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neuper@37906
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(* chapter 'Biegelinie' from the textbook:
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neuper@37906
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Timischl, Kaiser. Ingenieur-Mathematik 3. Wien 1999. p.268-271.
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neuper@37999
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author: Walther Neuper 050826,
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neuper@37906
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(c) due to copyright terms
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neuper@37906
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*)
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neuper@37906
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bonzai@41919
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theory Biegelinie imports Integrate Equation EqSystem Atools begin
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neuper@37906
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neuper@37906
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consts
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neuper@37906
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neuper@42385
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qq :: "real => real" (* Streckenlast *)
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neuper@37999
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Q :: "real => real" (* Querkraft *)
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neuper@37999
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Q' :: "real => real" (* Ableitung der Querkraft *)
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neuper@37999
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M'_b :: "real => real" ("M'_b") (* Biegemoment *)
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neuper@37999
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M'_b' :: "real => real" ("M'_b'") (* Ableitung des Biegemoments *)
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neuper@37999
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y'' :: "real => real" (* 2.Ableitung der Biegeline *)
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neuper@37999
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y' :: "real => real" (* Neigung der Biegeline *)
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neuper@37999
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(*y :: "real => real" (* Biegeline *)*)
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neuper@37999
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EI :: "real" (* Biegesteifigkeit *)
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neuper@37906
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neuper@37906
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(*new Descriptions in the related problems*)
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neuper@37999
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Traegerlaenge :: "real => una"
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neuper@37999
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Streckenlast :: "real => una"
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neuper@37999
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BiegemomentVerlauf :: "bool => una"
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neuper@37999
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Biegelinie :: "(real => real) => una"
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neuper@37999
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Randbedingungen :: "bool list => una"
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neuper@37999
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RandbedingungenBiegung :: "bool list => una"
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neuper@37999
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RandbedingungenNeigung :: "bool list => una"
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neuper@37999
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RandbedingungenMoment :: "bool list => una"
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neuper@37999
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RandbedingungenQuerkraft :: "bool list => una"
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neuper@37999
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FunktionsVariable :: "real => una"
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neuper@37999
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Funktionen :: "bool list => una"
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neuper@37999
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Gleichungen :: "bool list => una"
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neuper@37906
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neuper@37906
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(*Script-names*)
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neuper@37906
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Biegelinie2Script :: "[real,real,real,real=>real,bool list,
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neuper@37906
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bool] => bool"
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neuper@37906
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("((Script Biegelinie2Script (_ _ _ _ _ =))// (_))" 9)
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neuper@37906
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BiegelinieScript :: "[real,real,real,real=>real,bool list,bool list,
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neuper@37906
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bool] => bool"
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neuper@37906
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("((Script BiegelinieScript (_ _ _ _ _ _ =))// (_))" 9)
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neuper@37906
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Biege2xIntegrierenScript :: "[real,real,real,bool,real=>real,bool list,
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neuper@37906
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bool] => bool"
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neuper@37906
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("((Script Biege2xIntegrierenScript (_ _ _ _ _ _ =))// (_))" 9)
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neuper@37906
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Biege4x4SystemScript :: "[real,real,real,real=>real,bool list,
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neuper@37906
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bool] => bool"
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neuper@37906
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("((Script Biege4x4SystemScript (_ _ _ _ _ =))// (_))" 9)
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neuper@37906
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Biege1xIntegrierenScript ::
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neuper@37906
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"[real,real,real,real=>real,bool list,bool list,bool list,
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neuper@37906
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bool] => bool"
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neuper@37906
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("((Script Biege1xIntegrierenScript (_ _ _ _ _ _ _ =))// (_))" 9)
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neuper@37906
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Belastung2BiegelScript :: "[real,real,
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neuper@37906
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bool list] => bool list"
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neuper@37906
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("((Script Belastung2BiegelScript (_ _ =))// (_))" 9)
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neuper@37906
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SetzeRandbedScript :: "[bool list,bool list,
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neuper@37906
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bool list] => bool list"
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neuper@37906
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("((Script SetzeRandbedScript (_ _ =))// (_))" 9)
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neuper@37906
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neuper@52148
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axiomatization where
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neuper@37906
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neuper@52148
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Querkraft_Belastung: "Q' x = -qq x" and
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neuper@52148
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Belastung_Querkraft: "-qq x = Q' x" and
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neuper@37906
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neuper@52148
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Moment_Querkraft: "M_b' x = Q x" and
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neuper@52148
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Querkraft_Moment: "Q x = M_b' x" and
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neuper@37906
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neuper@52148
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Neigung_Moment: "y'' x = -M_b x/ EI" and
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neuper@52148
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Moment_Neigung: "M_b x = -EI * y'' x" and
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neuper@37906
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neuper@37906
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(*according to rls 'simplify_Integral': .. = 1/a * .. instead .. = ../ a*)
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neuper@37983
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make_fun_explicit: "Not (a =!= 0) ==> (a * (f x) = b) = (f x = 1/a * b)"
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neuper@37906
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neuper@37954
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ML {*
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neuper@37972
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val thy = @{theory};
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neuper@37972
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neuper@37954
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(** theory elements for transfer into html **)
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neuper@37954
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neuper@37954
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store_isa ["IsacKnowledge"] [];
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neuper@37972
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store_thy thy
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neuper@37954
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["Walther Neuper 2005 supported by a grant from NMI Austria"];
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neuper@37972
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store_isa ["IsacKnowledge", theory2thyID thy, "Theorems"]
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neuper@37954
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["Walther Neuper 2005 supported by a grant from NMI Austria"];
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neuper@42411
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store_thm thy "IsacKnowledge" ("Belastung_Querkraft", prop_of @{thm Belastung_Querkraft})
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neuper@37954
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["Walther Neuper 2005 supported by a grant from NMI Austria"];
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neuper@42411
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store_thm thy "IsacKnowledge" ("Moment_Neigung", prop_of @{thm Moment_Neigung})
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neuper@37954
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["Walther Neuper 2005 supported by a grant from NMI Austria"];
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neuper@42411
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store_thm thy "IsacKnowledge" ("Moment_Querkraft", prop_of @{thm Moment_Querkraft})
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neuper@37954
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["Walther Neuper 2005 supported by a grant from NMI Austria"];
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neuper@42411
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store_thm thy "IsacKnowledge" ("Neigung_Moment", prop_of @{thm Neigung_Moment})
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neuper@37954
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["Walther Neuper 2005 supported by a grant from NMI Austria"];
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neuper@42411
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store_thm thy "IsacKnowledge" ("Querkraft_Belastung", prop_of @{thm Querkraft_Belastung})
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neuper@37954
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["Walther Neuper 2005 supported by a grant from NMI Austria"];
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neuper@42411
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store_thm thy "IsacKnowledge" ("Querkraft_Moment", prop_of @{thm Querkraft_Moment})
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neuper@37954
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["Walther Neuper 2005 supported by a grant from NMI Austria"];
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neuper@42411
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store_thm thy "IsacKnowledge" ("make_fun_explicit", prop_of @{thm make_fun_explicit})
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neuper@37954
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["Walther Neuper 2005 supported by a grant from NMI Austria"];
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neuper@37954
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neuper@37999
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*}
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neuper@37954
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(** problems **)
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s1210629013@55359
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setup {* KEStore_Elems.add_pbts
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s1210629013@55339
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[(prep_pbt thy "pbl_bieg" [] e_pblID
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s1210629013@55339
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(["Biegelinien"],
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s1210629013@55339
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[("#Given" ,["Traegerlaenge l_l", "Streckenlast q_q"]),
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s1210629013@55339
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(*("#Where",["0 < l_l"]), ...wait for < and handling Arbfix*)
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s1210629013@55339
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("#Find" ,["Biegelinie b_b"]),
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s1210629013@55339
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("#Relate",["Randbedingungen r_b"])],
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s1210629013@55339
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append_rls "e_rls" e_rls [], NONE, [["IntegrierenUndKonstanteBestimmen2"]])),
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s1210629013@55339
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(prep_pbt thy "pbl_bieg_mom" [] e_pblID
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s1210629013@55339
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(["MomentBestimmte","Biegelinien"],
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s1210629013@55339
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[("#Given" ,["Traegerlaenge l_l", "Streckenlast q_q"]),
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s1210629013@55339
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(*("#Where",["0 < l_l"]), ...wait for < and handling Arbfix*)
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s1210629013@55339
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("#Find" ,["Biegelinie b_b"]),
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s1210629013@55339
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("#Relate",["RandbedingungenBiegung r_b","RandbedingungenMoment r_m"])
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s1210629013@55339
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],
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s1210629013@55339
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append_rls "e_rls" e_rls [], NONE, [["IntegrierenUndKonstanteBestimmen"]])),
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s1210629013@55339
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(prep_pbt thy "pbl_bieg_momg" [] e_pblID
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s1210629013@55339
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(["MomentGegebene","Biegelinien"], [], append_rls "e_rls" e_rls [], NONE,
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s1210629013@55339
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[["IntegrierenUndKonstanteBestimmen","2xIntegrieren"]])),
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s1210629013@55339
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(prep_pbt thy "pbl_bieg_einf" [] e_pblID
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s1210629013@55339
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(["einfache","Biegelinien"], [], append_rls "e_rls" e_rls [], NONE,
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s1210629013@55339
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[["IntegrierenUndKonstanteBestimmen","4x4System"]])),
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s1210629013@55339
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(prep_pbt thy "pbl_bieg_momquer" [] e_pblID
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s1210629013@55339
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(["QuerkraftUndMomentBestimmte","Biegelinien"], [], append_rls "e_rls" e_rls [], NONE,
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s1210629013@55339
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[["IntegrierenUndKonstanteBestimmen","1xIntegrieren"]])),
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s1210629013@55339
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(prep_pbt thy "pbl_bieg_vonq" [] e_pblID
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s1210629013@55339
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(["vonBelastungZu","Biegelinien"],
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s1210629013@55339
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[("#Given" ,["Streckenlast q_q","FunktionsVariable v_v"]),
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s1210629013@55339
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("#Find" ,["Funktionen funs'''"])],
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s1210629013@55339
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append_rls "e_rls" e_rls [], NONE, [["Biegelinien","ausBelastung"]])),
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s1210629013@55339
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(prep_pbt thy "pbl_bieg_randbed" [] e_pblID
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s1210629013@55339
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(["setzeRandbedingungen","Biegelinien"],
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s1210629013@55339
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[("#Given" ,["Funktionen fun_s","Randbedingungen r_b"]),
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s1210629013@55339
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("#Find" ,["Gleichungen equs'''"])],
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s1210629013@55339
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append_rls "e_rls" e_rls [], NONE, [["Biegelinien","setzeRandbedingungenEin"]])),
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s1210629013@55339
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(prep_pbt thy "pbl_equ_fromfun" [] e_pblID
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s1210629013@55339
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(["makeFunctionTo","equation"],
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s1210629013@55339
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[("#Given" ,["functionEq fu_n","substitution su_b"]),
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s1210629013@55339
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("#Find" ,["equality equ'''"])],
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s1210629013@55339
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append_rls "e_rls" e_rls [], NONE, [["Equation","fromFunction"]]))] *}
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neuper@37999
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ML {*
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neuper@37954
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(** methods **)
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neuper@37954
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neuper@37954
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val srls = Rls {id="srls_IntegrierenUnd..",
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neuper@37954
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preconds = [],
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neuper@37954
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rew_ord = ("termlessI",termlessI),
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neuper@37954
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erls = append_rls "erls_in_srls_IntegrierenUnd.." e_rls
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neuper@37999
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[(*for asm in NTH_CONS ...*)
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neuper@38045
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Calc ("Orderings.ord_class.less",eval_equ "#less_"),
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neuper@37999
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(*2nd NTH_CONS pushes n+-1 into asms*)
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neuper@38014
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Calc("Groups.plus_class.plus", eval_binop "#add_")
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neuper@37954
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],
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neuper@42451
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srls = Erls, calc = [], errpatts = [],
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neuper@37999
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rules = [Thm ("NTH_CONS",num_str @{thm NTH_CONS}),
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neuper@38014
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Calc("Groups.plus_class.plus", eval_binop "#add_"),
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neuper@37999
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Thm ("NTH_NIL",num_str @{thm NTH_NIL}),
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neuper@37954
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Calc("Tools.lhs", eval_lhs"eval_lhs_"),
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neuper@37954
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Calc("Tools.rhs", eval_rhs"eval_rhs_"),
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neuper@37954
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158 |
Calc("Atools.argument'_in",
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neuper@37954
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eval_argument_in "Atools.argument'_in")
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neuper@37954
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],
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neuper@37954
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scr = EmptyScr};
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neuper@37954
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neuper@37954
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val srls2 =
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neuper@37954
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Rls {id="srls_IntegrierenUnd..",
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neuper@37954
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preconds = [],
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neuper@37954
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rew_ord = ("termlessI",termlessI),
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neuper@37954
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erls = append_rls "erls_in_srls_IntegrierenUnd.." e_rls
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neuper@37999
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[(*for asm in NTH_CONS ...*)
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neuper@38045
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Calc ("Orderings.ord_class.less",eval_equ "#less_"),
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neuper@37999
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(*2nd NTH_CONS pushes n+-1 into asms*)
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neuper@38014
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Calc("Groups.plus_class.plus", eval_binop "#add_")
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neuper@37954
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],
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neuper@42451
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srls = Erls, calc = [], errpatts = [],
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neuper@37999
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rules = [Thm ("NTH_CONS",num_str @{thm NTH_CONS}),
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neuper@38014
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Calc("Groups.plus_class.plus", eval_binop "#add_"),
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neuper@37999
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Thm ("NTH_NIL", num_str @{thm NTH_NIL}),
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neuper@37954
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Calc("Tools.lhs", eval_lhs "eval_lhs_"),
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neuper@37954
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Calc("Atools.filter'_sameFunId",
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neuper@37954
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eval_filter_sameFunId "Atools.filter'_sameFunId"),
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neuper@37954
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(*WN070514 just for smltest/../biegelinie.sml ...*)
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neuper@37954
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Calc("Atools.sameFunId", eval_sameFunId "Atools.sameFunId"),
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neuper@37969
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Thm ("filter_Cons", num_str @{thm filter_Cons}),
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neuper@37969
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Thm ("filter_Nil", num_str @{thm filter_Nil}),
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neuper@37969
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Thm ("if_True", num_str @{thm if_True}),
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neuper@37969
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Thm ("if_False", num_str @{thm if_False}),
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neuper@37969
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Thm ("hd_thm", num_str @{thm hd_thm})
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neuper@37954
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],
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neuper@37954
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scr = EmptyScr};
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neuper@37999
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189 |
*}
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neuper@37999
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neuper@37999
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191 |
ML {*
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neuper@37954
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192 |
store_met
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neuper@42387
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(prep_met thy "met_biege" [] e_metID
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neuper@42387
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(["IntegrierenUndKonstanteBestimmen"],
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neuper@42387
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[("#Given" ,["Traegerlaenge l_l", "Streckenlast q__q", "FunktionsVariable v_v"]),
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neuper@37999
|
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(*("#Where",["0 < l_l"]), ...wait for < and handling Arbfix*)
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neuper@42387
|
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("#Find" ,["Biegelinie b_b"]),
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neuper@42387
|
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("#Relate",["RandbedingungenBiegung r_b", "RandbedingungenMoment r_m"])],
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neuper@42387
|
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{rew_ord'="tless_true",
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neuper@42387
|
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rls' = append_rls "erls_IntegrierenUndK.." e_rls
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neuper@42387
|
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[Calc ("Atools.ident",eval_ident "#ident_"),
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neuper@42387
|
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Thm ("not_true",num_str @{thm not_true}),
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neuper@42387
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Thm ("not_false",num_str @{thm not_false})],
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neuper@42425
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calc = [], srls = srls, prls = Erls, crls = Atools_erls, errpats = [], nrls = Erls},
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neuper@42387
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"Script BiegelinieScript " ^
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neuper@42387
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"(l_l::real) (q__q::real) (v_v::real) (b_b::real=>real) " ^
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neuper@42387
|
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"(r_b::bool list) (r_m::bool list) = " ^
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neuper@42387
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" (let q___q = Take (qq v_v = q__q); " ^
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neuper@42387
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209 |
" q___q = ((Rewrite sym_neg_equal_iff_equal True) @@ " ^
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neuper@42387
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210 |
" (Rewrite Belastung_Querkraft True)) q___q; " ^
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neuper@42387
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211 |
" (Q__Q:: bool) = " ^
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neuper@42387
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212 |
" (SubProblem (Biegelinie',[named,integrate,function], " ^
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neuper@42387
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" [diff,integration,named]) " ^
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neuper@37999
|
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" [REAL (rhs q___q), REAL v_v, REAL_REAL Q]); " ^
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neuper@42387
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" Q__Q = Rewrite Querkraft_Moment True Q__Q; " ^
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neuper@42387
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" (M__M::bool) = " ^
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neuper@42387
|
217 |
" (SubProblem (Biegelinie',[named,integrate,function], " ^
|
|
neuper@42387
|
218 |
" [diff,integration,named]) " ^
|
|
neuper@37999
|
219 |
" [REAL (rhs Q__Q), REAL v_v, REAL_REAL M_b]); " ^
|
|
neuper@42387
|
220 |
(*([5], Res), M_b x = c_2 + c * x + -1 * q_0 / 2 * x ^^^ 2*)
|
|
neuper@37999
|
221 |
" e__1 = NTH 1 r_m; " ^
|
|
neuper@42387
|
222 |
" (x__1::real) = argument_in (lhs e__1); " ^
|
|
neuper@42387
|
223 |
" (M__1::bool) = (Substitute [v_v = x__1]) M__M; " ^
|
|
neuper@42387
|
224 |
(*([6], Res), M_b 0 = c_2 + c * 0 + -1 * q_0 / 2 * 0 ^^^ 2*)
|
|
neuper@42387
|
225 |
" M__1 = (Substitute [e__1]) M__1; " ^
|
|
neuper@42387
|
226 |
(*([7], Res), 0 = c_2 + c * 0 + -1 * q_0 / 2 * 0 ^^^ 2*)
|
|
neuper@42387
|
227 |
" M__2 = Take M__M; " ^
|
|
neuper@42387
|
228 |
(*([8], Frm), M_b x = c_2 + c * x + -1 * q_0 / 2 * x ^^^ 2*)
|
|
neuper@42387
|
229 |
(*without above Take 'Substitute [v_v = x__2]' takes _last formula from ctree_*)
|
|
neuper@37999
|
230 |
" e__2 = NTH 2 r_m; " ^
|
|
neuper@42387
|
231 |
" (x__2::real) = argument_in (lhs e__2); " ^
|
|
neuper@42387
|
232 |
" (M__2::bool) = (Substitute [v_v = x__2]) M__M; " ^
|
|
neuper@42387
|
233 |
(*([8], Res), M_b L = c_2 + c * L + -1 * q_0 / 2 * L ^^^ 2*)
|
|
neuper@42387
|
234 |
" M__2 = (Substitute [e__2]) M__2; " ^
|
|
neuper@42387
|
235 |
(**)
|
|
neuper@42387
|
236 |
" (c_1_2::bool list) = " ^
|
|
neuper@55276
|
237 |
" (SubProblem (Biegelinie',[LINEAR,system],[no_met]) " ^
|
|
neuper@42387
|
238 |
" [BOOL_LIST [M__1, M__2], REAL_LIST [c,c_2]]); " ^
|
|
neuper@42387
|
239 |
" M__M = Take M__M; " ^
|
|
neuper@37999
|
240 |
" M__M = ((Substitute c_1_2) @@ " ^
|
|
neuper@42387
|
241 |
" (Try (Rewrite_Set_Inst [(bdv_1, c),(bdv_2, c_2)] " ^
|
|
neuper@42387
|
242 |
" simplify_System False)) @@ " ^
|
|
neuper@42387
|
243 |
" (Rewrite Moment_Neigung False) @@ " ^
|
|
neuper@42387
|
244 |
" (Rewrite make_fun_explicit False)) M__M; " ^
|
|
neuper@37954
|
245 |
(*----------------------- and the same once more ------------------------*)
|
|
neuper@42387
|
246 |
" (N__N:: bool) = " ^
|
|
neuper@42387
|
247 |
" (SubProblem (Biegelinie',[named,integrate,function], " ^
|
|
neuper@42387
|
248 |
" [diff,integration,named]) " ^
|
|
neuper@37999
|
249 |
" [REAL (rhs M__M), REAL v_v, REAL_REAL y']); " ^
|
|
neuper@42387
|
250 |
" (B__B:: bool) = " ^
|
|
neuper@42387
|
251 |
" (SubProblem (Biegelinie',[named,integrate,function], " ^
|
|
neuper@42387
|
252 |
" [diff,integration,named]) " ^
|
|
neuper@37999
|
253 |
" [REAL (rhs N__N), REAL v_v, REAL_REAL y]); " ^
|
|
neuper@37999
|
254 |
" e__1 = NTH 1 r_b; " ^
|
|
neuper@42387
|
255 |
" (x__1::real) = argument_in (lhs e__1); " ^
|
|
neuper@42387
|
256 |
" (B__1::bool) = (Substitute [v_v = x__1]) B__B; " ^
|
|
neuper@42387
|
257 |
" B__1 = (Substitute [e__1]) B__1 ; " ^
|
|
neuper@42387
|
258 |
" B__2 = Take B__B; " ^
|
|
neuper@37999
|
259 |
" e__2 = NTH 2 r_b; " ^
|
|
neuper@42387
|
260 |
" (x__2::real) = argument_in (lhs e__2); " ^
|
|
neuper@42387
|
261 |
" (B__2::bool) = (Substitute [v_v = x__2]) B__B; " ^
|
|
neuper@42387
|
262 |
" B__2 = (Substitute [e__2]) B__2 ; " ^
|
|
neuper@42387
|
263 |
" (c_1_2::bool list) = " ^
|
|
neuper@55276
|
264 |
" (SubProblem (Biegelinie',[LINEAR,system],[no_met]) " ^
|
|
neuper@42387
|
265 |
" [BOOL_LIST [B__1, B__2], REAL_LIST [c,c_2]]); " ^
|
|
neuper@42387
|
266 |
" B__B = Take B__B; " ^
|
|
neuper@37999
|
267 |
" B__B = ((Substitute c_1_2) @@ " ^
|
|
neuper@42387
|
268 |
" (Rewrite_Set_Inst [(bdv, x)] make_ratpoly_in False)) B__B " ^
|
|
neuper@37999
|
269 |
" in B__B)"
|
|
neuper@37954
|
270 |
));
|
|
neuper@37999
|
271 |
*}
|
|
neuper@37999
|
272 |
ML {*
|
|
neuper@37954
|
273 |
store_met
|
|
neuper@42387
|
274 |
(prep_met thy "met_biege_2" [] e_metID
|
|
neuper@42387
|
275 |
(["IntegrierenUndKonstanteBestimmen2"],
|
|
neuper@42387
|
276 |
[("#Given" ,["Traegerlaenge l_l", "Streckenlast q__q", "FunktionsVariable v_v"]),
|
|
neuper@37999
|
277 |
(*("#Where",["0 < l_l"]), ...wait for < and handling Arbfix*)
|
|
neuper@42387
|
278 |
("#Find" ,["Biegelinie b_b"]),
|
|
neuper@42387
|
279 |
("#Relate",["Randbedingungen r_b"])],
|
|
neuper@42387
|
280 |
{rew_ord'="tless_true",
|
|
neuper@42387
|
281 |
rls' = append_rls "erls_IntegrierenUndK.." e_rls
|
|
neuper@42387
|
282 |
[Calc ("Atools.ident",eval_ident "#ident_"),
|
|
neuper@42387
|
283 |
Thm ("not_true",num_str @{thm not_true}),
|
|
neuper@42387
|
284 |
Thm ("not_false",num_str @{thm not_false})],
|
|
neuper@42387
|
285 |
calc = [],
|
|
neuper@42387
|
286 |
srls = append_rls "erls_IntegrierenUndK.." e_rls
|
|
neuper@42387
|
287 |
[Calc("Tools.rhs", eval_rhs"eval_rhs_"),
|
|
neuper@42387
|
288 |
Calc ("Atools.ident",eval_ident "#ident_"),
|
|
neuper@42387
|
289 |
Thm ("last_thmI",num_str @{thm last_thmI}),
|
|
neuper@42387
|
290 |
Thm ("if_True",num_str @{thm if_True}),
|
|
neuper@42387
|
291 |
Thm ("if_False",num_str @{thm if_False})],
|
|
neuper@42425
|
292 |
prls = Erls, crls = Atools_erls, errpats = [], nrls = Erls},
|
|
neuper@42387
|
293 |
"Script Biegelinie2Script " ^
|
|
neuper@37999
|
294 |
"(l_l::real) (q__q::real) (v_v::real) (b_b::real=>real) (r_b::bool list) = " ^
|
|
neuper@42387
|
295 |
" (let " ^
|
|
neuper@42387
|
296 |
" (fun_s:: bool list) = " ^
|
|
neuper@42387
|
297 |
" (SubProblem (Biegelinie',[vonBelastungZu,Biegelinien], " ^
|
|
neuper@42387
|
298 |
" [Biegelinien,ausBelastung]) " ^
|
|
neuper@42387
|
299 |
" [REAL q__q, REAL v_v]); " ^
|
|
neuper@42387
|
300 |
" (equ_s::bool list) = " ^
|
|
neuper@42387
|
301 |
" (SubProblem (Biegelinie',[setzeRandbedingungen,Biegelinien], " ^
|
|
neuper@42387
|
302 |
" [Biegelinien,setzeRandbedingungenEin]) " ^
|
|
neuper@37999
|
303 |
" [BOOL_LIST fun_s, BOOL_LIST r_b]); " ^
|
|
neuper@42387
|
304 |
" (con_s::bool list) = " ^
|
|
neuper@55276
|
305 |
" (SubProblem (Biegelinie',[LINEAR,system],[no_met]) " ^
|
|
neuper@42387
|
306 |
" [BOOL_LIST equ_s, REAL_LIST [c,c_2,c_3,c_4]]); " ^
|
|
neuper@37999
|
307 |
" B_B = Take (lastI fun_s); " ^
|
|
neuper@37999
|
308 |
" B_B = ((Substitute con_s) @@ " ^
|
|
neuper@42387
|
309 |
" (Rewrite_Set_Inst [(bdv, v_v)] make_ratpoly_in False)) B_B " ^
|
|
neuper@37999
|
310 |
" in B_B)"
|
|
neuper@37954
|
311 |
));
|
|
neuper@37954
|
312 |
|
|
neuper@37999
|
313 |
*}
|
|
neuper@37999
|
314 |
ML {*
|
|
neuper@37954
|
315 |
store_met
|
|
neuper@37972
|
316 |
(prep_met thy "met_biege_intconst_2" [] e_metID
|
|
neuper@37954
|
317 |
(["IntegrierenUndKonstanteBestimmen","2xIntegrieren"],
|
|
neuper@37954
|
318 |
[],
|
|
neuper@37954
|
319 |
{rew_ord'="tless_true", rls'=Erls, calc = [],
|
|
neuper@37954
|
320 |
srls = e_rls,
|
|
neuper@37954
|
321 |
prls=e_rls,
|
|
neuper@42425
|
322 |
crls = Atools_erls, errpats = [], nrls = e_rls},
|
|
neuper@37954
|
323 |
"empty_script"
|
|
neuper@37954
|
324 |
));
|
|
neuper@37954
|
325 |
|
|
neuper@37954
|
326 |
store_met
|
|
neuper@37972
|
327 |
(prep_met thy "met_biege_intconst_4" [] e_metID
|
|
neuper@37954
|
328 |
(["IntegrierenUndKonstanteBestimmen","4x4System"],
|
|
neuper@37954
|
329 |
[],
|
|
neuper@37954
|
330 |
{rew_ord'="tless_true", rls'=Erls, calc = [],
|
|
neuper@37954
|
331 |
srls = e_rls,
|
|
neuper@37954
|
332 |
prls=e_rls,
|
|
neuper@42425
|
333 |
crls = Atools_erls, errpats = [], nrls = e_rls},
|
|
neuper@37954
|
334 |
"empty_script"
|
|
neuper@37954
|
335 |
));
|
|
neuper@37954
|
336 |
|
|
neuper@37954
|
337 |
store_met
|
|
neuper@37972
|
338 |
(prep_met thy "met_biege_intconst_1" [] e_metID
|
|
neuper@37954
|
339 |
(["IntegrierenUndKonstanteBestimmen","1xIntegrieren"],
|
|
neuper@37954
|
340 |
[],
|
|
neuper@37954
|
341 |
{rew_ord'="tless_true", rls'=Erls, calc = [],
|
|
neuper@37954
|
342 |
srls = e_rls,
|
|
neuper@37954
|
343 |
prls=e_rls,
|
|
neuper@42425
|
344 |
crls = Atools_erls, errpats = [], nrls = e_rls},
|
|
neuper@37954
|
345 |
"empty_script"
|
|
neuper@37954
|
346 |
));
|
|
neuper@37954
|
347 |
|
|
neuper@37954
|
348 |
store_met
|
|
neuper@37972
|
349 |
(prep_met thy "met_biege2" [] e_metID
|
|
neuper@37954
|
350 |
(["Biegelinien"],
|
|
neuper@37954
|
351 |
[],
|
|
neuper@37954
|
352 |
{rew_ord'="tless_true", rls'=Erls, calc = [],
|
|
neuper@37954
|
353 |
srls = e_rls,
|
|
neuper@37954
|
354 |
prls=e_rls,
|
|
neuper@42425
|
355 |
crls = Atools_erls, errpats = [], nrls = e_rls},
|
|
neuper@37954
|
356 |
"empty_script"
|
|
neuper@37954
|
357 |
));
|
|
neuper@37954
|
358 |
|
|
neuper@37999
|
359 |
*}
|
|
neuper@37999
|
360 |
ML {*
|
|
neuper@37954
|
361 |
store_met
|
|
neuper@42387
|
362 |
(prep_met thy "met_biege_ausbelast" [] e_metID
|
|
neuper@42387
|
363 |
(["Biegelinien", "ausBelastung"],
|
|
neuper@42387
|
364 |
[("#Given" ,["Streckenlast q__q", "FunktionsVariable v_v"]),
|
|
neuper@42387
|
365 |
("#Find" ,["Funktionen fun_s"])],
|
|
neuper@42387
|
366 |
{rew_ord'="tless_true",
|
|
neuper@42387
|
367 |
rls' = append_rls "erls_ausBelastung" e_rls
|
|
neuper@42387
|
368 |
[Calc ("Atools.ident", eval_ident "#ident_"),
|
|
neuper@42387
|
369 |
Thm ("not_true", num_str @{thm not_true}),
|
|
neuper@42387
|
370 |
Thm ("not_false", num_str @{thm not_false})],
|
|
neuper@42387
|
371 |
calc = [],
|
|
neuper@42387
|
372 |
srls = append_rls "srls_ausBelastung" e_rls
|
|
neuper@42387
|
373 |
[Calc ("Tools.rhs", eval_rhs "eval_rhs_")],
|
|
neuper@42425
|
374 |
prls = e_rls, crls = Atools_erls, errpats = [], nrls = e_rls},
|
|
neuper@42387
|
375 |
"Script Belastung2BiegelScript (q__q::real) (v_v::real) = " ^
|
|
neuper@42387
|
376 |
" (let q___q = Take (qq v_v = q__q); " ^
|
|
neuper@42387
|
377 |
" q___q = ((Rewrite sym_neg_equal_iff_equal True) @@ " ^
|
|
neuper@42387
|
378 |
" (Rewrite Belastung_Querkraft True)) q___q; " ^
|
|
neuper@42387
|
379 |
" (Q__Q:: bool) = " ^
|
|
neuper@42387
|
380 |
" (SubProblem (Biegelinie',[named,integrate,function], " ^
|
|
neuper@42387
|
381 |
" [diff,integration,named]) " ^
|
|
neuper@42387
|
382 |
" [REAL (rhs q___q), REAL v_v, REAL_REAL Q]); " ^
|
|
neuper@42387
|
383 |
" M__M = Rewrite Querkraft_Moment True Q__Q; " ^
|
|
neuper@42387
|
384 |
" (M__M::bool) = " ^
|
|
neuper@42387
|
385 |
" (SubProblem (Biegelinie',[named,integrate,function], " ^
|
|
neuper@42387
|
386 |
" [diff,integration,named]) " ^
|
|
neuper@42387
|
387 |
" [REAL (rhs M__M), REAL v_v, REAL_REAL M_b]); " ^
|
|
neuper@42387
|
388 |
" N__N = ((Rewrite Moment_Neigung False) @@ " ^
|
|
neuper@42387
|
389 |
" (Rewrite make_fun_explicit False)) M__M; " ^
|
|
neuper@42387
|
390 |
" (N__N:: bool) = " ^
|
|
neuper@42387
|
391 |
" (SubProblem (Biegelinie',[named,integrate,function], " ^
|
|
neuper@42387
|
392 |
" [diff,integration,named]) " ^
|
|
neuper@42387
|
393 |
" [REAL (rhs N__N), REAL v_v, REAL_REAL y']); " ^
|
|
neuper@42387
|
394 |
" (B__B:: bool) = " ^
|
|
neuper@42387
|
395 |
" (SubProblem (Biegelinie',[named,integrate,function], " ^
|
|
neuper@42387
|
396 |
" [diff,integration,named]) " ^
|
|
neuper@42387
|
397 |
" [REAL (rhs N__N), REAL v_v, REAL_REAL y]) " ^
|
|
neuper@37999
|
398 |
" in [Q__Q, M__M, N__N, B__B])"
|
|
neuper@37954
|
399 |
));
|
|
neuper@37954
|
400 |
|
|
neuper@37999
|
401 |
*}
|
|
neuper@37999
|
402 |
ML {*
|
|
neuper@37954
|
403 |
store_met
|
|
neuper@37972
|
404 |
(prep_met thy "met_biege_setzrand" [] e_metID
|
|
neuper@42387
|
405 |
(["Biegelinien", "setzeRandbedingungenEin"],
|
|
neuper@42387
|
406 |
[("#Given" , ["Funktionen fun_s", "Randbedingungen r_b"]),
|
|
neuper@42387
|
407 |
("#Find" , ["Gleichungen equs'''"])],
|
|
neuper@37954
|
408 |
{rew_ord'="tless_true", rls'=Erls, calc = [],
|
|
neuper@37954
|
409 |
srls = srls2,
|
|
neuper@37954
|
410 |
prls=e_rls,
|
|
neuper@42425
|
411 |
crls = Atools_erls, errpats = [], nrls = e_rls},
|
|
neuper@37999
|
412 |
"Script SetzeRandbedScript (fun_s::bool list) (r_b::bool list) = " ^
|
|
neuper@37999
|
413 |
" (let b_1 = NTH 1 r_b; " ^
|
|
neuper@37999
|
414 |
" f_s = filter_sameFunId (lhs b_1) fun_s; " ^
|
|
neuper@37999
|
415 |
" (e_1::bool) = " ^
|
|
neuper@37999
|
416 |
" (SubProblem (Biegelinie',[makeFunctionTo,equation]," ^
|
|
neuper@37954
|
417 |
" [Equation,fromFunction]) " ^
|
|
neuper@37999
|
418 |
" [BOOL (hd f_s), BOOL b_1]); " ^
|
|
neuper@37999
|
419 |
" b_2 = NTH 2 r_b; " ^
|
|
neuper@37999
|
420 |
" f_s = filter_sameFunId (lhs b_2) fun_s; " ^
|
|
neuper@37999
|
421 |
" (e_2::bool) = " ^
|
|
neuper@37999
|
422 |
" (SubProblem (Biegelinie',[makeFunctionTo,equation]," ^
|
|
neuper@37954
|
423 |
" [Equation,fromFunction]) " ^
|
|
neuper@37999
|
424 |
" [BOOL (hd f_s), BOOL b_2]); " ^
|
|
neuper@37999
|
425 |
" b_3 = NTH 3 r_b; " ^
|
|
neuper@37999
|
426 |
" f_s = filter_sameFunId (lhs b_3) fun_s; " ^
|
|
neuper@37999
|
427 |
" (e_3::bool) = " ^
|
|
neuper@37999
|
428 |
" (SubProblem (Biegelinie',[makeFunctionTo,equation]," ^
|
|
neuper@37954
|
429 |
" [Equation,fromFunction]) " ^
|
|
neuper@37999
|
430 |
" [BOOL (hd f_s), BOOL b_3]); " ^
|
|
neuper@37999
|
431 |
" b_4 = NTH 4 r_b; " ^
|
|
neuper@37999
|
432 |
" f_s = filter_sameFunId (lhs b_4) fun_s; " ^
|
|
neuper@37999
|
433 |
" (e_4::bool) = " ^
|
|
neuper@37999
|
434 |
" (SubProblem (Biegelinie',[makeFunctionTo,equation]," ^
|
|
neuper@37954
|
435 |
" [Equation,fromFunction]) " ^
|
|
neuper@37999
|
436 |
" [BOOL (hd f_s), BOOL b_4]) " ^
|
|
neuper@42387
|
437 |
" in [e_1, e_2, e_3, e_4])"
|
|
neuper@37954
|
438 |
(* filter requires more than 1 sec !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
|
|
neuper@37999
|
439 |
"Script SetzeRandbedScript (fun_s::bool list) (r_b::bool list) = " ^
|
|
neuper@37999
|
440 |
" (let b_1 = NTH 1 r_b; " ^
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|
neuper@37999
|
441 |
" f_s = filter (sameFunId (lhs b_1)) fun_s; " ^
|
|
neuper@37999
|
442 |
" (e_1::bool) = " ^
|
|
neuper@37999
|
443 |
" (SubProblem (Biegelinie',[makeFunctionTo,equation]," ^
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|
neuper@37954
|
444 |
" [Equation,fromFunction]) " ^
|
|
neuper@37999
|
445 |
" [BOOL (hd f_s), BOOL b_1]); " ^
|
|
neuper@37999
|
446 |
" b_2 = NTH 2 r_b; " ^
|
|
neuper@37999
|
447 |
" f_s = filter (sameFunId (lhs b_2)) fun_s; " ^
|
|
neuper@37999
|
448 |
" (e_2::bool) = " ^
|
|
neuper@37999
|
449 |
" (SubProblem (Biegelinie',[makeFunctionTo,equation]," ^
|
|
neuper@37954
|
450 |
" [Equation,fromFunction]) " ^
|
|
neuper@37999
|
451 |
" [BOOL (hd f_s), BOOL b_2]); " ^
|
|
neuper@37999
|
452 |
" b_3 = NTH 3 r_b; " ^
|
|
neuper@37999
|
453 |
" f_s = filter (sameFunId (lhs b_3)) fun_s; " ^
|
|
neuper@37999
|
454 |
" (e_3::bool) = " ^
|
|
neuper@37999
|
455 |
" (SubProblem (Biegelinie',[makeFunctionTo,equation]," ^
|
|
neuper@37954
|
456 |
" [Equation,fromFunction]) " ^
|
|
neuper@37999
|
457 |
" [BOOL (hd f_s), BOOL b_3]); " ^
|
|
neuper@37999
|
458 |
" b_4 = NTH 4 r_b; " ^
|
|
neuper@37999
|
459 |
" f_s = filter (sameFunId (lhs b_4)) fun_s; " ^
|
|
neuper@37999
|
460 |
" (e_4::bool) = " ^
|
|
neuper@37999
|
461 |
" (SubProblem (Biegelinie',[makeFunctionTo,equation]," ^
|
|
neuper@37954
|
462 |
" [Equation,fromFunction]) " ^
|
|
neuper@37999
|
463 |
" [BOOL (hd f_s), BOOL b_4]) " ^
|
|
neuper@37999
|
464 |
" in [e_1,e_2,e_3,e_4])"*)
|
|
neuper@37954
|
465 |
));
|
|
neuper@37954
|
466 |
|
|
neuper@37999
|
467 |
*}
|
|
neuper@37999
|
468 |
ML {*
|
|
neuper@37954
|
469 |
store_met
|
|
neuper@42387
|
470 |
(prep_met thy "met_equ_fromfun" [] e_metID
|
|
neuper@42387
|
471 |
(["Equation","fromFunction"],
|
|
neuper@42387
|
472 |
[("#Given" ,["functionEq fu_n","substitution su_b"]),
|
|
neuper@42387
|
473 |
("#Find" ,["equality equ'''"])],
|
|
neuper@42387
|
474 |
{rew_ord'="tless_true", rls'=Erls, calc = [],
|
|
neuper@42387
|
475 |
srls = append_rls "srls_in_EquationfromFunc" e_rls
|
|
neuper@42387
|
476 |
[Calc("Tools.lhs", eval_lhs"eval_lhs_"),
|
|
neuper@42387
|
477 |
Calc("Atools.argument'_in", eval_argument_in "Atools.argument'_in")],
|
|
neuper@42425
|
478 |
prls=e_rls, crls = Atools_erls, errpats = [], nrls = e_rls},
|
|
neuper@37954
|
479 |
(*(M_b x = c_2 + c * x + -1 * q_0 / 2 * x ^^^ 2) (M_b L = 0) -->
|
|
neuper@37954
|
480 |
0 = c_2 + c * L + -1 * q_0 / 2 * L ^^^ 2*)
|
|
neuper@37999
|
481 |
"Script Function2Equality (fu_n::bool) (su_b::bool) =" ^
|
|
neuper@37999
|
482 |
" (let fu_n = Take fu_n; " ^
|
|
neuper@37999
|
483 |
" bd_v = argument_in (lhs fu_n); " ^
|
|
neuper@37999
|
484 |
" va_l = argument_in (lhs su_b); " ^
|
|
neuper@37999
|
485 |
" eq_u = (Substitute [bd_v = va_l]) fu_n; " ^
|
|
neuper@42387
|
486 |
(*([1], Res), M_b L = c_2 + c * L + -1 * q_0 / 2 * L ^^^ 2*)
|
|
neuper@42387
|
487 |
" eq_u = (Substitute [su_b]) eq_u " ^
|
|
neuper@42387
|
488 |
" in (Rewrite_Set norm_Rational False) eq_u) "
|
|
neuper@37954
|
489 |
));
|
|
neuper@37954
|
490 |
*}
|
|
neuper@37954
|
491 |
|
|
neuper@37906
|
492 |
end
|
|
neuper@37906
|
493 |
|