
Calc("Tools.lhs", eval_lhs"eval_lhs_"),
|
|
neuper@37954
|
195 |
Calc("Tools.rhs", eval_rhs"eval_rhs_"),
|
|
neuper@37954
|
196 |
Calc("Atools.argument'_in",
|
|
neuper@37954
|
197 |
eval_argument_in "Atools.argument'_in")
|
|
neuper@37954
|
198 |
],
|
|
neuper@37954
|
199 |
scr = EmptyScr};
|
|
neuper@37954
|
200 |
|
|
neuper@37954
|
201 |
val srls2 =
|
|
neuper@37954
|
202 |
Rls {id="srls_IntegrierenUnd..",
|
|
neuper@37954
|
203 |
preconds = [],
|
|
neuper@37954
|
204 |
rew_ord = ("termlessI",termlessI),
|
|
neuper@37954
|
205 |
erls = append_rls "erls_in_srls_IntegrierenUnd.." e_rls
|
|
neuper@37999
|
206 |
[(*for asm in NTH_CONS ...*)
|
|
neuper@38045
|
207 |
Calc ("Orderings.ord_class.less",eval_equ "#less_"),
|
|
neuper@37999
|
208 |
(*2nd NTH_CONS pushes n+-1 into asms*)
|
|
neuper@38014
|
209 |
Calc("Groups.plus_class.plus", eval_binop "#add_")
|
|
neuper@37954
|
210 |
],
|
|
neuper@42451
|
211 |
srls = Erls, calc = [], errpatts = [],
|
|
neuper@37999
|
212 |
rules = [Thm ("NTH_CONS",num_str @{thm NTH_CONS}),
|
|
neuper@38014
|
213 |
Calc("Groups.plus_class.plus", eval_binop "#add_"),
|
|
neuper@37999
|
214 |
Thm ("NTH_NIL", num_str @{thm NTH_NIL}),
|
|
neuper@37954
|
215 |
Calc("Tools.lhs", eval_lhs "eval_lhs_"),
|
|
neuper@37954
|
216 |
Calc("Atools.filter'_sameFunId",
|
|
neuper@37954
|
217 |
eval_filter_sameFunId "Atools.filter'_sameFunId"),
|
|
neuper@37954
|
218 |
(*WN070514 just for smltest/../biegelinie.sml ...*)
|
|
neuper@37954
|
219 |
Calc("Atools.sameFunId", eval_sameFunId "Atools.sameFunId"),
|
|
neuper@37969
|
220 |
Thm ("filter_Cons", num_str @{thm filter_Cons}),
|
|
neuper@37969
|
221 |
Thm ("filter_Nil", num_str @{thm filter_Nil}),
|
|
neuper@37969
|
222 |
Thm ("if_True", num_str @{thm if_True}),
|
|
neuper@37969
|
223 |
Thm ("if_False", num_str @{thm if_False}),
|
|
neuper@37969
|
224 |
Thm ("hd_thm", num_str @{thm hd_thm})
|
|
neuper@37954
|
225 |
],
|
|
neuper@37954
|
226 |
scr = EmptyScr};
|
|
neuper@37999
|
227 |
*}
|
|
neuper@37999
|
228 |
|
|
neuper@37999
|
229 |
ML {*
|
|
neuper@37954
|
230 |
store_met
|
|
neuper@42387
|
231 |
(prep_met thy "met_biege" [] e_metID
|
|
neuper@42387
|
232 |
(["IntegrierenUndKonstanteBestimmen"],
|
|
neuper@42387
|
233 |
[("#Given" ,["Traegerlaenge l_l", "Streckenlast q__q", "FunktionsVariable v_v"]),
|
|
neuper@37999
|
234 |
(*("#Where",["0 < l_l"]), ...wait for < and handling Arbfix*)
|
|
neuper@42387
|
235 |
("#Find" ,["Biegelinie b_b"]),
|
|
neuper@42387
|
236 |
("#Relate",["RandbedingungenBiegung r_b", "RandbedingungenMoment r_m"])],
|
|
neuper@42387
|
237 |
{rew_ord'="tless_true",
|
|
neuper@42387
|
238 |
rls' = append_rls "erls_IntegrierenUndK.." e_rls
|
|
neuper@42387
|
239 |
[Calc ("Atools.ident",eval_ident "#ident_"),
|
|
neuper@42387
|
240 |
Thm ("not_true",num_str @{thm not_true}),
|
|
neuper@42387
|
241 |
Thm ("not_false",num_str @{thm not_false})],
|
|
neuper@42425
|
242 |
calc = [], srls = srls, prls = Erls, crls = Atools_erls, errpats = [], nrls = Erls},
|
|
neuper@42387
|
243 |
"Script BiegelinieScript " ^
|
|
neuper@42387
|
244 |
"(l_l::real) (q__q::real) (v_v::real) (b_b::real=>real) " ^
|
|
neuper@42387
|
245 |
"(r_b::bool list) (r_m::bool list) = " ^
|
|
neuper@42387
|
246 |
" (let q___q = Take (qq v_v = q__q); " ^
|
|
neuper@42387
|
247 |
" q___q = ((Rewrite sym_neg_equal_iff_equal True) @@ " ^
|
|
neuper@42387
|
248 |
" (Rewrite Belastung_Querkraft True)) q___q; " ^
|
|
neuper@42387
|
249 |
" (Q__Q:: bool) = " ^
|
|
neuper@42387
|
250 |
" (SubProblem (Biegelinie',[named,integrate,function], " ^
|
|
neuper@42387
|
251 |
" [diff,integration,named]) " ^
|
|
neuper@37999
|
252 |
" [REAL (rhs q___q), REAL v_v, REAL_REAL Q]); " ^
|
|
neuper@42387
|
253 |
" Q__Q = Rewrite Querkraft_Moment True Q__Q; " ^
|
|
neuper@42387
|
254 |
" (M__M::bool) = " ^
|
|
neuper@42387
|
255 |
" (SubProblem (Biegelinie',[named,integrate,function], " ^
|
|
neuper@42387
|
256 |
" [diff,integration,named]) " ^
|
|
neuper@37999
|
257 |
" [REAL (rhs Q__Q), REAL v_v, REAL_REAL M_b]); " ^
|
|
neuper@42387
|
258 |
(*([5], Res), M_b x = c_2 + c * x + -1 * q_0 / 2 * x ^^^ 2*)
|
|
neuper@37999
|
259 |
" e__1 = NTH 1 r_m; " ^
|
|
neuper@42387
|
260 |
" (x__1::real) = argument_in (lhs e__1); " ^
|
|
neuper@42387
|
261 |
" (M__1::bool) = (Substitute [v_v = x__1]) M__M; " ^
|
|
neuper@42387
|
262 |
(*([6], Res), M_b 0 = c_2 + c * 0 + -1 * q_0 / 2 * 0 ^^^ 2*)
|
|
neuper@42387
|
263 |
" M__1 = (Substitute [e__1]) M__1; " ^
|
|
neuper@42387
|
264 |
(*([7], Res), 0 = c_2 + c * 0 + -1 * q_0 / 2 * 0 ^^^ 2*)
|
|
neuper@42387
|
265 |
" M__2 = Take M__M; " ^
|
|
neuper@42387
|
266 |
(*([8], Frm), M_b x = c_2 + c * x + -1 * q_0 / 2 * x ^^^ 2*)
|
|
neuper@42387
|
267 |
(*without above Take 'Substitute [v_v = x__2]' takes _last formula from ctree_*)
|
|
neuper@37999
|
268 |
" e__2 = NTH 2 r_m; " ^
|
|
neuper@42387
|
269 |
" (x__2::real) = argument_in (lhs e__2); " ^
|
|
neuper@42387
|
270 |
" (M__2::bool) = (Substitute [v_v = x__2]) M__M; " ^
|
|
neuper@42387
|
271 |
(*([8], Res), M_b L = c_2 + c * L + -1 * q_0 / 2 * L ^^^ 2*)
|
|
neuper@42387
|
272 |
" M__2 = (Substitute [e__2]) M__2; " ^
|
|
neuper@42387
|
273 |
(**)
|
|
neuper@42387
|
274 |
" (c_1_2::bool list) = " ^
|
|
neuper@55276
|
275 |
" (SubProblem (Biegelinie',[LINEAR,system],[no_met]) " ^
|
|
neuper@42387
|
276 |
" [BOOL_LIST [M__1, M__2], REAL_LIST [c,c_2]]); " ^
|
|
neuper@42387
|
277 |
" M__M = Take M__M; " ^
|
|
neuper@37999
|
278 |
" M__M = ((Substitute c_1_2) @@ " ^
|
|
neuper@42387
|
279 |
" (Try (Rewrite_Set_Inst [(bdv_1, c),(bdv_2, c_2)] " ^
|
|
neuper@42387
|
280 |
" simplify_System False)) @@ " ^
|
|
neuper@42387
|
281 |
" (Rewrite Moment_Neigung False) @@ " ^
|
|
neuper@42387
|
282 |
" (Rewrite make_fun_explicit False)) M__M; " ^
|
|
neuper@37954
|
283 |
(*----------------------- and the same once more ------------------------*)
|
|
neuper@42387
|
284 |
" (N__N:: bool) = " ^
|
|
neuper@42387
|
285 |
" (SubProblem (Biegelinie',[named,integrate,function], " ^
|
|
neuper@42387
|
286 |
" [diff,integration,named]) " ^
|
|
neuper@37999
|
287 |
" [REAL (rhs M__M), REAL v_v, REAL_REAL y']); " ^
|
|
neuper@42387
|
288 |
" (B__B:: bool) = " ^
|
|
neuper@42387
|
289 |
" (SubProblem (Biegelinie',[named,integrate,function], " ^
|
|
neuper@42387
|
290 |
" [diff,integration,named]) " ^
|
|
neuper@37999
|
291 |
" [REAL (rhs N__N), REAL v_v, REAL_REAL y]); " ^
|
|
neuper@37999
|
292 |
" e__1 = NTH 1 r_b; " ^
|
|
neuper@42387
|
293 |
" (x__1::real) = argument_in (lhs e__1); " ^
|
|
neuper@42387
|
294 |
" (B__1::bool) = (Substitute [v_v = x__1]) B__B; " ^
|
|
neuper@42387
|
295 |
" B__1 = (Substitute [e__1]) B__1 ; " ^
|
|
neuper@42387
|
296 |
" B__2 = Take B__B; " ^
|
|
neuper@37999
|
297 |
" e__2 = NTH 2 r_b; " ^
|
|
neuper@42387
|
298 |
" (x__2::real) = argument_in (lhs e__2); " ^
|
|
neuper@42387
|
299 |
" (B__2::bool) = (Substitute [v_v = x__2]) B__B; " ^
|
|
neuper@42387
|
300 |
" B__2 = (Substitute [e__2]) B__2 ; " ^
|
|
neuper@42387
|
301 |
" (c_1_2::bool list) = " ^
|
|
neuper@55276
|
302 |
" (SubProblem (Biegelinie',[LINEAR,system],[no_met]) " ^
|
|
neuper@42387
|
303 |
" [BOOL_LIST [B__1, B__2], REAL_LIST [c,c_2]]); " ^
|
|
neuper@42387
|
304 |
" B__B = Take B__B; " ^
|
|
neuper@37999
|
305 |
" B__B = ((Substitute c_1_2) @@ " ^
|
|
neuper@42387
|
306 |
" (Rewrite_Set_Inst [(bdv, x)] make_ratpoly_in False)) B__B " ^
|
|
neuper@37999
|
307 |
" in B__B)"
|
|
neuper@37954
|
308 |
));
|
|
neuper@37999
|
309 |
*}
|
|
neuper@37999
|
310 |
ML {*
|
|
neuper@37954
|
311 |
store_met
|
|
neuper@42387
|
312 |
(prep_met thy "met_biege_2" [] e_metID
|
|
neuper@42387
|
313 |
(["IntegrierenUndKonstanteBestimmen2"],
|
|
neuper@42387
|
314 |
[("#Given" ,["Traegerlaenge l_l", "Streckenlast q__q", "FunktionsVariable v_v"]),
|
|
neuper@37999
|
315 |
(*("#Where",["0 < l_l"]), ...wait for < and handling Arbfix*)
|
|
neuper@42387
|
316 |
("#Find" ,["Biegelinie b_b"]),
|
|
neuper@42387
|
317 |
("#Relate",["Randbedingungen r_b"])],
|
|
neuper@42387
|
318 |
{rew_ord'="tless_true",
|
|
neuper@42387
|
319 |
rls' = append_rls "erls_IntegrierenUndK.." e_rls
|
|
neuper@42387
|
320 |
[Calc ("Atools.ident",eval_ident "#ident_"),
|
|
neuper@42387
|
321 |
Thm ("not_true",num_str @{thm not_true}),
|
|
neuper@42387
|
322 |
Thm ("not_false",num_str @{thm not_false})],
|
|
neuper@42387
|
323 |
calc = [],
|
|
neuper@42387
|
324 |
srls = append_rls "erls_IntegrierenUndK.." e_rls
|
|
neuper@42387
|
325 |
[Calc("Tools.rhs", eval_rhs"eval_rhs_"),
|
|
neuper@42387
|
326 |
Calc ("Atools.ident",eval_ident "#ident_"),
|
|
neuper@42387
|
327 |
Thm ("last_thmI",num_str @{thm last_thmI}),
|
|
neuper@42387
|
328 |
Thm ("if_True",num_str @{thm if_True}),
|
|
neuper@42387
|
329 |
Thm ("if_False",num_str @{thm if_False})],
|
|
neuper@42425
|
330 |
prls = Erls, crls = Atools_erls, errpats = [], nrls = Erls},
|
|
neuper@42387
|
331 |
"Script Biegelinie2Script " ^
|
|
neuper@37999
|
332 |
"(l_l::real) (q__q::real) (v_v::real) (b_b::real=>real) (r_b::bool list) = " ^
|
|
neuper@42387
|
333 |
" (let " ^
|
|
neuper@42387
|
334 |
" (fun_s:: bool list) = " ^
|
|
neuper@42387
|
335 |
" (SubProblem (Biegelinie',[vonBelastungZu,Biegelinien], " ^
|
|
neuper@42387
|
336 |
" [Biegelinien,ausBelastung]) " ^
|
|
neuper@42387
|
337 |
" [REAL q__q, REAL v_v]); " ^
|
|
neuper@42387
|
338 |
" (equ_s::bool list) = " ^
|
|
neuper@42387
|
339 |
" (SubProblem (Biegelinie',[setzeRandbedingungen,Biegelinien], " ^
|
|
neuper@42387
|
340 |
" [Biegelinien,setzeRandbedingungenEin]) " ^
|
|
neuper@37999
|
341 |
" [BOOL_LIST fun_s, BOOL_LIST r_b]); " ^
|
|
neuper@42387
|
342 |
" (con_s::bool list) = " ^
|
|
neuper@55276
|
343 |
" (SubProblem (Biegelinie',[LINEAR,system],[no_met]) " ^
|
|
neuper@42387
|
344 |
" [BOOL_LIST equ_s, REAL_LIST [c,c_2,c_3,c_4]]); " ^
|
|
neuper@37999
|
345 |
" B_B = Take (lastI fun_s); " ^
|
|
neuper@37999
|
346 |
" B_B = ((Substitute con_s) @@ " ^
|
|
neuper@42387
|
347 |
" (Rewrite_Set_Inst [(bdv, v_v)] make_ratpoly_in False)) B_B " ^
|
|
neuper@37999
|
348 |
" in B_B)"
|
|
neuper@37954
|
349 |
));
|
|
neuper@37954
|
350 |
|
|
neuper@37999
|
351 |
*}
|
|
neuper@37999
|
352 |
ML {*
|
|
neuper@37954
|
353 |
store_met
|
|
neuper@37972
|
354 |
(prep_met thy "met_biege_intconst_2" [] e_metID
|
|
neuper@37954
|
355 |
(["IntegrierenUndKonstanteBestimmen","2xIntegrieren"],
|
|
neuper@37954
|
356 |
[],
|
|
neuper@37954
|
357 |
{rew_ord'="tless_true", rls'=Erls, calc = [],
|
|
neuper@37954
|
358 |
srls = e_rls,
|
|
neuper@37954
|
359 |
prls=e_rls,
|
|
neuper@42425
|
360 |
crls = Atools_erls, errpats = [], nrls = e_rls},
|
|
neuper@37954
|
361 |
"empty_script"
|
|
neuper@37954
|
362 |
));
|
|
neuper@37954
|
363 |
|
|
neuper@37954
|
364 |
store_met
|
|
neuper@37972
|
365 |
(prep_met thy "met_biege_intconst_4" [] e_metID
|
|
neuper@37954
|
366 |
(["IntegrierenUndKonstanteBestimmen","4x4System"],
|
|
neuper@37954
|
367 |
[],
|
|
neuper@37954
|
368 |
{rew_ord'="tless_true", rls'=Erls, calc = [],
|
|
neuper@37954
|
369 |
srls = e_rls,
|
|
neuper@37954
|
370 |
prls=e_rls,
|
|
neuper@42425
|
371 |
crls = Atools_erls, errpats = [], nrls = e_rls},
|
|
neuper@37954
|
372 |
"empty_script"
|
|
neuper@37954
|
373 |
));
|
|
neuper@37954
|
374 |
|
|
neuper@37954
|
375 |
store_met
|
|
neuper@37972
|
376 |
(prep_met thy "met_biege_intconst_1" [] e_metID
|
|
neuper@37954
|
377 |
(["IntegrierenUndKonstanteBestimmen","1xIntegrieren"],
|
|
neuper@37954
|
378 |
[],
|
|
neuper@37954
|
379 |
{rew_ord'="tless_true", rls'=Erls, calc = [],
|
|
neuper@37954
|
380 |
srls = e_rls,
|
|
neuper@37954
|
381 |
prls=e_rls,
|
|
neuper@42425
|
382 |
crls = Atools_erls, errpats = [], nrls = e_rls},
|
|
neuper@37954
|
383 |
"empty_script"
|
|
neuper@37954
|
384 |
));
|
|
neuper@37954
|
385 |
|
|
neuper@37954
|
386 |
store_met
|
|
neuper@37972
|
387 |
(prep_met thy "met_biege2" [] e_metID
|
|
neuper@37954
|
388 |
(["Biegelinien"],
|
|
neuper@37954
|
389 |
[],
|
|
neuper@37954
|
390 |
{rew_ord'="tless_true", rls'=Erls, calc = [],
|
|
neuper@37954
|
391 |
srls = e_rls,
|
|
neuper@37954
|
392 |
prls=e_rls,
|
|
neuper@42425
|
393 |
crls = Atools_erls, errpats = [], nrls = e_rls},
|
|
neuper@37954
|
394 |
"empty_script"
|
|
neuper@37954
|
395 |
));
|
|
neuper@37954
|
396 |
|
|
neuper@37999
|
397 |
*}
|
|
neuper@37999
|
398 |
ML {*
|
|
neuper@37954
|
399 |
store_met
|
|
neuper@42387
|
400 |
(prep_met thy "met_biege_ausbelast" [] e_metID
|
|
neuper@42387
|
401 |
(["Biegelinien", "ausBelastung"],
|
|
neuper@42387
|
402 |
[("#Given" ,["Streckenlast q__q", "FunktionsVariable v_v"]),
|
|
neuper@42387
|
403 |
("#Find" ,["Funktionen fun_s"])],
|
|
neuper@42387
|
404 |
{rew_ord'="tless_true",
|
|
neuper@42387
|
405 |
rls' = append_rls "erls_ausBelastung" e_rls
|
|
neuper@42387
|
406 |
[Calc ("Atools.ident", eval_ident "#ident_"),
|
|
neuper@42387
|
407 |
Thm ("not_true", num_str @{thm not_true}),
|
|
neuper@42387
|
408 |
Thm ("not_false", num_str @{thm not_false})],
|
|
neuper@42387
|
409 |
calc = [],
|
|
neuper@42387
|
410 |
srls = append_rls "srls_ausBelastung" e_rls
|
|
neuper@42387
|
411 |
[Calc ("Tools.rhs", eval_rhs "eval_rhs_")],
|
|
neuper@42425
|
412 |
prls = e_rls, crls = Atools_erls, errpats = [], nrls = e_rls},
|
|
neuper@42387
|
413 |
"Script Belastung2BiegelScript (q__q::real) (v_v::real) = " ^
|
|
neuper@42387
|
414 |
" (let q___q = Take (qq v_v = q__q); " ^
|
|
neuper@42387
|
415 |
" q___q = ((Rewrite sym_neg_equal_iff_equal True) @@ " ^
|
|
neuper@42387
|
416 |
" (Rewrite Belastung_Querkraft True)) q___q; " ^
|
|
neuper@42387
|
417 |
" (Q__Q:: bool) = " ^
|
|
neuper@42387
|
418 |
" (SubProblem (Biegelinie',[named,integrate,function], " ^
|
|
neuper@42387
|
419 |
" [diff,integration,named]) " ^
|
|
neuper@42387
|
420 |
" [REAL (rhs q___q), REAL v_v, REAL_REAL Q]); " ^
|
|
neuper@42387
|
421 |
" M__M = Rewrite Querkraft_Moment True Q__Q; " ^
|
|
neuper@42387
|
422 |
" (M__M::bool) = " ^
|
|
neuper@42387
|
423 |
" (SubProblem (Biegelinie',[named,integrate,function], " ^
|
|
neuper@42387
|
424 |
" [diff,integration,named]) " ^
|
|
neuper@42387
|
425 |
" [REAL (rhs M__M), REAL v_v, REAL_REAL M_b]); " ^
|
|
neuper@42387
|
426 |
" N__N = ((Rewrite Moment_Neigung False) @@ " ^
|
|
neuper@42387
|
427 |
" (Rewrite make_fun_explicit False)) M__M; " ^
|
|
neuper@42387
|
428 |
" (N__N:: bool) = " ^
|
|
neuper@42387
|
429 |
" (SubProblem (Biegelinie',[named,integrate,function], " ^
|
|
neuper@42387
|
430 |
" [diff,integration,named]) " ^
|
|
neuper@42387
|
431 |
" [REAL (rhs N__N), REAL v_v, REAL_REAL y']); " ^
|
|
neuper@42387
|
432 |
" (B__B:: bool) = " ^
|
|
neuper@42387
|
433 |
" (SubProblem (Biegelinie',[named,integrate,function], " ^
|
|
neuper@42387
|
434 |
" [diff,integration,named]) " ^
|
|
neuper@42387
|
435 |
" [REAL (rhs N__N), REAL v_v, REAL_REAL y]) " ^
|
|
neuper@37999
|
436 |
" in [Q__Q, M__M, N__N, B__B])"
|
|
neuper@37954
|
437 |
));
|
|
neuper@37954
|
438 |
|
|
neuper@37999
|
439 |
*}
|
|
neuper@37999
|
440 |
ML {*
|
|
neuper@37954
|
441 |
store_met
|
|
neuper@37972
|
442 |
(prep_met thy "met_biege_setzrand" [] e_metID
|
|
neuper@42387
|
443 |
(["Biegelinien", "setzeRandbedingungenEin"],
|
|
neuper@42387
|
444 |
[("#Given" , ["Funktionen fun_s", "Randbedingungen r_b"]),
|
|
neuper@42387
|
445 |
("#Find" , ["Gleichungen equs'''"])],
|
|
neuper@37954
|
446 |
{rew_ord'="tless_true", rls'=Erls, calc = [],
|
|
neuper@37954
|
447 |
srls = srls2,
|
|
neuper@37954
|
448 |
prls=e_rls,
|
|
neuper@42425
|
449 |
crls = Atools_erls, errpats = [], nrls = e_rls},
|
|
neuper@37999
|
450 |
"Script SetzeRandbedScript (fun_s::bool list) (r_b::bool list) = " ^
|
|
neuper@37999
|
451 |
" (let b_1 = NTH 1 r_b; " ^
|
|
neuper@37999
|
452 |
" f_s = filter_sameFunId (lhs b_1) fun_s; " ^
|
|
neuper@37999
|
453 |
" (e_1::bool) = " ^
|
|
neuper@37999
|
454 |
" (SubProblem (Biegelinie',[makeFunctionTo,equation]," ^
|
|
neuper@37954
|
455 |
" [Equation,fromFunction]) " ^
|
|
neuper@37999
|
456 |
" [BOOL (hd f_s), BOOL b_1]); " ^
|
|
neuper@37999
|
457 |
" b_2 = NTH 2 r_b; " ^
|
|
neuper@37999
|
458 |
" f_s = filter_sameFunId (lhs b_2) fun_s; " ^
|
|
neuper@37999
|
459 |
" (e_2::bool) = " ^
|
|
neuper@37999
|
460 |
" (SubProblem (Biegelinie',[makeFunctionTo,equation]," ^
|
|
neuper@37954
|
461 |
" [Equation,fromFunction]) " ^
|
|
neuper@37999
|
462 |
" [BOOL (hd f_s), BOOL b_2]); " ^
|
|
neuper@37999
|
463 |
" b_3 = NTH 3 r_b; " ^
|
|
neuper@37999
|
464 |
" f_s = filter_sameFunId (lhs b_3) fun_s; " ^
|
|
neuper@37999
|
465 |
" (e_3::bool) = " ^
|
|
neuper@37999
|
466 |
" (SubProblem (Biegelinie',[makeFunctionTo,equation]," ^
|
|
neuper@37954
|
467 |
" [Equation,fromFunction]) " ^
|
|
neuper@37999
|
468 |
" [BOOL (hd f_s), BOOL b_3]); " ^
|
|
neuper@37999
|
469 |
" b_4 = NTH 4 r_b; " ^
|
|
neuper@37999
|
470 |
" f_s = filter_sameFunId (lhs b_4) fun_s; " ^
|
|
neuper@37999
|
471 |
" (e_4::bool) = " ^
|
|
neuper@37999
|
472 |
" (SubProblem (Biegelinie',[makeFunctionTo,equation]," ^
|
|
neuper@37954
|
473 |
" [Equation,fromFunction]) " ^
|
|
neuper@37999
|
474 |
" [BOOL (hd f_s), BOOL b_4]) " ^
|
|
neuper@42387
|
475 |
" in [e_1, e_2, e_3, e_4])"
|
|
neuper@37954
|
476 |
(* filter requires more than 1 sec !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
|
|
neuper@37999
|
477 |
"Script SetzeRandbedScript (fun_s::bool list) (r_b::bool list) = " ^
|
|
neuper@37999
|
478 |
" (let b_1 = NTH 1 r_b; " ^
|
|
neuper@37999
|
479 |
" f_s = filter (sameFunId (lhs b_1)) fun_s; " ^
|
|
neuper@37999
|
480 |
" (e_1::bool) = " ^
|
|
neuper@37999
|
481 |
" (SubProblem (Biegelinie',[makeFunctionTo,equation]," ^
|
|
neuper@37954
|
482 |
" [Equation,fromFunction]) " ^
|
|
neuper@37999
|
483 |
" [BOOL (hd f_s), BOOL b_1]); " ^
|
|
neuper@37999
|
484 |
" b_2 = NTH 2 r_b; " ^
|
|
neuper@37999
|
485 |
" f_s = filter (sameFunId (lhs b_2)) fun_s; " ^
|
|
neuper@37999
|
486 |
" (e_2::bool) = " ^
|
|
neuper@37999
|
487 |
" (SubProblem (Biegelinie',[makeFunctionTo,equation]," ^
|
|
neuper@37954
|
488 |
" [Equation,fromFunction]) " ^
|
|
neuper@37999
|
489 |
" [BOOL (hd f_s), BOOL b_2]); " ^
|
|
neuper@37999
|
490 |
" b_3 = NTH 3 r_b; " ^
|
|
neuper@37999
|
491 |
" f_s = filter (sameFunId (lhs b_3)) fun_s; " ^
|
|
neuper@37999
|
492 |
" (e_3::bool) = " ^
|
|
neuper@37999
|
493 |
" (SubProblem (Biegelinie',[makeFunctionTo,equation]," ^
|
|
neuper@37954
|
494 |
" [Equation,fromFunction]) " ^
|
|
neuper@37999
|
495 |
" [BOOL (hd f_s), BOOL b_3]); " ^
|
|
neuper@37999
|
496 |
" b_4 = NTH 4 r_b; " ^
|
|
neuper@37999
|
497 |
" f_s = filter (sameFunId (lhs b_4)) fun_s; " ^
|
|
neuper@37999
|
498 |
" (e_4::bool) = " ^
|
|
neuper@37999
|
499 |
" (SubProblem (Biegelinie',[makeFunctionTo,equation]," ^
|
|
neuper@37954
|
500 |
" [Equation,fromFunction]) " ^
|
|
neuper@37999
|
501 |
" [BOOL (hd f_s), BOOL b_4]) " ^
|
|
neuper@37999
|
502 |
" in [e_1,e_2,e_3,e_4])"*)
|
|
neuper@37954
|
503 |
));
|
|
neuper@37954
|
504 |
|
|
neuper@37999
|
505 |
*}
|
|
neuper@37999
|
506 |
ML {*
|
|
neuper@37954
|
507 |
store_met
|
|
neuper@42387
|
508 |
(prep_met thy "met_equ_fromfun" [] e_metID
|
|
neuper@42387
|
509 |
(["Equation","fromFunction"],
|
|
neuper@42387
|
510 |
[("#Given" ,["functionEq fu_n","substitution su_b"]),
|
|
neuper@42387
|
511 |
("#Find" ,["equality equ'''"])],
|
|
neuper@42387
|
512 |
{rew_ord'="tless_true", rls'=Erls, calc = [],
|
|
neuper@42387
|
513 |
srls = append_rls "srls_in_EquationfromFunc" e_rls
|
|
neuper@42387
|
514 |
[Calc("Tools.lhs", eval_lhs"eval_lhs_"),
|
|
neuper@42387
|
515 |
Calc("Atools.argument'_in", eval_argument_in "Atools.argument'_in")],
|
|
neuper@42425
|
516 |
prls=e_rls, crls = Atools_erls, errpats = [], nrls = e_rls},
|
|
neuper@37954
|
517 |
(*(M_b x = c_2 + c * x + -1 * q_0 / 2 * x ^^^ 2) (M_b L = 0) -->
|
|
neuper@37954
|
518 |
0 = c_2 + c * L + -1 * q_0 / 2 * L ^^^ 2*)
|
|
neuper@37999
|
519 |
"Script Function2Equality (fu_n::bool) (su_b::bool) =" ^
|
|
neuper@37999
|
520 |
" (let fu_n = Take fu_n; " ^
|
|
neuper@37999
|
521 |
" bd_v = argument_in (lhs fu_n); " ^
|
|
neuper@37999
|
522 |
" va_l = argument_in (lhs su_b); " ^
|
|
neuper@37999
|
523 |
" eq_u = (Substitute [bd_v = va_l]) fu_n; " ^
|
|
neuper@42387
|
524 |
(*([1], Res), M_b L = c_2 + c * L + -1 * q_0 / 2 * L ^^^ 2*)
|
|
neuper@42387
|
525 |
" eq_u = (Substitute [su_b]) eq_u " ^
|
|
neuper@42387
|
526 |
" in (Rewrite_Set norm_Rational False) eq_u) "
|
|
neuper@37954
|
527 |
));
|
|
neuper@37954
|
528 |
*}
|
|
neuper@37954
|
529 |
|
|
neuper@37906
|
530 |
end
|
|
neuper@37906
|
531 |
|