neuper@37906
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(* testexamples for Poly, polynomials
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neuper@37906
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author: Matthias Goldgruber 2003
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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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neuper@38022
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12345678901234567890123456789012345678901234567890123456789012345678901234567890
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neuper@38022
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10 20 30 40 50 60 70 80
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neuper@42395
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LEGEND:
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neuper@42395
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WN060104: examples marked with 'SPB' came into 'exp_IsacCore_Simp_Poly_Book.xml'
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neuper@42395
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examples marked with 'SPO' came into 'exp_IsacCore_Simp_Poly_Other.xml'
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neuper@38022
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*)
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neuper@42395
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neuper@38022
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"--------------------------------------------------------";
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neuper@38022
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"--------------------------------------------------------";
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neuper@38022
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"table of contents --------------------------------------";
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neuper@38022
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"--------------------------------------------------------";
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wneuper@59529
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"----------- fun is_polyexp --------------------------------------------------------------------";
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wneuper@59522
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"----------- fun has_degree_in -----------------------------------------------------------------";
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wneuper@59522
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"----------- fun mono_deg_in -------------------------------------------------------------------";
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wneuper@59522
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"----------- fun mono_deg_in -------------------------------------------------------------------";
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wneuper@59522
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"----------- eval_ for is_expanded_in, is_poly_in, has_degree_in -------------------------------";
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neuper@42395
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"-------- investigate (new 2002) uniary minus -----------";
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neuper@38036
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"-------- check make_polynomial with simple terms -------";
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neuper@38036
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"-------- fun is_multUnordered --------------------------";
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neuper@38036
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"-------- examples from textbook Schalk I ---------------";
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neuper@38022
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"-------- check pbl 'polynomial simplification' --------";
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neuper@38022
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"-------- me 'poly. simpl.' Schalk I p.63 No.267b -------";
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neuper@38036
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"-------- interSteps for Schalk 299a --------------------";
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neuper@38022
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"-------- norm_Poly NOT COMPLETE ------------------------";
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neuper@38022
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"-------- ord_make_polynomial ---------------------------";
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neuper@38022
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"--------------------------------------------------------";
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neuper@38022
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"--------------------------------------------------------";
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neuper@38022
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"--------------------------------------------------------";
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neuper@37906
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neuper@37906
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wneuper@59529
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"----------- fun is_polyexp --------------------------------------------------------------------";
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wneuper@59529
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"----------- fun is_polyexp --------------------------------------------------------------------";
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wneuper@59529
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"----------- fun is_polyexp --------------------------------------------------------------------";
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wneuper@59529
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val thy = @{theory Partial_Fractions};
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wneuper@59529
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val ctxt = Proof_Context.init_global thy;
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wneuper@59529
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wneuper@59529
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val t = (the o (parseNEW ctxt)) "x / x";
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wneuper@59529
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if is_polyexp t then error "NOT is_polyexp (x / x)" else ();
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wneuper@59529
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wneuper@59529
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val t = (the o (parseNEW ctxt)) "-1 * A * 3";
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wneuper@59529
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if is_polyexp t then () else error "is_polyexp (-1 * A * 3)";
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wneuper@59529
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wneuper@59529
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val t = (the o (parseNEW ctxt)) "-1 * AA * 3";
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wneuper@59529
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if is_polyexp t then () else error "is_polyexp (-1 * AA * 3)";
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neuper@38022
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wneuper@59522
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"----------- fun has_degree_in -----------------------------------------------------------------";
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wneuper@59522
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"----------- fun has_degree_in -----------------------------------------------------------------";
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wneuper@59522
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"----------- fun has_degree_in -----------------------------------------------------------------";
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walther@60230
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val v = (Thm.term_of o the o (TermC.parse thy)) "x";
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walther@60230
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val t = (Thm.term_of o the o (TermC.parse thy)) "1";
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wneuper@59522
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if has_degree_in t v = 0 then () else error "has_degree_in (1) x";
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wneuper@59522
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walther@60230
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val v = (Thm.term_of o the o (TermC.parse thy)) "AA";
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walther@60230
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val t = (Thm.term_of o the o (TermC.parse thy)) "1";
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wneuper@59522
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if has_degree_in t v = 0 then () else error "has_degree_in (1) AA";
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wneuper@59522
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wneuper@59522
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(*----------*)
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walther@60230
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val v = (Thm.term_of o the o (TermC.parse thy)) "x";
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walther@60230
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val t = (Thm.term_of o the o (TermC.parse thy)) "a*b+c";
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wneuper@59522
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if has_degree_in t v = 0 then () else error "has_degree_in (a*b+c) x";
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wneuper@59522
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walther@60230
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val v = (Thm.term_of o the o (TermC.parse thy)) "AA";
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walther@60230
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val t = (Thm.term_of o the o (TermC.parse thy)) "a*b+c";
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wneuper@59522
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if has_degree_in t v = 0 then () else error "has_degree_in (a*b+c) AA";
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wneuper@59522
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wneuper@59522
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(*----------*)
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walther@60230
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val v = (Thm.term_of o the o (TermC.parse thy)) "x";
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walther@60230
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val t = (Thm.term_of o the o (TermC.parse thy)) "a*x+c";
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wneuper@59522
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if has_degree_in t v = ~1 then () else error "has_degree_in (a*x+c) x";
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wneuper@59522
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walther@60230
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val v = (Thm.term_of o the o (TermC.parse thy)) "AA";
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walther@60230
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val t = (Thm.term_of o the o (TermC.parse thy)) "a*AA+c";
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wneuper@59522
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if has_degree_in t v = ~1 then () else error "has_degree_in (a*AA+c) AA";
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wneuper@59522
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wneuper@59522
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(*----------*)
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walther@60230
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val v = (Thm.term_of o the o (TermC.parse thy)) "x";
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walther@60242
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val t = (Thm.term_of o the o (TermC.parse thy)) "(a*b+c)*x \<up> 7";
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walther@60242
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if has_degree_in t v = 7 then () else error "has_degree_in ((a*b+c)*x \<up> 7) x";
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wneuper@59522
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walther@60230
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val v = (Thm.term_of o the o (TermC.parse thy)) "AA";
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walther@60242
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val t = (Thm.term_of o the o (TermC.parse thy)) "(a*b+c)*AA \<up> 7";
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walther@60242
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if has_degree_in t v = 7 then () else error "has_degree_in ((a*b+c)*AA \<up> 7) AA";
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wneuper@59522
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wneuper@59522
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(*----------*)
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walther@60230
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val v = (Thm.term_of o the o (TermC.parse thy)) "x";
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walther@60242
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val t = (Thm.term_of o the o (TermC.parse thy)) "x \<up> 7";
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walther@60242
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if has_degree_in t v = 7 then () else error "has_degree_in (x \<up> 7) x";
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wneuper@59522
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walther@60230
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val v = (Thm.term_of o the o (TermC.parse thy)) "AA";
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walther@60242
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val t = (Thm.term_of o the o (TermC.parse thy)) "AA \<up> 7";
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walther@60242
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if has_degree_in t v = 7 then () else error "has_degree_in (AA \<up> 7) AA";
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wneuper@59522
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wneuper@59522
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(*----------*)
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walther@60230
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val v = (Thm.term_of o the o (TermC.parse thy)) "x";
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walther@60230
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val t = (Thm.term_of o the o (TermC.parse thy)) "(a*b+c)*x";
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wneuper@59522
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if has_degree_in t v = 1 then () else error "has_degree_in ((a*b+c)*x) x";
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wneuper@59522
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walther@60230
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val v = (Thm.term_of o the o (TermC.parse thy)) "AA";
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walther@60230
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val t = (Thm.term_of o the o (TermC.parse thy)) "(a*b+c)*AA";
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wneuper@59522
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if has_degree_in t v = 1 then () else error "has_degree_in ((a*b+c)*AA) AA";
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wneuper@59522
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wneuper@59522
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(*----------*)
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walther@60230
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val v = (Thm.term_of o the o (TermC.parse thy)) "x";
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walther@60230
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val t = (Thm.term_of o the o (TermC.parse thy)) "(a*b+x)*x";
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wneuper@59522
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if has_degree_in t v = ~1 then () else error "has_degree_in (a*b+x)*x() x";
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wneuper@59522
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walther@60230
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val v = (Thm.term_of o the o (TermC.parse thy)) "AA";
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walther@60230
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val t = (Thm.term_of o the o (TermC.parse thy)) "(a*b+AA)*AA";
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wneuper@59522
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if has_degree_in t v = ~1 then () else error "has_degree_in ((a*b+AA)*AA) AA";
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wneuper@59522
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wneuper@59522
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(*----------*)
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walther@60230
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val v = (Thm.term_of o the o (TermC.parse thy)) "x";
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walther@60230
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val t = (Thm.term_of o the o (TermC.parse thy)) "x";
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wneuper@59522
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if has_degree_in t v = 1 then () else error "has_degree_in (x) x";
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wneuper@59522
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119 |
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walther@60230
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val v = (Thm.term_of o the o (TermC.parse thy)) "AA";
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walther@60230
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val t = (Thm.term_of o the o (TermC.parse thy)) "AA";
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wneuper@59522
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if has_degree_in t v = 1 then () else error "has_degree_in (AA) AA";
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wneuper@59522
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wneuper@59522
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(*----------*)
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walther@60230
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val v = (Thm.term_of o the o (TermC.parse thy)) "x";
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walther@60230
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val t = (Thm.term_of o the o (TermC.parse thy)) "ab - (a*b)*x";
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wneuper@59522
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if has_degree_in t v = 1 then () else error "has_degree_in (ab - (a*b)*x) x";
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wneuper@59522
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128 |
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walther@60230
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val v = (Thm.term_of o the o (TermC.parse thy)) "AA";
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walther@60230
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val t = (Thm.term_of o the o (TermC.parse thy)) "ab - (a*b)*AA";
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wneuper@59522
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if has_degree_in t v = 1 then () else error "has_degree_in (ab - (a*b)*AA) AA";
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wneuper@59522
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wneuper@59522
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"----------- fun mono_deg_in -------------------------------------------------------------------";
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wneuper@59522
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"----------- fun mono_deg_in -------------------------------------------------------------------";
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wneuper@59522
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"----------- fun mono_deg_in -------------------------------------------------------------------";
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walther@60230
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val v = (Thm.term_of o the o (TermC.parse thy)) "x";
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wneuper@59522
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137 |
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walther@60242
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val t = (Thm.term_of o the o (TermC.parse thy)) "(a*b+c)*x \<up> 7";
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walther@60242
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if mono_deg_in t v = SOME 7 then () else error "mono_deg_in ((a*b+c)*x \<up> 7) x changed";
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wneuper@59522
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140 |
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walther@60242
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val t = (Thm.term_of o the o (TermC.parse thy)) "x \<up> 7";
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walther@60242
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if mono_deg_in t v = SOME 7 then () else error "mono_deg_in (x \<up> 7) x changed";
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wneuper@59522
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143 |
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walther@60230
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val t = (Thm.term_of o the o (TermC.parse thy)) "(a*b+c)*x";
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wneuper@59522
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if mono_deg_in t v = SOME 1 then () else error "mono_deg_in ((a*b+c)*x) x changed";
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wneuper@59522
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146 |
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walther@60230
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val t = (Thm.term_of o the o (TermC.parse thy)) "(a*b+x)*x";
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wneuper@59522
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if mono_deg_in t v = NONE then () else error "mono_deg_in ((a*b+x)*x) x changed";
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wneuper@59522
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149 |
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walther@60230
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val t = (Thm.term_of o the o (TermC.parse thy)) "x";
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wneuper@59522
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if mono_deg_in t v = SOME 1 then () else error "mono_deg_in (x) x changed";
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wneuper@59522
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walther@60230
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val t = (Thm.term_of o the o (TermC.parse thy)) "(a*b+c)";
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wneuper@59522
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if mono_deg_in t v = SOME 0 then () else error "mono_deg_in ((a*b+c)) x changed";
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wneuper@59522
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walther@60230
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val t = (Thm.term_of o the o (TermC.parse thy)) "ab - (a*b)*x";
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wneuper@59522
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if mono_deg_in t v = NONE then () else error "mono_deg_in (ab - (a*b)*x) x changed";
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wneuper@59522
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wneuper@59522
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(*. . . . . . . . . . . . the same with Const ("Partial_Functions.AA", _) . . . . . . . . . . . *)
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wneuper@59522
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val thy = @{theory Partial_Fractions}
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walther@60230
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val v = (Thm.term_of o the o (TermC.parse thy)) "AA";
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wneuper@59522
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162 |
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walther@60242
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val t = (Thm.term_of o the o (TermC.parse thy)) "(a*b+c)*AA \<up> 7";
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walther@60242
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if mono_deg_in t v = SOME 7 then () else error "mono_deg_in ((a*b+c)*AA \<up> 7) AA changed";
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wneuper@59522
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165 |
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walther@60242
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val t = (Thm.term_of o the o (TermC.parse thy)) "AA \<up> 7";
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walther@60242
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167 |
if mono_deg_in t v = SOME 7 then () else error "mono_deg_in (AA \<up> 7) AA changed";
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wneuper@59522
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168 |
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walther@60230
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169 |
val t = (Thm.term_of o the o (TermC.parse thy)) "(a*b+c)*AA";
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wneuper@59522
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170 |
if mono_deg_in t v = SOME 1 then () else error "mono_deg_in ((a*b+c)*AA) AA changed";
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wneuper@59522
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171 |
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walther@60230
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val t = (Thm.term_of o the o (TermC.parse thy)) "(a*b+AA)*AA";
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wneuper@59522
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173 |
if mono_deg_in t v = NONE then () else error "mono_deg_in ((a*b+AA)*AA) AA changed";
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wneuper@59522
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174 |
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walther@60230
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175 |
val t = (Thm.term_of o the o (TermC.parse thy)) "AA";
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wneuper@59522
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176 |
if mono_deg_in t v = SOME 1 then () else error "mono_deg_in (AA) AA changed";
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wneuper@59522
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177 |
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walther@60230
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178 |
val t = (Thm.term_of o the o (TermC.parse thy)) "(a*b+c)";
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wneuper@59522
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179 |
if mono_deg_in t v = SOME 0 then () else error "mono_deg_in ((a*b+c)) AA changed";
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wneuper@59522
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180 |
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walther@60230
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181 |
val t = (Thm.term_of o the o (TermC.parse thy)) "ab - (a*b)*AA";
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wneuper@59522
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182 |
if mono_deg_in t v = NONE then () else error "mono_deg_in (ab - (a*b)*AA) AA changed";
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wneuper@59522
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183 |
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wneuper@59522
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184 |
"----------- rewrite_set_ has_degree_in Const ('Partial_Fractions', _) -------------------------";
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wneuper@59522
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185 |
"----------- rewrite_set_ has_degree_in Const ('Partial_Fractions', _) -------------------------";
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wneuper@59522
|
186 |
"----------- rewrite_set_ has_degree_in Const ('Partial_Fractions', _) -------------------------";
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wneuper@59522
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187 |
val thy = @{theory Partial_Fractions}
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walther@60242
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188 |
val expr = (Thm.term_of o the o (TermC.parse thy)) "((-8 - 2*x + x \<up> 2) has_degree_in x) = 2";
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wneuper@59522
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189 |
val SOME (Const ("HOL.True", _), []) = rewrite_set_ thy false PolyEq_prls expr;
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wneuper@59522
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190 |
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walther@60242
|
191 |
val expr = (Thm.term_of o the o (TermC.parse thy)) "((-8 - 2*AA + AA \<up> 2) has_degree_in AA) = 2";
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wneuper@59522
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192 |
val SOME (Const ("HOL.True", _), []) = rewrite_set_ thy false PolyEq_prls expr;
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wneuper@59522
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193 |
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wneuper@59522
|
194 |
"----------- eval_ for is_expanded_in, is_poly_in, has_degree_in -------------------------------";
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wneuper@59522
|
195 |
"----------- eval_ for is_expanded_in, is_poly_in, has_degree_in -------------------------------";
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wneuper@59522
|
196 |
"----------- eval_ for is_expanded_in, is_poly_in, has_degree_in -------------------------------";
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walther@60242
|
197 |
val t = (Thm.term_of o the o (TermC.parse thy)) "(-8 - 2*x + x \<up> 2) is_expanded_in x";
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wneuper@59522
|
198 |
val SOME (id, t') = eval_is_expanded_in 0 0 t 0;
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walther@60242
|
199 |
if UnparseC.term t' = "-8 - 2 * x + x \<up> 2 is_expanded_in x = True"
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walther@60242
|
200 |
andalso id = "-8 - 2 * x + x \<up> 2 is_expanded_in x = True"
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wneuper@59522
|
201 |
then () else error "eval_is_expanded_in x ..changed";
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wneuper@59522
|
202 |
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wneuper@59522
|
203 |
val thy = @{theory Partial_Fractions}
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walther@60242
|
204 |
val t = (Thm.term_of o the o (TermC.parse thy)) "(-8 - 2*AA + AA \<up> 2) is_expanded_in AA";
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wneuper@59522
|
205 |
val SOME (id, t') = eval_is_expanded_in 0 0 t 0;
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walther@60242
|
206 |
if UnparseC.term t' = "-8 - 2 * AA + AA \<up> 2 is_expanded_in AA = True"
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walther@60242
|
207 |
andalso id = "-8 - 2 * AA + AA \<up> 2 is_expanded_in AA = True"
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wneuper@59522
|
208 |
then () else error "eval_is_expanded_in AA ..changed";
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wneuper@59522
|
209 |
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wneuper@59522
|
210 |
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walther@60242
|
211 |
val t = (Thm.term_of o the o (TermC.parse thy)) "(8 + 2*x + x \<up> 2) is_poly_in x";
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wneuper@59522
|
212 |
val SOME (id, t') = eval_is_poly_in 0 0 t 0;
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walther@60242
|
213 |
if UnparseC.term t' = "8 + 2 * x + x \<up> 2 is_poly_in x = True"
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walther@60242
|
214 |
andalso id = "8 + 2 * x + x \<up> 2 is_poly_in x = True"
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wneuper@59522
|
215 |
then () else error "is_poly_in x ..changed";
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wneuper@59522
|
216 |
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walther@60242
|
217 |
val t = (Thm.term_of o the o (TermC.parse thy)) "(8 + 2*AA + AA \<up> 2) is_poly_in AA";
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wneuper@59522
|
218 |
val SOME (id, t') = eval_is_poly_in 0 0 t 0;
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walther@60242
|
219 |
if UnparseC.term t' = "8 + 2 * AA + AA \<up> 2 is_poly_in AA = True"
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walther@60242
|
220 |
andalso id = "8 + 2 * AA + AA \<up> 2 is_poly_in AA = True"
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wneuper@59522
|
221 |
then () else error "is_poly_in AA ..changed";
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wneuper@59522
|
222 |
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wneuper@59522
|
223 |
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wneuper@59522
|
224 |
val thy = @{theory Partial_Fractions}
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walther@60242
|
225 |
val expr = (Thm.term_of o the o (TermC.parse thy)) "((-8 - 2*x + x \<up> 2) has_degree_in x) = 2";
|
wneuper@59522
|
226 |
val SOME (Const ("HOL.True", _), []) = rewrite_set_ thy false PolyEq_prls expr;
|
wneuper@59522
|
227 |
|
walther@60242
|
228 |
val expr = (Thm.term_of o the o (TermC.parse thy)) "((-8 - 2*AA + AA \<up> 2) has_degree_in AA) = 2";
|
wneuper@59522
|
229 |
val SOME (Const ("HOL.True", _), []) = rewrite_set_ thy false PolyEq_prls expr;
|
wneuper@59522
|
230 |
|
neuper@42395
|
231 |
"-------- investigate (new 2002) uniary minus -----------";
|
neuper@42395
|
232 |
"-------- investigate (new 2002) uniary minus -----------";
|
neuper@42395
|
233 |
"-------- investigate (new 2002) uniary minus -----------";
|
neuper@42395
|
234 |
(*---------------------------------------------- vvvvvvvvvvvvvv -----------------------*)
|
wenzelm@60203
|
235 |
val t = Thm.prop_of @{thm real_diff_0}; (*"0 - ?x = - ?x"*)
|
walther@60230
|
236 |
TermC.atomty t;
|
wneuper@59117
|
237 |
(*
|
wneuper@59117
|
238 |
*** Const (HOL.Trueprop, bool => prop)
|
wneuper@59117
|
239 |
*** . Const (HOL.eq, real => real => bool)
|
wneuper@59117
|
240 |
*** . . Const (Groups.minus_class.minus, real => real => real)
|
wneuper@59117
|
241 |
*** . . . Const (Groups.zero_class.zero, real)
|
neuper@37906
|
242 |
*** . . . Var ((x, 0), real)
|
wneuper@59117
|
243 |
*** . . Const (Groups.uminus_class.uminus, real => real)
|
wneuper@59117
|
244 |
*** . . . Var ((x, 0), real)
|
wneuper@59117
|
245 |
*)
|
neuper@42395
|
246 |
case t of
|
neuper@42395
|
247 |
Const ("HOL.Trueprop", _) $
|
wneuper@59117
|
248 |
(Const ("HOL.eq", _) $
|
wneuper@59117
|
249 |
(Const ("Groups.minus_class.minus", _) $ Const ("Groups.zero_class.zero", _) $
|
wneuper@59117
|
250 |
Var (("x", 0), _)) $
|
wneuper@59117
|
251 |
(Const ("Groups.uminus_class.uminus", _) $ Var (("x", 0), _))) => ()
|
neuper@42395
|
252 |
| _ => error "internal representation of \"0 - ?x = - ?x\" changed";
|
neuper@37906
|
253 |
|
neuper@42395
|
254 |
(*----------------------------------- vvvv --------------------------------------------*)
|
walther@60230
|
255 |
val t = (Thm.term_of o the o (TermC.parse thy)) "-1";
|
walther@60230
|
256 |
TermC.atomty t;
|
neuper@37906
|
257 |
(*** -------------
|
neuper@37906
|
258 |
*** Free ( -1, real) *)
|
neuper@42395
|
259 |
case t of
|
neuper@42395
|
260 |
Free ("-1", _) => ()
|
neuper@42395
|
261 |
| _ => error "internal representation of \"-1\" changed";
|
neuper@42395
|
262 |
(*----------------------------------- vvvvv -------------------------------------------*)
|
walther@60230
|
263 |
val t = (Thm.term_of o the o (TermC.parse thy)) "- 1";
|
walther@60230
|
264 |
TermC.atomty t;
|
wneuper@59117
|
265 |
(*
|
wneuper@59117
|
266 |
***
|
wneuper@59117
|
267 |
*** Free (-1, real)
|
wneuper@59117
|
268 |
***
|
wneuper@59117
|
269 |
*)
|
neuper@42395
|
270 |
case t of
|
wneuper@59117
|
271 |
Free ("-1", _) => ()
|
neuper@42395
|
272 |
| _ => error "internal representation of \"- 1\" changed";
|
neuper@37906
|
273 |
|
neuper@42395
|
274 |
"======= these external values all have the same internal representation";
|
neuper@42395
|
275 |
(* "1-x" causes syntyx error --- binary minus detected by blank inbetween !!!*)
|
neuper@42395
|
276 |
(*----------------------------------- vvvvv -------------------------------------------*)
|
walther@60230
|
277 |
val t = (Thm.term_of o the o (TermC.parse thy)) "-x";
|
walther@60230
|
278 |
TermC.atomty t;
|
neuper@37906
|
279 |
(**** -------------
|
neuper@37906
|
280 |
*** Free ( -x, real)*)
|
neuper@42395
|
281 |
case t of
|
neuper@42395
|
282 |
Const ("Groups.uminus_class.uminus", _) $ Free ("x", _) => ()
|
neuper@42395
|
283 |
| _ => error "internal representation of \"-x\" changed";
|
neuper@42395
|
284 |
(*----------------------------------- vvvvv -------------------------------------------*)
|
walther@60230
|
285 |
val t = (Thm.term_of o the o (TermC.parse thy)) "- x";
|
walther@60230
|
286 |
TermC.atomty t;
|
neuper@37906
|
287 |
(**** -------------
|
neuper@37906
|
288 |
*** Free ( -x, real) !!!!!!!!!!!!!!!!!!!!!!!! is the same !!!*)
|
neuper@42395
|
289 |
case t of
|
neuper@42395
|
290 |
Const ("Groups.uminus_class.uminus", _) $ Free ("x", _) => ()
|
neuper@42395
|
291 |
| _ => error "internal representation of \"- x\" changed";
|
neuper@42395
|
292 |
(*----------------------------------- vvvvvv ------------------------------------------*)
|
walther@60230
|
293 |
val t = (Thm.term_of o the o (TermC.parse thy)) "-(x)";
|
walther@60230
|
294 |
TermC.atomty t;
|
neuper@37906
|
295 |
(**** -------------
|
neuper@37906
|
296 |
*** Free ( -x, real)*)
|
neuper@42395
|
297 |
case t of
|
neuper@42395
|
298 |
Const ("Groups.uminus_class.uminus", _) $ Free ("x", _) => ()
|
neuper@42395
|
299 |
| _ => error "internal representation of \"-(x)\" changed";
|
neuper@37906
|
300 |
|
neuper@38036
|
301 |
"-------- check make_polynomial with simple terms -------";
|
neuper@38036
|
302 |
"-------- check make_polynomial with simple terms -------";
|
neuper@38036
|
303 |
"-------- check make_polynomial with simple terms -------";
|
neuper@38036
|
304 |
"----- check 1 ---";
|
walther@60230
|
305 |
val t = TermC.str2term "2*3*a";
|
neuper@38036
|
306 |
val SOME (t, _) = rewrite_set_ thy false make_polynomial t;
|
walther@59868
|
307 |
if UnparseC.term t = "6 * a" then () else error "check make_polynomial 1";
|
neuper@38036
|
308 |
|
neuper@38036
|
309 |
"----- check 2 ---";
|
walther@60230
|
310 |
val t = TermC.str2term "2*a + 3*a";
|
neuper@38036
|
311 |
val SOME (t, _) = rewrite_set_ thy false make_polynomial t;
|
walther@59868
|
312 |
if UnparseC.term t = "5 * a" then () else error "check make_polynomial 2";
|
neuper@38036
|
313 |
|
neuper@38036
|
314 |
"----- check 3 ---";
|
walther@60230
|
315 |
val t = TermC.str2term "2*a + 3*a + 3*a";
|
neuper@38036
|
316 |
val SOME (t, _) = rewrite_set_ thy false make_polynomial t;
|
walther@59868
|
317 |
if UnparseC.term t = "8 * a" then () else error "check make_polynomial 3";
|
neuper@38036
|
318 |
|
neuper@38036
|
319 |
"----- check 4 ---";
|
walther@60230
|
320 |
val t = TermC.str2term "3*a - 2*a";
|
neuper@38036
|
321 |
val SOME (t, _) = rewrite_set_ thy false make_polynomial t;
|
walther@59868
|
322 |
if UnparseC.term t = "a" then () else error "check make_polynomial 4";
|
neuper@38036
|
323 |
|
neuper@38036
|
324 |
"----- check 5 ---";
|
walther@60230
|
325 |
val t = TermC.str2term "4*(3*a - 2*a)";
|
neuper@38036
|
326 |
val SOME (t, _) = rewrite_set_ thy false make_polynomial t;
|
walther@59868
|
327 |
if UnparseC.term t = "4 * a" then () else error "check make_polynomial 5";
|
neuper@38036
|
328 |
|
neuper@38036
|
329 |
"----- check 6 ---";
|
walther@60242
|
330 |
val t = TermC.str2term "4*(3*a \<up> 2 - 2*a \<up> 2)";
|
neuper@38036
|
331 |
val SOME (t, _) = rewrite_set_ thy false make_polynomial t;
|
walther@60242
|
332 |
if UnparseC.term t = "4 * a \<up> 2" then () else error "check make_polynomial 6";
|
neuper@38036
|
333 |
|
neuper@38036
|
334 |
"-------- fun is_multUnordered --------------------------";
|
neuper@38036
|
335 |
"-------- fun is_multUnordered --------------------------";
|
neuper@38036
|
336 |
"-------- fun is_multUnordered --------------------------";
|
wneuper@59592
|
337 |
val thy = @{theory "Isac_Knowledge"};
|
neuper@38040
|
338 |
"===== works for a simple example, see rewrite.sml -- fun app_rev ===";
|
walther@60242
|
339 |
val t = TermC.str2term "x \<up> 2 * x";
|
neuper@38040
|
340 |
val SOME (t', _) = rewrite_set_ thy true order_mult_ t;
|
walther@60242
|
341 |
if UnparseC.term t' = "x * x \<up> 2" then ()
|
walther@60278
|
342 |
else error "poly.sml Poly.is_multUnordered doesn't work";
|
neuper@38040
|
343 |
|
walther@59901
|
344 |
(* 100928 Rewrite.trace_on shows the first occurring difference in 267b:
|
walther@60242
|
345 |
### rls: order_mult_ on: 5 * x \<up> 2 * (2 * x \<up> 7) + 5 * x \<up> 2 * 3 + (6 * x \<up> 7 + 9) + (-1 * (3 * x \<up> 5 * (6 * x \<up> 4)) + -1 * (3 * x \<up> 5 * -1) +
|
walther@60242
|
346 |
(-48 * x \<up> 4 + 8))
|
walther@59852
|
347 |
###### rls: Rule_Set.empty-is_multUnordered on: p is_multUnordered
|
walther@60278
|
348 |
####### try calc: Poly.is_multUnordered'
|
neuper@38036
|
349 |
======= calc. to: False !!!!!!!!!!!!! INSTEAD OF TRUE in 2002 !!!!!!!!!!!!!
|
neuper@38036
|
350 |
*)
|
walther@60242
|
351 |
val t = TermC.str2term "5 * x \<up> 2 * (2 * x \<up> 7) + 5 * x \<up> 2 * 3 + (6 * x \<up> 7 + 9) + (-1 * (3 * x \<up> 5 * (6 * x \<up> 4)) + -1 * (3 * x \<up> 5 * -1) + (-48 * x \<up> 4 + 8))";
|
neuper@38036
|
352 |
|
neuper@38036
|
353 |
"----- is_multUnordered ---";
|
neuper@38036
|
354 |
val tsort = sort_variables t;
|
walther@60242
|
355 |
UnparseC.term tsort = "2 * (5 * (x \<up> 2 * x \<up> 7)) + 3 * (5 * x \<up> 2) + 6 * x \<up> 7 + 9 +\n-1 * (3 * (6 * (x \<up> 4 * x \<up> 5))) +\n-1 * (-1 * (3 * x \<up> 5)) +\n-48 * x \<up> 4 +\n8";
|
neuper@38036
|
356 |
is_polyexp t;
|
neuper@38036
|
357 |
tsort = t;
|
neuper@38036
|
358 |
is_polyexp t andalso not (t = sort_variables t);
|
neuper@38036
|
359 |
if is_multUnordered t then () else error "poly.sml diff. is_multUnordered 1";
|
neuper@38036
|
360 |
|
neuper@38036
|
361 |
"----- eval_is_multUnordered ---";
|
walther@60242
|
362 |
val tm = TermC.str2term "(5 * x \<up> 2 * (2 * x \<up> 7) + 5 * x \<up> 2 * 3 + (6 * x \<up> 7 + 9) + (-1 * (3 * x \<up> 5 * (6 * x \<up> 4)) + -1 * (3 * x \<up> 5 * -1) + (-48 * x \<up> 4 + 8))) is_multUnordered";
|
neuper@38036
|
363 |
case eval_is_multUnordered "testid" "" tm thy of
|
neuper@41924
|
364 |
SOME (_, Const ("HOL.Trueprop", _) $
|
neuper@41922
|
365 |
(Const ("HOL.eq", _) $
|
walther@60278
|
366 |
(Const ("Poly.is_multUnordered", _) $ _) $
|
neuper@41928
|
367 |
Const ("HOL.True", _))) => ()
|
neuper@38036
|
368 |
| _ => error "poly.sml diff. eval_is_multUnordered";
|
neuper@38036
|
369 |
|
neuper@38040
|
370 |
"----- rewrite_set_ STILL DIDN'T WORK";
|
neuper@38040
|
371 |
val SOME (t, _) = rewrite_set_ thy true order_mult_ t;
|
walther@59868
|
372 |
UnparseC.term t;
|
neuper@38036
|
373 |
|
neuper@38036
|
374 |
"-------- examples from textbook Schalk I ---------------";
|
neuper@38036
|
375 |
"-------- examples from textbook Schalk I ---------------";
|
neuper@38036
|
376 |
"-------- examples from textbook Schalk I ---------------";
|
neuper@38036
|
377 |
"-----SPB Schalk I p.63 No.267b ---";
|
walther@60242
|
378 |
(*associate poly* )
|
walther@60242
|
379 |
val t = TermC.str2term "(5*x \<up> 2 + 3) * (2*x \<up> 7 + 3) - (3*x \<up> 5 + 8) * (6*x \<up> 4 - 1)";
|
walther@59868
|
380 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t; UnparseC.term t;
|
walther@60242
|
381 |
if (UnparseC.term t) = "17 + 15 * x \<up> 2 + -48 * x \<up> 4 + 3 * x \<up> 5 + 6 * x \<up> 7 + -8 * x \<up> 9"
|
neuper@42395
|
382 |
then () else error "poly.sml: diff.behav. in make_polynomial 1";
|
neuper@37906
|
383 |
|
neuper@38036
|
384 |
"-----SPB Schalk I p.63 No.275b ---";
|
walther@60242
|
385 |
val t = TermC.str2term "(3*x \<up> 2 - 2*x*y + y \<up> 2) * (x \<up> 2 - 2*y \<up> 2)";
|
neuper@42395
|
386 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t;
|
walther@60242
|
387 |
if (UnparseC.term t) = ("3 * x \<up> 4 + -2 * x \<up> 3 * y + -5 * x \<up> 2 * y \<up> 2 + " ^
|
walther@60242
|
388 |
"4 * x * y \<up> 3 +\n-2 * y \<up> 4")
|
neuper@42395
|
389 |
then () else error "poly.sml: diff.behav. in make_polynomial 2";
|
neuper@37906
|
390 |
|
neuper@38036
|
391 |
"-----SPB Schalk I p.63 No.279b ---";
|
walther@60230
|
392 |
val t = TermC.str2term "(x-a)*(x-b)*(x-c)*(x-d)";
|
neuper@42395
|
393 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t;
|
walther@59868
|
394 |
if (UnparseC.term t) =
|
walther@60242
|
395 |
("a * b * c * d + -1 * a * b * c * x + -1 * a * b * d * x + a * b * x \<up> 2 +\n" ^
|
walther@60242
|
396 |
"-1 * a * c * d * x +\na * c * x \<up> 2 +\na * d * x \<up> 2 +\n-1 * a * x \<up> 3 +\n" ^
|
walther@60242
|
397 |
"-1 * b * c * d * x +\nb * c * x \<up> 2 +\nb * d * x \<up> 2 +\n-1 * b * x \<up> 3 +\n" ^
|
walther@60242
|
398 |
"c * d * x \<up> 2 +\n-1 * c * x \<up> 3 +\n-1 * d * x \<up> 3 +\nx \<up> 4")
|
neuper@42395
|
399 |
then () else error "poly.sml: diff.behav. in make_polynomial 3";
|
walther@60242
|
400 |
( *associate poly*)
|
neuper@37906
|
401 |
|
neuper@38036
|
402 |
"-----SPB Schalk I p.63 No.291 ---";
|
walther@60242
|
403 |
val t = TermC.str2term "(5+96*x \<up> 3+8*x*(-4+(7- 3*x)*4*x))*(5*(2- 3*x)- (-15*x*(-8*x- 5)))";
|
neuper@42395
|
404 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t;
|
walther@60242
|
405 |
if (UnparseC.term t) = "50 + -770 * x + 4520 * x \<up> 2 + -16320 * x \<up> 3 + -26880 * x \<up> 4"
|
neuper@42395
|
406 |
then () else error "poly.sml: diff.behav. in make_polynomial 4";
|
neuper@37906
|
407 |
|
walther@60242
|
408 |
(*associate poly* )
|
neuper@38036
|
409 |
"-----SPB Schalk I p.64 No.295c ---";
|
walther@60242
|
410 |
val t = TermC.str2term "(13*a \<up> 4*b \<up> 9*c - 12*a \<up> 3*b \<up> 6*c \<up> 9) \<up> 2";
|
neuper@42395
|
411 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t;
|
walther@60242
|
412 |
if (UnparseC.term t) = ("169 * a \<up> 8 * b \<up> 18 * c \<up> 2 + -312 * a \<up> 7 * b \<up> 15 * c \<up> 10" ^
|
walther@60242
|
413 |
" +\n144 * a \<up> 6 * b \<up> 12 * c \<up> 18")
|
neuper@42395
|
414 |
then ()else error "poly.sml: diff.behav. in make_polynomial 5";
|
walther@60242
|
415 |
( *associate poly*)
|
neuper@37906
|
416 |
|
neuper@38036
|
417 |
"-----SPB Schalk I p.64 No.299a ---";
|
walther@60230
|
418 |
val t = TermC.str2term "(x - y)*(x + y)";
|
neuper@42395
|
419 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t;
|
walther@60242
|
420 |
if (UnparseC.term t) = "x \<up> 2 + -1 * y \<up> 2"
|
neuper@42395
|
421 |
then () else error "poly.sml: diff.behav. in make_polynomial 6";
|
neuper@37906
|
422 |
|
neuper@38036
|
423 |
"-----SPB Schalk I p.64 No.300c ---";
|
walther@60242
|
424 |
val t = TermC.str2term "(3*x \<up> 2*y - 1)*(3*x \<up> 2*y + 1)";
|
neuper@42395
|
425 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t;
|
walther@60242
|
426 |
if (UnparseC.term t) = "-1 + 9 * x \<up> 4 * y \<up> 2"
|
neuper@42395
|
427 |
then () else error "poly.sml: diff.behav. in make_polynomial 7";
|
neuper@37906
|
428 |
|
neuper@38036
|
429 |
"-----SPB Schalk I p.64 No.302 ---";
|
walther@60230
|
430 |
val t = TermC.str2term
|
walther@60242
|
431 |
"(13*x \<up> 2 + 5)*(13*x \<up> 2 - 5) - (5*x \<up> 2 + 3)*(5*x \<up> 2 - 3) - (12*x \<up> 2 + 4)*(12*x \<up> 2 - 4)";
|
neuper@42395
|
432 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t;
|
walther@59868
|
433 |
if UnparseC.term t = "0"
|
neuper@42395
|
434 |
then () else error "poly.sml: diff.behav. in make_polynomial 8";
|
neuper@42395
|
435 |
(* RL?MG?: Bei Berechnung sollte 3 mal real_plus_minus_binom1_p aus expand_poly verwendet werden *)
|
neuper@37906
|
436 |
|
neuper@38036
|
437 |
"-----SPB Schalk I p.64 No.306a ---";
|
walther@60242
|
438 |
val t = TermC.str2term "((x \<up> 2 + 1)*(x \<up> 2 - 1)) \<up> 2";
|
walther@59868
|
439 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t; UnparseC.term t;
|
walther@60242
|
440 |
if (UnparseC.term t) = "1 + 2 * x \<up> 4 + 2 * -2 * x \<up> 4 + x \<up> 8" then ()
|
walther@60242
|
441 |
else error "poly.sml: diff.behav. in 2 * x \<up> 4 + 2 * -2 * x \<up> 4 = -2 * x \<up> 4";
|
neuper@37906
|
442 |
|
neuper@37906
|
443 |
(*WN071729 when reducing "rls reduce_012_" for Schaerding,
|
neuper@37906
|
444 |
the above resulted in the term below ... but reduces from then correctly*)
|
walther@60242
|
445 |
val t = TermC.str2term "1 + 2 * x \<up> 4 + 2 * -2 * x \<up> 4 + x \<up> 8";
|
walther@59868
|
446 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t; UnparseC.term t;
|
walther@60242
|
447 |
if (UnparseC.term t) = "1 + -2 * x \<up> 4 + x \<up> 8"
|
neuper@42395
|
448 |
then () else error "poly.sml: diff.behav. in make_polynomial 9b";
|
neuper@37906
|
449 |
|
neuper@38036
|
450 |
"-----SPB Schalk I p.64 No.296a ---";
|
walther@60242
|
451 |
val t = TermC.str2term "(x - a) \<up> 3";
|
walther@59868
|
452 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t; UnparseC.term t;
|
walther@60242
|
453 |
if (UnparseC.term t) = "-1 * a \<up> 3 + 3 * a \<up> 2 * x + -3 * a * x \<up> 2 + x \<up> 3"
|
neuper@38031
|
454 |
then () else error "poly.sml: diff.behav. in make_polynomial 10";
|
neuper@37906
|
455 |
|
neuper@38036
|
456 |
"-----SPB Schalk I p.64 No.296c ---";
|
walther@60242
|
457 |
val t = TermC.str2term "(-3*x - 4*y) \<up> 3";
|
walther@59868
|
458 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t; UnparseC.term t;
|
walther@60248
|
459 |
if (UnparseC.term t) = "-27 * x \<up> 3 + -108 * x \<up> 2 * y + -144 * x * y \<up> 2 +\n-64 * y \<up> 3"
|
neuper@38031
|
460 |
then () else error "poly.sml: diff.behav. in make_polynomial 11";
|
neuper@37906
|
461 |
|
neuper@38036
|
462 |
"-----SPB Schalk I p.62 No.242c ---";
|
walther@60242
|
463 |
val t = TermC.str2term "x \<up> (-4)*(x \<up> (-4)*y \<up> (-2)) \<up> (-1)*y \<up> (-2)";
|
walther@59868
|
464 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t; UnparseC.term t;
|
walther@59868
|
465 |
if (UnparseC.term t) = "1"
|
neuper@42395
|
466 |
then () else error "poly.sml: diff.behav. in make_polynomial 12";
|
neuper@37906
|
467 |
|
neuper@38036
|
468 |
"-----SPB Schalk I p.60 No.209a ---";
|
walther@60242
|
469 |
val t = TermC.str2term "a \<up> (7-x) * a \<up> x";
|
walther@59868
|
470 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t; UnparseC.term t;
|
walther@60242
|
471 |
if UnparseC.term t = "a \<up> 7"
|
neuper@42395
|
472 |
then () else error "poly.sml: diff.behav. in make_polynomial 13";
|
neuper@37906
|
473 |
|
neuper@38036
|
474 |
"-----SPB Schalk I p.60 No.209d ---";
|
walther@60242
|
475 |
val t = TermC.str2term "d \<up> x * d \<up> (x+1) * d \<up> (2 - 2*x)";
|
walther@59868
|
476 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t; UnparseC.term t;
|
walther@60242
|
477 |
if UnparseC.term t = "d \<up> 3"
|
neuper@42395
|
478 |
then () else error "poly.sml: diff.behav. in make_polynomial 14";
|
neuper@37906
|
479 |
|
neuper@37906
|
480 |
(*---------------------------------------------------------------------*)
|
neuper@42395
|
481 |
(*---------------- ?RL?Bsple bei denen es Probleme gibt----------------*)
|
neuper@37906
|
482 |
(*---------------------------------------------------------------------*)
|
neuper@38036
|
483 |
"-----Schalk I p.64 No.303 ---";
|
walther@60242
|
484 |
val t = TermC.str2term "(a + 2*b)*(a \<up> 2 + 4*b \<up> 2)*(a - 2*b) - (a - 6*b)*(a \<up> 2 + 36*b \<up> 2)*(a + 6*b)";
|
walther@59868
|
485 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t; UnparseC.term t;
|
walther@60242
|
486 |
if UnparseC.term t = "1280 * b \<up> 4"
|
neuper@42395
|
487 |
then () else error "poly.sml: diff.behav. in make_polynomial 14b";
|
neuper@37906
|
488 |
(* Richtig - aber Binomische Formel wurde nicht verwendet! *)
|
neuper@37906
|
489 |
|
neuper@37906
|
490 |
(*--------------------------------------------------------------------*)
|
neuper@37906
|
491 |
(*----------------------- Eigene Beispiele ---------------------------*)
|
neuper@37906
|
492 |
(*--------------------------------------------------------------------*)
|
neuper@38036
|
493 |
"-----SPO ---";
|
walther@60242
|
494 |
val t = TermC.str2term "a \<up> 2*a \<up> (-2)";
|
walther@59868
|
495 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t; UnparseC.term t;
|
walther@59868
|
496 |
if UnparseC.term t = "1" then ()
|
neuper@38031
|
497 |
else error "poly.sml: diff.behav. in make_polynomial 15";
|
neuper@38036
|
498 |
"-----SPO ---";
|
walther@60230
|
499 |
val t = TermC.str2term "a + a + a";
|
walther@59868
|
500 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t; UnparseC.term t;
|
walther@59868
|
501 |
if UnparseC.term t = "3 * a" then ()
|
neuper@38031
|
502 |
else error "poly.sml: diff.behav. in make_polynomial 16";
|
neuper@38036
|
503 |
"-----SPO ---";
|
walther@60230
|
504 |
val t = TermC.str2term "a + b + b + b";
|
walther@59868
|
505 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t; UnparseC.term t;
|
walther@59868
|
506 |
if UnparseC.term t = "a + 3 * b" then ()
|
neuper@38031
|
507 |
else error "poly.sml: diff.behav. in make_polynomial 17";
|
neuper@38036
|
508 |
"-----SPO ---";
|
walther@60242
|
509 |
val t = TermC.str2term "a \<up> 2*b*b \<up> (-1)";
|
walther@59868
|
510 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t; UnparseC.term t;
|
walther@60242
|
511 |
if UnparseC.term t = "a \<up> 2" then ()
|
neuper@38031
|
512 |
else error "poly.sml: diff.behav. in make_polynomial 18";
|
neuper@38036
|
513 |
"-----SPO ---";
|
walther@60242
|
514 |
val t = TermC.str2term "a \<up> 2*a \<up> (-2)";
|
walther@59868
|
515 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t; UnparseC.term t;
|
walther@59868
|
516 |
if (UnparseC.term t) = "1" then ()
|
neuper@38031
|
517 |
else error "poly.sml: diff.behav. in make_polynomial 19";
|
neuper@38036
|
518 |
"-----SPO ---";
|
walther@60230
|
519 |
val t = TermC.str2term "b + a - b";
|
walther@59868
|
520 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t; UnparseC.term t;
|
walther@59868
|
521 |
if (UnparseC.term t) = "a" then ()
|
neuper@38031
|
522 |
else error "poly.sml: diff.behav. in make_polynomial 20";
|
neuper@38036
|
523 |
"-----SPO ---";
|
walther@60230
|
524 |
val t = TermC.str2term "b * a * a";
|
walther@59868
|
525 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t; UnparseC.term t;
|
walther@60242
|
526 |
if UnparseC.term t = "a \<up> 2 * b" then ()
|
neuper@38031
|
527 |
else error "poly.sml: diff.behav. in make_polynomial 21";
|
neuper@38036
|
528 |
"-----SPO ---";
|
walther@60242
|
529 |
val t = TermC.str2term "(a \<up> 2) \<up> 3";
|
walther@59868
|
530 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t; UnparseC.term t;
|
walther@60242
|
531 |
if UnparseC.term t = "a \<up> 6" then ()
|
neuper@38031
|
532 |
else error "poly.sml: diff.behav. in make_polynomial 22";
|
neuper@38036
|
533 |
"-----SPO ---";
|
walther@60242
|
534 |
val t = TermC.str2term "x \<up> 2 * y \<up> 2 + x * x \<up> 2 * y";
|
walther@59868
|
535 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t; UnparseC.term t;
|
walther@60242
|
536 |
if UnparseC.term t = "x \<up> 3 * y + x \<up> 2 * y \<up> 2" then ()
|
neuper@38031
|
537 |
else error "poly.sml: diff.behav. in make_polynomial 23";
|
neuper@38036
|
538 |
"-----SPO ---";
|
walther@60242
|
539 |
val t = (Thm.term_of o the o (TermC.parse thy)) "a \<up> 2 * (-a) \<up> 2";
|
walther@59868
|
540 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t; UnparseC.term t;
|
walther@60242
|
541 |
if (UnparseC.term t) = "a \<up> 4" then ()
|
neuper@38031
|
542 |
else error "poly.sml: diff.behav. in make_polynomial 24";
|
neuper@38036
|
543 |
"-----SPO ---";
|
walther@60242
|
544 |
val t = TermC.str2term "a * b * b \<up> (-1) + a";
|
walther@59868
|
545 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t; UnparseC.term t;
|
walther@59868
|
546 |
if (UnparseC.term t) = "2 * a" then ()
|
neuper@38031
|
547 |
else error "poly.sml: diff.behav. in make_polynomial 25";
|
neuper@38036
|
548 |
"-----SPO ---";
|
walther@60242
|
549 |
val t = TermC.str2term "a*c*b \<up> (2*n) + 3*a + 5*b \<up> (2*n)*c*b";
|
walther@59868
|
550 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t; UnparseC.term t;
|
walther@60242
|
551 |
if (UnparseC.term t) = "3 * a + 5 * b \<up> (1 + 2 * n) * c + a * b \<up> (2 * n) * c"
|
neuper@38031
|
552 |
then () else error "poly.sml: diff.behav. in make_polynomial 26";
|
neuper@37906
|
553 |
|
neuper@42395
|
554 |
(*MG030627 -------------vvv-: Verschachtelte Terme -----------*)
|
neuper@38036
|
555 |
"-----SPO ---";
|
walther@60242
|
556 |
val t = TermC.str2term "(1 + (x*y*a) + x) \<up> (1 + (x*y*a) + x)";
|
neuper@42395
|
557 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t;
|
walther@60242
|
558 |
if UnparseC.term t = "(1 + x + a * x * y) \<up> (1 + x + a * x * y)"
|
neuper@42395
|
559 |
then () else error "poly.sml: diff.behav. in make_polynomial 27";(*SPO*)
|
neuper@42395
|
560 |
|
walther@60242
|
561 |
val t = TermC.str2term "(1 + x*(y*z)*zz) \<up> (1 + x*(y*z)*zz)";
|
neuper@42395
|
562 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t;
|
walther@60242
|
563 |
if UnparseC.term t = "(1 + x * y * z * zz) \<up> (1 + x * y * z * zz)"
|
neuper@42395
|
564 |
then () else error "poly.sml: diff.behav. in make_polynomial 28";
|
neuper@37906
|
565 |
|
neuper@38036
|
566 |
"-------- check pbl 'polynomial simplification' --------";
|
neuper@38036
|
567 |
"-------- check pbl 'polynomial simplification' --------";
|
neuper@38036
|
568 |
"-------- check pbl 'polynomial simplification' --------";
|
walther@60242
|
569 |
val fmz = ["Term ((5*x \<up> 2 + 3) * (2*x \<up> 7 + 3) - (3*x \<up> 5 + 8) * (6*x \<up> 4 - 1))", "normalform N"];
|
neuper@38036
|
570 |
"-----0 ---";
|
walther@59997
|
571 |
case Refine.refine fmz ["polynomial", "simplification"]of
|
walther@59984
|
572 |
[M_Match.Matches (["polynomial", "simplification"], _)] => ()
|
walther@59968
|
573 |
| _ => error "poly.sml diff.behav. in check pbl, Refine.refine";
|
neuper@37906
|
574 |
(*...if there is an error, then ...*)
|
neuper@37906
|
575 |
|
neuper@38036
|
576 |
"-----1 ---";
|
wneuper@59348
|
577 |
(*default_print_depth 7;*)
|
walther@59997
|
578 |
val pbt = Problem.from_store ["polynomial", "simplification"];
|
wneuper@59348
|
579 |
(*default_print_depth 3;*)
|
neuper@37906
|
580 |
(*if there is ...
|
walther@59984
|
581 |
> val M_Match.NoMatch' {Given=gi, Where=wh, Find=fi,...} = M_Match.match_pbl fmz pbt;
|
walther@59901
|
582 |
... then Rewrite.trace_on:*)
|
walther@60242
|
583 |
|
neuper@38036
|
584 |
"-----2 ---";
|
walther@59901
|
585 |
Rewrite.trace_on := false;
|
walther@59984
|
586 |
M_Match.match_pbl fmz pbt;
|
walther@59901
|
587 |
Rewrite.trace_on := false;
|
neuper@37906
|
588 |
(*... if there is no rewrite, then there is something wrong with prls*)
|
neuper@52101
|
589 |
|
neuper@38036
|
590 |
"-----3 ---";
|
wneuper@59348
|
591 |
(*default_print_depth 7;*)
|
walther@59997
|
592 |
val prls = (#prls o Problem.from_store) ["polynomial", "simplification"];
|
wneuper@59348
|
593 |
(*default_print_depth 3;*)
|
walther@60242
|
594 |
val t = TermC.str2term "((5*x \<up> 2 + 3) * (2*x \<up> 7 + 3) - (3*x \<up> 5 + 8) * (6*x \<up> 4 - 1)) is_polyexp";
|
neuper@37926
|
595 |
val SOME (t',_) = rewrite_set_ thy false prls t;
|
neuper@48760
|
596 |
if t' = @{term True} then ()
|
neuper@38031
|
597 |
else error "poly.sml: diff.behav. in check pbl 'polynomial..";
|
neuper@42395
|
598 |
(*... if this works, but --1-- does still NOT work, check types:*)
|
neuper@37906
|
599 |
|
neuper@38036
|
600 |
"-----4 ---";
|
neuper@42395
|
601 |
(*show_types:=true;*)
|
neuper@37906
|
602 |
(*
|
walther@59984
|
603 |
> val M_Match.NoMatch' {Given=gi, Where=wh, Find=fi,...} = M_Match.match_pbl fmz pbt;
|
neuper@37906
|
604 |
val wh = [False "(t_::real => real) (is_polyexp::real)"]
|
walther@60242
|
605 |
...................... \<up> \<up> \<up> \<up> ............... \<up> ^*)
|
walther@59984
|
606 |
val M_Match.Matches' _ = M_Match.match_pbl fmz pbt;
|
neuper@42395
|
607 |
(*show_types:=false;*)
|
neuper@37906
|
608 |
|
walther@59787
|
609 |
|
neuper@38036
|
610 |
"-------- me 'poly. simpl.' Schalk I p.63 No.267b -------";
|
neuper@38036
|
611 |
"-------- me 'poly. simpl.' Schalk I p.63 No.267b -------";
|
neuper@38036
|
612 |
"-------- me 'poly. simpl.' Schalk I p.63 No.267b -------";
|
walther@60242
|
613 |
val fmz = ["Term ((5*x \<up> 2 + 3) * (2*x \<up> 7 + 3) - (3*x \<up> 5 + 8) * (6*x \<up> 4 - 1))", "normalform N"];
|
neuper@37906
|
614 |
val (dI',pI',mI') =
|
walther@59997
|
615 |
("Poly",["polynomial", "simplification"],
|
walther@59997
|
616 |
["simplification", "for_polynomials"]);
|
neuper@37906
|
617 |
val p = e_pos'; val c = [];
|
neuper@37906
|
618 |
val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
|
walther@60242
|
619 |
(*[], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p c pt;(*Add_Given "Term\n ((5 * x \<up> 2 + 3) * (2 * x \<up> 7 + 3) -\n (3 * x \<up> 5 + 8) * (6 * x \<up> 4 - 1))"*)
|
walther@59787
|
620 |
(*[], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p c pt;(*Add_Find "normalform N"*)
|
walther@59787
|
621 |
|
walther@59997
|
622 |
(*+* )if I_Model.to_string ctxt (get_obj g_pbl pt (fst p)) =
|
walther@60242
|
623 |
(*+*) "[\n(0 ,[] ,false ,#Find ,Inc ??.Simplify.normalform ,(??.empty, [])), \n(1 ,[1] ,true ,#Given ,Cor ??.Simplify.Term\n ((5 * x \<up> 2 + 3) * (2 * x \<up> 7 + 3) -\n (3 * x \<up> 5 + 8) * (6 * x \<up> 4 - 1)) ,(t_t, [(5 * x \<up> 2 + 3) * (2 * x \<up> 7 + 3) -\n(3 * x \<up> 5 + 8) * (6 * x \<up> 4 - 1)]))]"
|
walther@59943
|
624 |
(*+*)then () else error "No.267b: I_Model.T CHANGED";
|
walther@59997
|
625 |
( *+ ...could not be repaired in child of 7e314dd233fd ?!?*)
|
walther@59787
|
626 |
|
walther@59787
|
627 |
(*[], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p c pt;(*nxt = Specify_Theory "Poly"*)
|
walther@59787
|
628 |
(*[], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p c pt;(*Specify_Problem ["polynomial", "simplification"]*)
|
walther@59787
|
629 |
(*[], Pbl*)val (p,_,f,nxt,_,pt) = me nxt p c pt;(*Specify_Method ["simplification", "for_polynomials"]*)
|
walther@59787
|
630 |
(*[], Met*)val (p,_,f,nxt,_,pt) = me nxt p c pt;(*Apply_Method ["simplification", "for_polynomials"]*)
|
walther@59787
|
631 |
(*[1], Frm*)val (p,_,f,nxt,_,pt) = me nxt p c pt;(*Rewrite_Set "norm_Poly"*)
|
walther@59787
|
632 |
|
walther@60242
|
633 |
(*+*)if f2str f = "(5 * x \<up> 2 + 3) * (2 * x \<up> 7 + 3) -\n(3 * x \<up> 5 + 8) * (6 * x \<up> 4 - 1)"
|
walther@59787
|
634 |
(*+*)then () else error "";
|
walther@59787
|
635 |
|
walther@59787
|
636 |
(*[1], Res*)val (p,_,f,nxt,_,pt) = me nxt p c pt;(*Empty_Tac: ERROR DETECTED Feb.2020*)
|
walther@59787
|
637 |
|
walther@60248
|
638 |
(*+*)if f2str f = "17 + 15 * x \<up> 2 + -48 * x \<up> 4 + 3 * x \<up> 5 + 6 * x \<up> 7 +\n-8 * x \<up> 9"
|
walther@60248
|
639 |
(*+*)then () else error "poly.sml diff.behav. in me Schalk I p.63 No.267b -1";
|
walther@59787
|
640 |
|
walther@59790
|
641 |
(*[1], Res* )val (p,_,f,nxt,_,pt) = me nxt p c pt;( *SINCE Feb.2020 LItool.find_next_step without result*)
|
walther@59787
|
642 |
|
walther@59787
|
643 |
|
neuper@37906
|
644 |
|
neuper@38036
|
645 |
"-------- interSteps for Schalk 299a --------------------";
|
neuper@38036
|
646 |
"-------- interSteps for Schalk 299a --------------------";
|
neuper@38036
|
647 |
"-------- interSteps for Schalk 299a --------------------";
|
s1210629013@55445
|
648 |
reset_states ();
|
neuper@37906
|
649 |
CalcTree
|
neuper@42395
|
650 |
[(["Term ((x - y)*(x + (y::real)))", "normalform N"],
|
walther@59997
|
651 |
("Poly",["polynomial", "simplification"],
|
walther@59997
|
652 |
["simplification", "for_polynomials"]))];
|
neuper@37906
|
653 |
Iterator 1;
|
neuper@37906
|
654 |
moveActiveRoot 1;
|
wneuper@59248
|
655 |
autoCalculate 1 CompleteCalc;
|
walther@59983
|
656 |
val ((pt,p),_) = get_calc 1; Test_Tool.show_pt pt;
|
neuper@37906
|
657 |
|
walther@59833
|
658 |
interSteps 1 ([1],Res)(*<ERROR> syserror in Detail_Step.go </ERROR>*);
|
walther@59983
|
659 |
val ((pt,p),_) = get_calc 1; Test_Tool.show_pt pt;
|
neuper@37906
|
660 |
if existpt' ([1,1], Frm) pt then ()
|
neuper@38031
|
661 |
else error "poly.sml: interSteps doesnt work again 1";
|
neuper@37906
|
662 |
|
walther@59833
|
663 |
interSteps 1 ([1,1],Res)(*<ERROR> syserror in Detail_Step.go </ERROR>*);
|
walther@59983
|
664 |
val ((pt,p),_) = get_calc 1; Test_Tool.show_pt pt;
|
neuper@42395
|
665 |
(*============ inhibit exn WN120316 ==============================================
|
neuper@37906
|
666 |
if existpt' ([1,1,1], Frm) pt then ()
|
neuper@38031
|
667 |
else error "poly.sml: interSteps doesnt work again 2";
|
neuper@42395
|
668 |
============ inhibit exn WN120316 ==============================================*)
|
neuper@37906
|
669 |
|
neuper@38036
|
670 |
"-------- norm_Poly NOT COMPLETE ------------------------";
|
neuper@38036
|
671 |
"-------- norm_Poly NOT COMPLETE ------------------------";
|
neuper@38036
|
672 |
"-------- norm_Poly NOT COMPLETE ------------------------";
|
walther@60267
|
673 |
val thy = @{theory AlgEin};
|
wneuper@59529
|
674 |
|
wneuper@59529
|
675 |
val SOME (f',_) = rewrite_set_ thy false norm_Poly
|
walther@60230
|
676 |
(TermC.str2term "L = k - 2 * q + (k - 2 * q) + (k - 2 * q) + (k - 2 * q) + senkrecht + oben");
|
walther@60267
|
677 |
if UnparseC.term f' = "L = senkrecht + oben + 2 * 2 * k + 2 * -4 * q"
|
neuper@42395
|
678 |
then ((*norm_Poly NOT COMPLETE -- TODO MG*))
|
neuper@42395
|
679 |
else error "norm_Poly changed behavior";
|
neuper@38036
|
680 |
|
neuper@38036
|
681 |
"-------- ord_make_polynomial ---------------------------";
|
neuper@38036
|
682 |
"-------- ord_make_polynomial ---------------------------";
|
neuper@38036
|
683 |
"-------- ord_make_polynomial ---------------------------";
|
walther@60230
|
684 |
val t1 = TermC.str2term "2 * b + (3 * a + 3 * b)";
|
walther@60230
|
685 |
val t2 = TermC.str2term "3 * a + 3 * b + 2 * b";
|
neuper@37906
|
686 |
|
neuper@42395
|
687 |
if ord_make_polynomial true thy [] (t1, t2) then ()
|
neuper@38031
|
688 |
else error "poly.sml: diff.behav. in ord_make_polynomial";
|
neuper@37906
|
689 |
|
walther@60242
|
690 |
(*WN071202: \<up> why then is there no rewriting ...*)
|
walther@60230
|
691 |
val term = TermC.str2term "2*b + (3*a + 3*b)";
|
wneuper@59592
|
692 |
val NONE = rewrite_set_ (@{theory "Isac_Knowledge"}) false order_add_mult term;
|
neuper@37906
|
693 |
|
neuper@37906
|
694 |
(*or why is there no rewriting this way...*)
|
walther@60230
|
695 |
val t1 = TermC.str2term "2 * b + (3 * a + 3 * b)";
|
walther@60230
|
696 |
val t2 = TermC.str2term "3 * a + (2 * b + 3 * b)";
|
neuper@37906
|
697 |
|