neuper@37906
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(*.(c) by Richard Lang, 2003 .*)
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neuper@37906
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(* collecting all knowledge for Root Equations
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created by: rlang
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date: 02.08
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changed by: rlang
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last change by: rlang
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date: 02.11.14
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*)
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theory RootEq imports Root begin
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consts
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is'_rootTerm'_in :: "[real, real] => bool" ("_ is'_rootTerm'_in _")
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is'_sqrtTerm'_in :: "[real, real] => bool" ("_ is'_sqrtTerm'_in _")
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is'_normSqrtTerm'_in :: "[real, real] => bool" ("_ is'_normSqrtTerm'_in _")
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(*----------------------scripts-----------------------*)
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Norm'_sq'_root'_equation
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:: "[bool,real,
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bool list] => bool list"
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("((Script Norm'_sq'_root'_equation (_ _ =))//
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(_))" 9)
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Solve'_sq'_root'_equation
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:: "[bool,real,
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bool list] => bool list"
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("((Script Solve'_sq'_root'_equation (_ _ =))//
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(_))" 9)
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Solve'_left'_sq'_root'_equation
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:: "[bool,real,
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bool list] => bool list"
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("((Script Solve'_left'_sq'_root'_equation (_ _ =))//
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(_))" 9)
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Solve'_right'_sq'_root'_equation
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:: "[bool,real,
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bool list] => bool list"
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("((Script Solve'_right'_sq'_root'_equation (_ _ =))//
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(_))" 9)
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axioms
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(* normalize *)
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makex1_x: "a^^^1 = a"
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real_assoc_1: "a+(b+c) = a+b+c"
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real_assoc_2: "a*(b*c) = a*b*c"
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(* simplification of root*)
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sqrt_square_1: "[|0 <= a|] ==> (sqrt a)^^^2 = a"
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sqrt_square_2: "sqrt (a ^^^ 2) = a"
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sqrt_times_root_1: "sqrt a * sqrt b = sqrt(a*b)"
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sqrt_times_root_2: "a * sqrt b * sqrt c = a * sqrt(b*c)"
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(* isolate one root on the LEFT or RIGHT hand side of the equation *)
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sqrt_isolate_l_add1: "[|bdv occurs_in c|] ==>
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(a + b*sqrt(c) = d) = (b * sqrt(c) = d+ (-1) * a)"
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sqrt_isolate_l_add2: "[|bdv occurs_in c|] ==>
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(a + sqrt(c) = d) = ((sqrt(c) = d+ (-1) * a))"
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sqrt_isolate_l_add3: "[|bdv occurs_in c|] ==>
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(a + b*(e/sqrt(c)) = d) = (b * (e/sqrt(c)) = d + (-1) * a)"
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sqrt_isolate_l_add4: "[|bdv occurs_in c|] ==>
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(a + b/(f*sqrt(c)) = d) = (b / (f*sqrt(c)) = d + (-1) * a)"
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sqrt_isolate_l_add5: "[|bdv occurs_in c|] ==>
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(a + b*(e/(f*sqrt(c))) = d) = (b * (e/(f*sqrt(c))) = d+ (-1) * a)"
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sqrt_isolate_l_add6: "[|bdv occurs_in c|] ==>
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(a + b/sqrt(c) = d) = (b / sqrt(c) = d+ (-1) * a)"
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sqrt_isolate_r_add1: "[|bdv occurs_in f|] ==>
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(a = d + e*sqrt(f)) = (a + (-1) * d = e*sqrt(f))"
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sqrt_isolate_r_add2: "[|bdv occurs_in f|] ==>
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(a = d + sqrt(f)) = (a + (-1) * d = sqrt(f))"
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(* small hack: thm 3,5,6 are not needed if rootnormalize is well done*)
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sqrt_isolate_r_add3: "[|bdv occurs_in f|] ==>
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(a = d + e*(g/sqrt(f))) = (a + (-1) * d = e*(g/sqrt(f)))"
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sqrt_isolate_r_add4: "[|bdv occurs_in f|] ==>
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(a = d + g/sqrt(f)) = (a + (-1) * d = g/sqrt(f))"
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sqrt_isolate_r_add5: "[|bdv occurs_in f|] ==>
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(a = d + e*(g/(h*sqrt(f)))) = (a + (-1) * d = e*(g/(h*sqrt(f))))"
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sqrt_isolate_r_add6: "[|bdv occurs_in f|] ==>
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(a = d + g/(h*sqrt(f))) = (a + (-1) * d = g/(h*sqrt(f)))"
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(* eliminate isolates sqrt *)
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sqrt_square_equation_both_1: "[|bdv occurs_in b; bdv occurs_in d|] ==>
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( (sqrt a + sqrt b = sqrt c + sqrt d) =
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(a+2*sqrt(a)*sqrt(b)+b = c+2*sqrt(c)*sqrt(d)+d))"
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sqrt_square_equation_both_2: "[|bdv occurs_in b; bdv occurs_in d|] ==>
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( (sqrt a - sqrt b = sqrt c + sqrt d) =
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(a - 2*sqrt(a)*sqrt(b)+b = c+2*sqrt(c)*sqrt(d)+d))"
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sqrt_square_equation_both_3: "[|bdv occurs_in b; bdv occurs_in d|] ==>
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( (sqrt a + sqrt b = sqrt c - sqrt d) =
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(a + 2*sqrt(a)*sqrt(b)+b = c - 2*sqrt(c)*sqrt(d)+d))"
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sqrt_square_equation_both_4: "[|bdv occurs_in b; bdv occurs_in d|] ==>
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( (sqrt a - sqrt b = sqrt c - sqrt d) =
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(a - 2*sqrt(a)*sqrt(b)+b = c - 2*sqrt(c)*sqrt(d)+d))"
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sqrt_square_equation_left_1: "[|bdv occurs_in a; 0 <= a; 0 <= b|] ==>
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( (sqrt (a) = b) = (a = (b^^^2)))"
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sqrt_square_equation_left_2: "[|bdv occurs_in a; 0 <= a; 0 <= b*c|] ==>
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( (c*sqrt(a) = b) = (c^^^2*a = b^^^2))"
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sqrt_square_equation_left_3: "[|bdv occurs_in a; 0 <= a; 0 <= b*c|] ==>
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( c/sqrt(a) = b) = (c^^^2 / a = b^^^2)"
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(* small hack: thm 4-6 are not needed if rootnormalize is well done*)
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sqrt_square_equation_left_4: "[|bdv occurs_in a; 0 <= a; 0 <= b*c*d|] ==>
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( (c*(d/sqrt (a)) = b) = (c^^^2*(d^^^2/a) = b^^^2))"
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sqrt_square_equation_left_5: "[|bdv occurs_in a; 0 <= a; 0 <= b*c*d|] ==>
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( c/(d*sqrt(a)) = b) = (c^^^2 / (d^^^2*a) = b^^^2)"
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sqrt_square_equation_left_6: "[|bdv occurs_in a; 0 <= a; 0 <= b*c*d*e|] ==>
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( (c*(d/(e*sqrt (a))) = b) = (c^^^2*(d^^^2/(e^^^2*a)) = b^^^2))"
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sqrt_square_equation_right_1: "[|bdv occurs_in b; 0 <= a; 0 <= b|] ==>
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( (a = sqrt (b)) = (a^^^2 = b))"
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sqrt_square_equation_right_2: "[|bdv occurs_in b; 0 <= a*c; 0 <= b|] ==>
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( (a = c*sqrt (b)) = ((a^^^2) = c^^^2*b))"
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sqrt_square_equation_right_3: "[|bdv occurs_in b; 0 <= a*c; 0 <= b|] ==>
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( (a = c/sqrt (b)) = (a^^^2 = c^^^2/b))"
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(* small hack: thm 4-6 are not needed if rootnormalize is well done*)
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sqrt_square_equation_right_4: "[|bdv occurs_in b; 0 <= a*c*d; 0 <= b|] ==>
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( (a = c*(d/sqrt (b))) = ((a^^^2) = c^^^2*(d^^^2/b)))"
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sqrt_square_equation_right_5: "[|bdv occurs_in b; 0 <= a*c*d; 0 <= b|] ==>
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( (a = c/(d*sqrt (b))) = (a^^^2 = c^^^2/(d^^^2*b)))"
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sqrt_square_equation_right_6: "[|bdv occurs_in b; 0 <= a*c*d*e; 0 <= b|] ==>
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( (a = c*(d/(e*sqrt (b)))) = ((a^^^2) = c^^^2*(d^^^2/(e^^^2*b))))"
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ML {*
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val thy = @{theory};
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(*-------------------------functions---------------------*)
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(* true if bdv is under sqrt of a Equation*)
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fun is_rootTerm_in t v =
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let
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fun coeff_in c v = member op = (vars c) v;
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fun findroot (_ $ _ $ _ $ _) v = error("is_rootTerm_in:")
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(* at the moment there is no term like this, but ....*)
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| findroot (t as (Const ("Root.nroot",_) $ _ $ t3)) v = coeff_in t3 v
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| findroot (_ $ t2 $ t3) v = (findroot t2 v) orelse (findroot t3 v)
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| findroot (t as (Const ("NthRoot.sqrt",_) $ t2)) v = coeff_in t2 v
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| findroot (_ $ t2) v = (findroot t2 v)
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| findroot _ _ = false;
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in
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findroot t v
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end;
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fun is_sqrtTerm_in t v =
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let
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fun coeff_in c v = member op = (vars c) v;
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fun findsqrt (_ $ _ $ _ $ _) v = error("is_sqrteqation_in:")
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(* at the moment there is no term like this, but ....*)
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| findsqrt (_ $ t1 $ t2) v = (findsqrt t1 v) orelse (findsqrt t2 v)
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neuper@37982
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| findsqrt (t as (Const ("NthRoot.sqrt",_) $ a)) v = coeff_in a v
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| findsqrt (_ $ t1) v = (findsqrt t1 v)
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| findsqrt _ _ = false;
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in
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findsqrt t v
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end;
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(* RL: 030518: Is in the rightest subterm of a term a sqrt with bdv,
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and the subterm ist connected with + or * --> is normalized*)
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fun is_normSqrtTerm_in t v =
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let
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fun coeff_in c v = member op = (vars c) v;
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neuper@38031
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fun isnorm (_ $ _ $ _ $ _) v = error("is_normSqrtTerm_in:")
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(* at the moment there is no term like this, but ....*)
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| isnorm (Const ("Groups.plus_class.plus",_) $ _ $ t2) v = is_sqrtTerm_in t2 v
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| isnorm (Const ("op *",_) $ _ $ t2) v = is_sqrtTerm_in t2 v
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neuper@38014
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| isnorm (Const ("Groups.minus_class.minus",_) $ _ $ _) v = false
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neuper@38014
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| isnorm (Const ("Rings.inverse_class.divide",_) $ t1 $ t2) v = (is_sqrtTerm_in t1 v) orelse
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(is_sqrtTerm_in t2 v)
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| isnorm (Const ("NthRoot.sqrt",_) $ t1) v = coeff_in t1 v
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| isnorm (_ $ t1) v = is_sqrtTerm_in t1 v
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| isnorm _ _ = false;
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in
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isnorm t v
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end;
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fun eval_is_rootTerm_in _ _
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(p as (Const ("RootEq.is'_rootTerm'_in",_) $ t $ v)) _ =
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if is_rootTerm_in t v then
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SOME ((term2str p) ^ " = True",
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Trueprop $ (mk_equality (p, HOLogic.true_const)))
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else SOME ((term2str p) ^ " = True",
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Trueprop $ (mk_equality (p, HOLogic.false_const)))
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| eval_is_rootTerm_in _ _ _ _ = ((*tracing"### nichts matcht";*) NONE);
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fun eval_is_sqrtTerm_in _ _
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(p as (Const ("RootEq.is'_sqrtTerm'_in",_) $ t $ v)) _ =
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if is_sqrtTerm_in t v then
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SOME ((term2str p) ^ " = True",
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Trueprop $ (mk_equality (p, HOLogic.true_const)))
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else SOME ((term2str p) ^ " = True",
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Trueprop $ (mk_equality (p, HOLogic.false_const)))
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| eval_is_sqrtTerm_in _ _ _ _ = ((*tracing"### nichts matcht";*) NONE);
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fun eval_is_normSqrtTerm_in _ _
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(p as (Const ("RootEq.is'_normSqrtTerm'_in",_) $ t $ v)) _ =
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if is_normSqrtTerm_in t v then
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SOME ((term2str p) ^ " = True",
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Trueprop $ (mk_equality (p, HOLogic.true_const)))
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else SOME ((term2str p) ^ " = True",
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Trueprop $ (mk_equality (p, HOLogic.false_const)))
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neuper@38015
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| eval_is_normSqrtTerm_in _ _ _ _ = ((*tracing"### nichts matcht";*) NONE);
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(*-------------------------rulse-------------------------*)
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val RootEq_prls =(*15.10.02:just the following order due to subterm evaluation*)
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append_rls "RootEq_prls" e_rls
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neuper@37950
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[Calc ("Atools.ident",eval_ident "#ident_"),
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Calc ("Tools.matches",eval_matches ""),
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Calc ("Tools.lhs" ,eval_lhs ""),
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Calc ("Tools.rhs" ,eval_rhs ""),
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Calc ("RootEq.is'_sqrtTerm'_in",eval_is_sqrtTerm_in ""),
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Calc ("RootEq.is'_rootTerm'_in",eval_is_rootTerm_in ""),
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Calc ("RootEq.is'_normSqrtTerm'_in",eval_is_normSqrtTerm_in ""),
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Calc ("op =",eval_equal "#equal_"),
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neuper@37969
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Thm ("not_true",num_str @{thm not_true}),
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neuper@37969
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Thm ("not_false",num_str @{thm not_false}),
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Thm ("and_true",num_str @{thm and_true}),
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Thm ("and_false",num_str @{thm and_false}),
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Thm ("or_true",num_str @{thm or_true}),
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Thm ("or_false",num_str @{thm or_false})
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];
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val RootEq_erls =
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append_rls "RootEq_erls" Root_erls
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neuper@37965
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[Thm ("divide_divide_eq_left",num_str @{thm divide_divide_eq_left})
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];
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val RootEq_crls =
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append_rls "RootEq_crls" Root_crls
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[Thm ("divide_divide_eq_left",num_str @{thm divide_divide_eq_left})
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];
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val rooteq_srls =
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append_rls "rooteq_srls" e_rls
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neuper@37950
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[Calc ("RootEq.is'_sqrtTerm'_in",eval_is_sqrtTerm_in ""),
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Calc ("RootEq.is'_normSqrtTerm'_in",eval_is_normSqrtTerm_in""),
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Calc ("RootEq.is'_rootTerm'_in",eval_is_rootTerm_in "")
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];
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neuper@37950
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233 |
|
neuper@37967
|
234 |
ruleset' := overwritelthy @{theory} (!ruleset',
|
neuper@37950
|
235 |
[("RootEq_erls",RootEq_erls),
|
neuper@37950
|
236 |
(*FIXXXME:del with rls.rls'*)
|
neuper@37950
|
237 |
("rooteq_srls",rooteq_srls)
|
neuper@37950
|
238 |
]);
|
neuper@37950
|
239 |
|
neuper@37950
|
240 |
(*isolate the bound variable in an sqrt equation; 'bdv' is a meta-constant*)
|
neuper@37950
|
241 |
val sqrt_isolate = prep_rls(
|
neuper@37950
|
242 |
Rls {id = "sqrt_isolate", preconds = [], rew_ord = ("termlessI",termlessI),
|
neuper@37950
|
243 |
erls = RootEq_erls, srls = Erls, calc = [],
|
neuper@37950
|
244 |
rules = [
|
neuper@37969
|
245 |
Thm("sqrt_square_1",num_str @{thm sqrt_square_1}),
|
neuper@37950
|
246 |
(* (sqrt a)^^^2 -> a *)
|
neuper@37969
|
247 |
Thm("sqrt_square_2",num_str @{thm sqrt_square_2}),
|
neuper@37950
|
248 |
(* sqrt (a^^^2) -> a *)
|
neuper@37969
|
249 |
Thm("sqrt_times_root_1",num_str @{thm sqrt_times_root_1}),
|
neuper@37950
|
250 |
(* sqrt a sqrt b -> sqrt(ab) *)
|
neuper@37969
|
251 |
Thm("sqrt_times_root_2",num_str @{thm sqrt_times_root_2}),
|
neuper@37950
|
252 |
(* a sqrt b sqrt c -> a sqrt(bc) *)
|
neuper@37950
|
253 |
Thm("sqrt_square_equation_both_1",
|
neuper@37969
|
254 |
num_str @{thm sqrt_square_equation_both_1}),
|
neuper@37950
|
255 |
(* (sqrt a + sqrt b = sqrt c + sqrt d) ->
|
neuper@37950
|
256 |
(a+2*sqrt(a)*sqrt(b)+b) = c+2*sqrt(c)*sqrt(d)+d) *)
|
neuper@37950
|
257 |
Thm("sqrt_square_equation_both_2",
|
neuper@37969
|
258 |
num_str @{thm sqrt_square_equation_both_2}),
|
neuper@37950
|
259 |
(* (sqrt a - sqrt b = sqrt c + sqrt d) ->
|
neuper@37950
|
260 |
(a-2*sqrt(a)*sqrt(b)+b) = c+2*sqrt(c)*sqrt(d)+d) *)
|
neuper@37950
|
261 |
Thm("sqrt_square_equation_both_3",
|
neuper@37969
|
262 |
num_str @{thm sqrt_square_equation_both_3}),
|
neuper@37950
|
263 |
(* (sqrt a + sqrt b = sqrt c - sqrt d) ->
|
neuper@37950
|
264 |
(a+2*sqrt(a)*sqrt(b)+b) = c-2*sqrt(c)*sqrt(d)+d) *)
|
neuper@37950
|
265 |
Thm("sqrt_square_equation_both_4",
|
neuper@37969
|
266 |
num_str @{thm sqrt_square_equation_both_4}),
|
neuper@37950
|
267 |
(* (sqrt a - sqrt b = sqrt c - sqrt d) ->
|
neuper@37950
|
268 |
(a-2*sqrt(a)*sqrt(b)+b) = c-2*sqrt(c)*sqrt(d)+d) *)
|
neuper@37950
|
269 |
Thm("sqrt_isolate_l_add1",
|
neuper@37969
|
270 |
num_str @{thm sqrt_isolate_l_add1}),
|
neuper@37950
|
271 |
(* a+b*sqrt(x)=d -> b*sqrt(x) = d-a *)
|
neuper@37950
|
272 |
Thm("sqrt_isolate_l_add2",
|
neuper@37969
|
273 |
num_str @{thm sqrt_isolate_l_add2}),
|
neuper@37950
|
274 |
(* a+ sqrt(x)=d -> sqrt(x) = d-a *)
|
neuper@37950
|
275 |
Thm("sqrt_isolate_l_add3",
|
neuper@37969
|
276 |
num_str @{thm sqrt_isolate_l_add3}),
|
neuper@37950
|
277 |
(* a+b*c/sqrt(x)=d->b*c/sqrt(x)=d-a *)
|
neuper@37950
|
278 |
Thm("sqrt_isolate_l_add4",
|
neuper@37969
|
279 |
num_str @{thm sqrt_isolate_l_add4}),
|
neuper@37950
|
280 |
(* a+c/sqrt(x)=d -> c/sqrt(x) = d-a *)
|
neuper@37950
|
281 |
Thm("sqrt_isolate_l_add5",
|
neuper@37969
|
282 |
num_str @{thm sqrt_isolate_l_add5}),
|
neuper@37950
|
283 |
(* a+b*c/f*sqrt(x)=d->b*c/f*sqrt(x)=d-a *)
|
neuper@37950
|
284 |
Thm("sqrt_isolate_l_add6",
|
neuper@37969
|
285 |
num_str @{thm sqrt_isolate_l_add6}),
|
neuper@37950
|
286 |
(* a+c/f*sqrt(x)=d -> c/f*sqrt(x) = d-a *)
|
neuper@37969
|
287 |
(*Thm("sqrt_isolate_l_div",num_str @{thm sqrt_isolate_l_div}),*)
|
neuper@37950
|
288 |
(* b*sqrt(x) = d sqrt(x) d/b *)
|
neuper@37950
|
289 |
Thm("sqrt_isolate_r_add1",
|
neuper@37969
|
290 |
num_str @{thm sqrt_isolate_r_add1}),
|
neuper@37950
|
291 |
(* a= d+e*sqrt(x) -> a-d=e*sqrt(x) *)
|
neuper@37950
|
292 |
Thm("sqrt_isolate_r_add2",
|
neuper@37969
|
293 |
num_str @{thm sqrt_isolate_r_add2}),
|
neuper@37950
|
294 |
(* a= d+ sqrt(x) -> a-d= sqrt(x) *)
|
neuper@37950
|
295 |
Thm("sqrt_isolate_r_add3",
|
neuper@37969
|
296 |
num_str @{thm sqrt_isolate_r_add3}),
|
neuper@37950
|
297 |
(* a=d+e*g/sqrt(x)->a-d=e*g/sqrt(x)*)
|
neuper@37950
|
298 |
Thm("sqrt_isolate_r_add4",
|
neuper@37969
|
299 |
num_str @{thm sqrt_isolate_r_add4}),
|
neuper@37950
|
300 |
(* a= d+g/sqrt(x) -> a-d=g/sqrt(x) *)
|
neuper@37950
|
301 |
Thm("sqrt_isolate_r_add5",
|
neuper@37969
|
302 |
num_str @{thm sqrt_isolate_r_add5}),
|
neuper@37950
|
303 |
(* a=d+e*g/h*sqrt(x)->a-d=e*g/h*sqrt(x)*)
|
neuper@37950
|
304 |
Thm("sqrt_isolate_r_add6",
|
neuper@37969
|
305 |
num_str @{thm sqrt_isolate_r_add6}),
|
neuper@37950
|
306 |
(* a= d+g/h*sqrt(x) -> a-d=g/h*sqrt(x) *)
|
neuper@37969
|
307 |
(*Thm("sqrt_isolate_r_div",num_str @{thm sqrt_isolate_r_div}),*)
|
neuper@37950
|
308 |
(* a=e*sqrt(x) -> a/e = sqrt(x) *)
|
neuper@37950
|
309 |
Thm("sqrt_square_equation_left_1",
|
neuper@37969
|
310 |
num_str @{thm sqrt_square_equation_left_1}),
|
neuper@37950
|
311 |
(* sqrt(x)=b -> x=b^2 *)
|
neuper@37950
|
312 |
Thm("sqrt_square_equation_left_2",
|
neuper@37969
|
313 |
num_str @{thm sqrt_square_equation_left_2}),
|
neuper@37950
|
314 |
(* c*sqrt(x)=b -> c^2*x=b^2 *)
|
neuper@37969
|
315 |
Thm("sqrt_square_equation_left_3",num_str @{thm sqrt_square_equation_left_3}),
|
neuper@37950
|
316 |
(* c/sqrt(x)=b -> c^2/x=b^2 *)
|
neuper@37969
|
317 |
Thm("sqrt_square_equation_left_4",num_str @{thm sqrt_square_equation_left_4}),
|
neuper@37950
|
318 |
(* c*d/sqrt(x)=b -> c^2*d^2/x=b^2 *)
|
neuper@37969
|
319 |
Thm("sqrt_square_equation_left_5",num_str @{thm sqrt_square_equation_left_5}),
|
neuper@37950
|
320 |
(* c/d*sqrt(x)=b -> c^2/d^2x=b^2 *)
|
neuper@37969
|
321 |
Thm("sqrt_square_equation_left_6",num_str @{thm sqrt_square_equation_left_6}),
|
neuper@37950
|
322 |
(* c*d/g*sqrt(x)=b -> c^2*d^2/g^2x=b^2 *)
|
neuper@37969
|
323 |
Thm("sqrt_square_equation_right_1",num_str @{thm sqrt_square_equation_right_1}),
|
neuper@37950
|
324 |
(* a=sqrt(x) ->a^2=x *)
|
neuper@37969
|
325 |
Thm("sqrt_square_equation_right_2",num_str @{thm sqrt_square_equation_right_2}),
|
neuper@37950
|
326 |
(* a=c*sqrt(x) ->a^2=c^2*x *)
|
neuper@37969
|
327 |
Thm("sqrt_square_equation_right_3",num_str @{thm sqrt_square_equation_right_3}),
|
neuper@37950
|
328 |
(* a=c/sqrt(x) ->a^2=c^2/x *)
|
neuper@37969
|
329 |
Thm("sqrt_square_equation_right_4",num_str @{thm sqrt_square_equation_right_4}),
|
neuper@37950
|
330 |
(* a=c*d/sqrt(x) ->a^2=c^2*d^2/x *)
|
neuper@37969
|
331 |
Thm("sqrt_square_equation_right_5",num_str @{thm sqrt_square_equation_right_5}),
|
neuper@37950
|
332 |
(* a=c/e*sqrt(x) ->a^2=c^2/e^2x *)
|
neuper@37969
|
333 |
Thm("sqrt_square_equation_right_6",num_str @{thm sqrt_square_equation_right_6})
|
neuper@37950
|
334 |
(* a=c*d/g*sqrt(x) ->a^2=c^2*d^2/g^2*x *)
|
neuper@37950
|
335 |
],scr = Script ((term_of o the o (parse thy)) "empty_script")
|
neuper@37950
|
336 |
}:rls);
|
neuper@37950
|
337 |
|
neuper@37967
|
338 |
ruleset' := overwritelthy @{theory} (!ruleset',
|
neuper@37950
|
339 |
[("sqrt_isolate",sqrt_isolate)
|
neuper@37950
|
340 |
]);
|
neuper@37950
|
341 |
(* -- left 28.08.02--*)
|
neuper@37950
|
342 |
(*isolate the bound variable in an sqrt left equation; 'bdv' is a meta-constant*)
|
neuper@37950
|
343 |
val l_sqrt_isolate = prep_rls(
|
neuper@37950
|
344 |
Rls {id = "l_sqrt_isolate", preconds = [],
|
neuper@37950
|
345 |
rew_ord = ("termlessI",termlessI),
|
neuper@37950
|
346 |
erls = RootEq_erls, srls = Erls, calc = [],
|
neuper@37950
|
347 |
rules = [
|
neuper@37969
|
348 |
Thm("sqrt_square_1",num_str @{thm sqrt_square_1}),
|
neuper@37950
|
349 |
(* (sqrt a)^^^2 -> a *)
|
neuper@37969
|
350 |
Thm("sqrt_square_2",num_str @{thm sqrt_square_2}),
|
neuper@37950
|
351 |
(* sqrt (a^^^2) -> a *)
|
neuper@37969
|
352 |
Thm("sqrt_times_root_1",num_str @{thm sqrt_times_root_1}),
|
neuper@37950
|
353 |
(* sqrt a sqrt b -> sqrt(ab) *)
|
neuper@37969
|
354 |
Thm("sqrt_times_root_2",num_str @{thm sqrt_times_root_2}),
|
neuper@37950
|
355 |
(* a sqrt b sqrt c -> a sqrt(bc) *)
|
neuper@37969
|
356 |
Thm("sqrt_isolate_l_add1",num_str @{thm sqrt_isolate_l_add1}),
|
neuper@37950
|
357 |
(* a+b*sqrt(x)=d -> b*sqrt(x) = d-a *)
|
neuper@37969
|
358 |
Thm("sqrt_isolate_l_add2",num_str @{thm sqrt_isolate_l_add2}),
|
neuper@37950
|
359 |
(* a+ sqrt(x)=d -> sqrt(x) = d-a *)
|
neuper@37969
|
360 |
Thm("sqrt_isolate_l_add3",num_str @{thm sqrt_isolate_l_add3}),
|
neuper@37950
|
361 |
(* a+b*c/sqrt(x)=d->b*c/sqrt(x)=d-a *)
|
neuper@37969
|
362 |
Thm("sqrt_isolate_l_add4",num_str @{thm sqrt_isolate_l_add4}),
|
neuper@37950
|
363 |
(* a+c/sqrt(x)=d -> c/sqrt(x) = d-a *)
|
neuper@37969
|
364 |
Thm("sqrt_isolate_l_add5",num_str @{thm sqrt_isolate_l_add5}),
|
neuper@37950
|
365 |
(* a+b*c/f*sqrt(x)=d->b*c/f*sqrt(x)=d-a *)
|
neuper@37969
|
366 |
Thm("sqrt_isolate_l_add6",num_str @{thm sqrt_isolate_l_add6}),
|
neuper@37950
|
367 |
(* a+c/f*sqrt(x)=d -> c/f*sqrt(x) = d-a *)
|
neuper@37969
|
368 |
(*Thm("sqrt_isolate_l_div",num_str @{thm sqrt_isolate_l_div}),*)
|
neuper@37950
|
369 |
(* b*sqrt(x) = d sqrt(x) d/b *)
|
neuper@37969
|
370 |
Thm("sqrt_square_equation_left_1",num_str @{thm sqrt_square_equation_left_1}),
|
neuper@37950
|
371 |
(* sqrt(x)=b -> x=b^2 *)
|
neuper@37969
|
372 |
Thm("sqrt_square_equation_left_2",num_str @{thm sqrt_square_equation_left_2}),
|
neuper@37950
|
373 |
(* a*sqrt(x)=b -> a^2*x=b^2*)
|
neuper@37969
|
374 |
Thm("sqrt_square_equation_left_3",num_str @{thm sqrt_square_equation_left_3}),
|
neuper@37950
|
375 |
(* c/sqrt(x)=b -> c^2/x=b^2 *)
|
neuper@37969
|
376 |
Thm("sqrt_square_equation_left_4",num_str @{thm sqrt_square_equation_left_4}),
|
neuper@37950
|
377 |
(* c*d/sqrt(x)=b -> c^2*d^2/x=b^2 *)
|
neuper@37969
|
378 |
Thm("sqrt_square_equation_left_5",num_str @{thm sqrt_square_equation_left_5}),
|
neuper@37950
|
379 |
(* c/d*sqrt(x)=b -> c^2/d^2x=b^2 *)
|
neuper@37969
|
380 |
Thm("sqrt_square_equation_left_6",num_str @{thm sqrt_square_equation_left_6})
|
neuper@37950
|
381 |
(* c*d/g*sqrt(x)=b -> c^2*d^2/g^2x=b^2 *)
|
neuper@37950
|
382 |
],
|
neuper@37950
|
383 |
scr = Script ((term_of o the o (parse thy)) "empty_script")
|
neuper@37950
|
384 |
}:rls);
|
neuper@37950
|
385 |
|
neuper@37967
|
386 |
ruleset' := overwritelthy @{theory} (!ruleset',
|
neuper@37950
|
387 |
[("l_sqrt_isolate",l_sqrt_isolate)
|
neuper@37950
|
388 |
]);
|
neuper@37950
|
389 |
|
neuper@37950
|
390 |
(* -- right 28.8.02--*)
|
neuper@37950
|
391 |
(*isolate the bound variable in an sqrt right equation; 'bdv' is a meta-constant*)
|
neuper@37950
|
392 |
val r_sqrt_isolate = prep_rls(
|
neuper@37950
|
393 |
Rls {id = "r_sqrt_isolate", preconds = [],
|
neuper@37950
|
394 |
rew_ord = ("termlessI",termlessI),
|
neuper@37950
|
395 |
erls = RootEq_erls, srls = Erls, calc = [],
|
neuper@37950
|
396 |
rules = [
|
neuper@37969
|
397 |
Thm("sqrt_square_1",num_str @{thm sqrt_square_1}),
|
neuper@37950
|
398 |
(* (sqrt a)^^^2 -> a *)
|
neuper@37969
|
399 |
Thm("sqrt_square_2",num_str @{thm sqrt_square_2}),
|
neuper@37950
|
400 |
(* sqrt (a^^^2) -> a *)
|
neuper@37969
|
401 |
Thm("sqrt_times_root_1",num_str @{thm sqrt_times_root_1}),
|
neuper@37950
|
402 |
(* sqrt a sqrt b -> sqrt(ab) *)
|
neuper@37969
|
403 |
Thm("sqrt_times_root_2",num_str @{thm sqrt_times_root_2}),
|
neuper@37950
|
404 |
(* a sqrt b sqrt c -> a sqrt(bc) *)
|
neuper@37969
|
405 |
Thm("sqrt_isolate_r_add1",num_str @{thm sqrt_isolate_r_add1}),
|
neuper@37950
|
406 |
(* a= d+e*sqrt(x) -> a-d=e*sqrt(x) *)
|
neuper@37969
|
407 |
Thm("sqrt_isolate_r_add2",num_str @{thm sqrt_isolate_r_add2}),
|
neuper@37950
|
408 |
(* a= d+ sqrt(x) -> a-d= sqrt(x) *)
|
neuper@37969
|
409 |
Thm("sqrt_isolate_r_add3",num_str @{thm sqrt_isolate_r_add3}),
|
neuper@37950
|
410 |
(* a=d+e*g/sqrt(x)->a-d=e*g/sqrt(x)*)
|
neuper@37969
|
411 |
Thm("sqrt_isolate_r_add4",num_str @{thm sqrt_isolate_r_add4}),
|
neuper@37950
|
412 |
(* a= d+g/sqrt(x) -> a-d=g/sqrt(x) *)
|
neuper@37969
|
413 |
Thm("sqrt_isolate_r_add5",num_str @{thm sqrt_isolate_r_add5}),
|
neuper@37950
|
414 |
(* a=d+e*g/h*sqrt(x)->a-d=e*g/h*sqrt(x)*)
|
neuper@37969
|
415 |
Thm("sqrt_isolate_r_add6",num_str @{thm sqrt_isolate_r_add6}),
|
neuper@37950
|
416 |
(* a= d+g/h*sqrt(x) -> a-d=g/h*sqrt(x) *)
|
neuper@37969
|
417 |
(*Thm("sqrt_isolate_r_div",num_str @{thm sqrt_isolate_r_div}),*)
|
neuper@37950
|
418 |
(* a=e*sqrt(x) -> a/e = sqrt(x) *)
|
neuper@37969
|
419 |
Thm("sqrt_square_equation_right_1",num_str @{thm sqrt_square_equation_right_1}),
|
neuper@37950
|
420 |
(* a=sqrt(x) ->a^2=x *)
|
neuper@37969
|
421 |
Thm("sqrt_square_equation_right_2",num_str @{thm sqrt_square_equation_right_2}),
|
neuper@37950
|
422 |
(* a=c*sqrt(x) ->a^2=c^2*x *)
|
neuper@37969
|
423 |
Thm("sqrt_square_equation_right_3",num_str @{thm sqrt_square_equation_right_3}),
|
neuper@37950
|
424 |
(* a=c/sqrt(x) ->a^2=c^2/x *)
|
neuper@37969
|
425 |
Thm("sqrt_square_equation_right_4",num_str @{thm sqrt_square_equation_right_4}),
|
neuper@37950
|
426 |
(* a=c*d/sqrt(x) ->a^2=c^2*d^2/x *)
|
neuper@37969
|
427 |
Thm("sqrt_square_equation_right_5",num_str @{thm sqrt_square_equation_right_5}),
|
neuper@37950
|
428 |
(* a=c/e*sqrt(x) ->a^2=c^2/e^2x *)
|
neuper@37969
|
429 |
Thm("sqrt_square_equation_right_6",num_str @{thm sqrt_square_equation_right_6})
|
neuper@37950
|
430 |
(* a=c*d/g*sqrt(x) ->a^2=c^2*d^2/g^2*x *)
|
neuper@37950
|
431 |
],
|
neuper@37950
|
432 |
scr = Script ((term_of o the o (parse thy)) "empty_script")
|
neuper@37950
|
433 |
}:rls);
|
neuper@37950
|
434 |
|
neuper@37967
|
435 |
ruleset' := overwritelthy @{theory} (!ruleset',
|
neuper@37950
|
436 |
[("r_sqrt_isolate",r_sqrt_isolate)
|
neuper@37950
|
437 |
]);
|
neuper@37950
|
438 |
|
neuper@37950
|
439 |
val rooteq_simplify = prep_rls(
|
neuper@37950
|
440 |
Rls {id = "rooteq_simplify",
|
neuper@37950
|
441 |
preconds = [], rew_ord = ("termlessI",termlessI),
|
neuper@37950
|
442 |
erls = RootEq_erls, srls = Erls, calc = [],
|
neuper@37950
|
443 |
(*asm_thm = [("sqrt_square_1","")],*)
|
neuper@37969
|
444 |
rules = [Thm ("real_assoc_1",num_str @{thm real_assoc_1}),
|
neuper@37950
|
445 |
(* a+(b+c) = a+b+c *)
|
neuper@37969
|
446 |
Thm ("real_assoc_2",num_str @{thm real_assoc_2}),
|
neuper@37950
|
447 |
(* a*(b*c) = a*b*c *)
|
neuper@38014
|
448 |
Calc ("Groups.plus_class.plus",eval_binop "#add_"),
|
neuper@38014
|
449 |
Calc ("Groups.minus_class.minus",eval_binop "#sub_"),
|
neuper@37950
|
450 |
Calc ("op *",eval_binop "#mult_"),
|
neuper@38014
|
451 |
Calc ("Rings.inverse_class.divide", eval_cancel "#divide_e"),
|
neuper@37982
|
452 |
Calc ("NthRoot.sqrt",eval_sqrt "#sqrt_"),
|
neuper@37950
|
453 |
Calc ("Atools.pow" ,eval_binop "#power_"),
|
neuper@37969
|
454 |
Thm("real_plus_binom_pow2",num_str @{thm real_plus_binom_pow2}),
|
neuper@37969
|
455 |
Thm("real_minus_binom_pow2",num_str @{thm real_minus_binom_pow2}),
|
neuper@37969
|
456 |
Thm("realpow_mul",num_str @{thm realpow_mul}),
|
neuper@37950
|
457 |
(* (a * b)^n = a^n * b^n*)
|
neuper@37969
|
458 |
Thm("sqrt_times_root_1",num_str @{thm sqrt_times_root_1}),
|
neuper@37950
|
459 |
(* sqrt b * sqrt c = sqrt(b*c) *)
|
neuper@37969
|
460 |
Thm("sqrt_times_root_2",num_str @{thm sqrt_times_root_2}),
|
neuper@37950
|
461 |
(* a * sqrt a * sqrt b = a * sqrt(a*b) *)
|
neuper@37969
|
462 |
Thm("sqrt_square_2",num_str @{thm sqrt_square_2}),
|
neuper@37950
|
463 |
(* sqrt (a^^^2) = a *)
|
neuper@37969
|
464 |
Thm("sqrt_square_1",num_str @{thm sqrt_square_1})
|
neuper@37950
|
465 |
(* sqrt a ^^^ 2 = a *)
|
neuper@37950
|
466 |
],
|
neuper@37950
|
467 |
scr = Script ((term_of o the o (parse thy)) "empty_script")
|
neuper@37950
|
468 |
}:rls);
|
neuper@37967
|
469 |
ruleset' := overwritelthy @{theory} (!ruleset',
|
neuper@37950
|
470 |
[("rooteq_simplify",rooteq_simplify)
|
neuper@37950
|
471 |
]);
|
neuper@37950
|
472 |
|
neuper@37950
|
473 |
(*-------------------------Problem-----------------------*)
|
neuper@37950
|
474 |
(*
|
neuper@37986
|
475 |
(get_pbt ["root'","univariate","equation"]);
|
neuper@37950
|
476 |
show_ptyps();
|
neuper@37950
|
477 |
*)
|
neuper@37950
|
478 |
(* ---------root----------- *)
|
neuper@37950
|
479 |
store_pbt
|
neuper@37972
|
480 |
(prep_pbt thy "pbl_equ_univ_root" [] e_pblID
|
neuper@37986
|
481 |
(["root'","univariate","equation"],
|
neuper@37981
|
482 |
[("#Given" ,["equality e_e","solveFor v_v"]),
|
neuper@37982
|
483 |
("#Where" ,["(lhs e_e) is_rootTerm_in (v_v::real) | " ^
|
neuper@37982
|
484 |
"(rhs e_e) is_rootTerm_in (v_v::real)"]),
|
neuper@38012
|
485 |
("#Find" ,["solutions v_v'i'"])
|
neuper@37950
|
486 |
],
|
neuper@37981
|
487 |
RootEq_prls, SOME "solve (e_e::bool, v_v)",
|
neuper@37950
|
488 |
[]));
|
neuper@37950
|
489 |
(* ---------sqrt----------- *)
|
neuper@37950
|
490 |
store_pbt
|
neuper@37972
|
491 |
(prep_pbt thy "pbl_equ_univ_root_sq" [] e_pblID
|
neuper@37986
|
492 |
(["sq","root'","univariate","equation"],
|
neuper@37981
|
493 |
[("#Given" ,["equality e_e","solveFor v_v"]),
|
neuper@37982
|
494 |
("#Where" ,["( ((lhs e_e) is_sqrtTerm_in (v_v::real)) &" ^
|
neuper@37982
|
495 |
" ((lhs e_e) is_normSqrtTerm_in (v_v::real)) ) |" ^
|
neuper@37982
|
496 |
"( ((rhs e_e) is_sqrtTerm_in (v_v::real)) &" ^
|
neuper@37982
|
497 |
" ((rhs e_e) is_normSqrtTerm_in (v_v::real)) )"]),
|
neuper@38012
|
498 |
("#Find" ,["solutions v_v'i'"])
|
neuper@37950
|
499 |
],
|
neuper@37981
|
500 |
RootEq_prls, SOME "solve (e_e::bool, v_v)",
|
neuper@37950
|
501 |
[["RootEq","solve_sq_root_equation"]]));
|
neuper@37950
|
502 |
(* ---------normalize----------- *)
|
neuper@37950
|
503 |
store_pbt
|
neuper@37972
|
504 |
(prep_pbt thy "pbl_equ_univ_root_norm" [] e_pblID
|
neuper@37986
|
505 |
(["normalize","root'","univariate","equation"],
|
neuper@37981
|
506 |
[("#Given" ,["equality e_e","solveFor v_v"]),
|
neuper@37982
|
507 |
("#Where" ,["( ((lhs e_e) is_sqrtTerm_in (v_v::real)) &" ^
|
neuper@37982
|
508 |
" Not((lhs e_e) is_normSqrtTerm_in (v_v::real))) | " ^
|
neuper@37982
|
509 |
"( ((rhs e_e) is_sqrtTerm_in (v_v::real)) &" ^
|
neuper@37982
|
510 |
" Not((rhs e_e) is_normSqrtTerm_in (v_v::real)))"]),
|
neuper@38012
|
511 |
("#Find" ,["solutions v_v'i'"])
|
neuper@37950
|
512 |
],
|
neuper@37981
|
513 |
RootEq_prls, SOME "solve (e_e::bool, v_v)",
|
neuper@37950
|
514 |
[["RootEq","norm_sq_root_equation"]]));
|
neuper@37950
|
515 |
|
neuper@37950
|
516 |
(*-------------------------methods-----------------------*)
|
neuper@37950
|
517 |
(* ---- root 20.8.02 ---*)
|
neuper@37950
|
518 |
store_met
|
neuper@37972
|
519 |
(prep_met thy "met_rooteq" [] e_metID
|
neuper@37950
|
520 |
(["RootEq"],
|
neuper@37950
|
521 |
[],
|
neuper@37950
|
522 |
{rew_ord'="tless_true",rls'=Atools_erls,calc = [], srls = e_rls, prls=e_rls,
|
neuper@37950
|
523 |
crls=RootEq_crls, nrls=norm_Poly(*,
|
neuper@37950
|
524 |
asm_rls=[],asm_thm=[]*)}, "empty_script"));
|
neuper@37985
|
525 |
|
neuper@37950
|
526 |
(*-- normalize 20.10.02 --*)
|
neuper@37950
|
527 |
store_met
|
neuper@37972
|
528 |
(prep_met thy "met_rooteq_norm" [] e_metID
|
neuper@37950
|
529 |
(["RootEq","norm_sq_root_equation"],
|
neuper@37981
|
530 |
[("#Given" ,["equality e_e","solveFor v_v"]),
|
neuper@37982
|
531 |
("#Where" ,["( ((lhs e_e) is_sqrtTerm_in (v_v::real)) &" ^
|
neuper@37982
|
532 |
" Not((lhs e_e) is_normSqrtTerm_in (v_v::real))) | " ^
|
neuper@37982
|
533 |
"( ((rhs e_e) is_sqrtTerm_in (v_v::real)) &" ^
|
neuper@37982
|
534 |
" Not((rhs e_e) is_normSqrtTerm_in (v_v::real)))"]),
|
neuper@38012
|
535 |
("#Find" ,["solutions v_v'i'"])
|
neuper@37950
|
536 |
],
|
neuper@37985
|
537 |
{rew_ord'="termlessI", rls'=RootEq_erls, srls=e_rls, prls=RootEq_prls,
|
neuper@37985
|
538 |
calc=[], crls=RootEq_crls, nrls=norm_Poly},
|
neuper@37982
|
539 |
"Script Norm_sq_root_equation (e_e::bool) (v_v::real) = " ^
|
neuper@37981
|
540 |
"(let e_e = ((Repeat(Try (Rewrite makex1_x False))) @@ " ^
|
neuper@37950
|
541 |
" (Try (Repeat (Rewrite_Set expand_rootbinoms False))) @@ " ^
|
neuper@37950
|
542 |
" (Try (Rewrite_Set rooteq_simplify True)) @@ " ^
|
neuper@37950
|
543 |
" (Try (Repeat (Rewrite_Set make_rooteq False))) @@ " ^
|
neuper@37981
|
544 |
" (Try (Rewrite_Set rooteq_simplify True))) e_e " ^
|
neuper@37987
|
545 |
" in ((SubProblem (RootEq',[univariate,equation], " ^
|
neuper@37985
|
546 |
" [no_met]) [BOOL e_e, REAL v_v])))"
|
neuper@37950
|
547 |
));
|
neuper@37950
|
548 |
|
neuper@37985
|
549 |
*}
|
neuper@37985
|
550 |
|
neuper@37985
|
551 |
ML {*
|
neuper@37985
|
552 |
val -------------------------------------------------- = "00000";
|
neuper@37950
|
553 |
store_met
|
neuper@37972
|
554 |
(prep_met thy "met_rooteq_sq" [] e_metID
|
neuper@37950
|
555 |
(["RootEq","solve_sq_root_equation"],
|
neuper@37985
|
556 |
[("#Given" ,["equality e_e", "solveFor v_v"]),
|
neuper@37985
|
557 |
("#Where" ,["(((lhs e_e) is_sqrtTerm_in (v_v::real)) & " ^
|
neuper@37985
|
558 |
" ((lhs e_e) is_normSqrtTerm_in (v_v::real))) |" ^
|
neuper@37985
|
559 |
"(((rhs e_e) is_sqrtTerm_in (v_v::real)) & " ^
|
neuper@37985
|
560 |
" ((rhs e_e) is_normSqrtTerm_in (v_v::real)))"]),
|
neuper@38012
|
561 |
("#Find" ,["solutions v_v'i'"])
|
neuper@37950
|
562 |
],
|
neuper@37985
|
563 |
{rew_ord'="termlessI", rls'=RootEq_erls, srls = rooteq_srls,
|
neuper@37985
|
564 |
prls = RootEq_prls, calc = [], crls=RootEq_crls, nrls=norm_Poly},
|
neuper@37985
|
565 |
"Script Solve_sq_root_equation (e_e::bool) (v_v::real) = " ^
|
neuper@37985
|
566 |
"(let e_e = " ^
|
neuper@37985
|
567 |
" ((Try (Rewrite_Set_Inst [(bdv,v_v::real)] sqrt_isolate True)) @@ " ^
|
neuper@37985
|
568 |
" (Try (Rewrite_Set rooteq_simplify True)) @@ " ^
|
neuper@37985
|
569 |
" (Try (Repeat (Rewrite_Set expand_rootbinoms False))) @@ " ^
|
neuper@37985
|
570 |
" (Try (Repeat (Rewrite_Set make_rooteq False))) @@ " ^
|
neuper@37985
|
571 |
" (Try (Rewrite_Set rooteq_simplify True)) ) e_e; " ^
|
neuper@37985
|
572 |
" (L_L::bool list) = " ^
|
neuper@37985
|
573 |
" (if (((lhs e_e) is_sqrtTerm_in v_v) | ((rhs e_e) is_sqrtTerm_in v_v))" ^
|
neuper@37987
|
574 |
" then (SubProblem (RootEq',[normalize,root',univariate,equation], " ^
|
neuper@37985
|
575 |
" [no_met]) [BOOL e_e, REAL v_v]) " ^
|
neuper@37987
|
576 |
" else (SubProblem (RootEq',[univariate,equation], [no_met]) " ^
|
neuper@37985
|
577 |
" [BOOL e_e, REAL v_v])) " ^
|
neuper@37991
|
578 |
"in Check_elementwise L_LL {(v_v::real). Assumptions})"
|
neuper@37950
|
579 |
));
|
neuper@37985
|
580 |
*}
|
neuper@37950
|
581 |
|
neuper@37985
|
582 |
ML {*
|
neuper@37950
|
583 |
(*-- right 28.08.02 --*)
|
neuper@37950
|
584 |
store_met
|
neuper@37972
|
585 |
(prep_met thy "met_rooteq_sq_right" [] e_metID
|
neuper@37950
|
586 |
(["RootEq","solve_right_sq_root_equation"],
|
neuper@37981
|
587 |
[("#Given" ,["equality e_e","solveFor v_v"]),
|
neuper@37981
|
588 |
("#Where" ,["(rhs e_e) is_sqrtTerm_in v_v"]),
|
neuper@38012
|
589 |
("#Find" ,["solutions v_v'i'"])
|
neuper@37950
|
590 |
],
|
neuper@37985
|
591 |
{rew_ord' = "termlessI", rls' = RootEq_erls, srls = e_rls,
|
neuper@37985
|
592 |
prls = RootEq_prls, calc = [], crls = RootEq_crls, nrls = norm_Poly},
|
neuper@37985
|
593 |
"Script Solve_right_sq_root_equation (e_e::bool) (v_v::real) = " ^
|
neuper@37985
|
594 |
"(let e_e = " ^
|
neuper@37985
|
595 |
" ((Try (Rewrite_Set_Inst [(bdv,v_v::real)] r_sqrt_isolate False)) @@ " ^
|
neuper@37985
|
596 |
" (Try (Rewrite_Set rooteq_simplify False)) @@ " ^
|
neuper@37985
|
597 |
" (Try (Repeat (Rewrite_Set expand_rootbinoms False))) @@ " ^
|
neuper@37985
|
598 |
" (Try (Repeat (Rewrite_Set make_rooteq False))) @@ " ^
|
neuper@37981
|
599 |
" (Try (Rewrite_Set rooteq_simplify False))) e_e " ^
|
neuper@37985
|
600 |
" in if ((rhs e_e) is_sqrtTerm_in v_v) " ^
|
neuper@37987
|
601 |
" then (SubProblem (RootEq',[normalize,root',univariate,equation], " ^
|
neuper@37985
|
602 |
" [no_met]) [BOOL e_e, REAL v_v]) " ^
|
neuper@37987
|
603 |
" else ((SubProblem (RootEq',[univariate,equation], " ^
|
neuper@37985
|
604 |
" [no_met]) [BOOL e_e, REAL v_v])))"
|
neuper@37950
|
605 |
));
|
neuper@37985
|
606 |
val --------------------------------------------------+++ = "33333";
|
neuper@37950
|
607 |
|
neuper@37950
|
608 |
(*-- left 28.08.02 --*)
|
neuper@37950
|
609 |
store_met
|
neuper@37972
|
610 |
(prep_met thy "met_rooteq_sq_left" [] e_metID
|
neuper@37950
|
611 |
(["RootEq","solve_left_sq_root_equation"],
|
neuper@37981
|
612 |
[("#Given" ,["equality e_e","solveFor v_v"]),
|
neuper@37981
|
613 |
("#Where" ,["(lhs e_e) is_sqrtTerm_in v_v"]),
|
neuper@38012
|
614 |
("#Find" ,["solutions v_v'i'"])
|
neuper@37950
|
615 |
],
|
neuper@37950
|
616 |
{rew_ord'="termlessI",
|
neuper@37950
|
617 |
rls'=RootEq_erls,
|
neuper@37950
|
618 |
srls=e_rls,
|
neuper@37950
|
619 |
prls=RootEq_prls,
|
neuper@37950
|
620 |
calc=[],
|
neuper@37950
|
621 |
crls=RootEq_crls, nrls=norm_Poly},
|
neuper@37982
|
622 |
"Script Solve_left_sq_root_equation (e_e::bool) (v_v::real) = " ^
|
neuper@37981
|
623 |
"(let e_e = " ^
|
neuper@37985
|
624 |
" ((Try (Rewrite_Set_Inst [(bdv,v_v::real)] l_sqrt_isolate False)) @@ " ^
|
neuper@37950
|
625 |
" (Try (Rewrite_Set rooteq_simplify False)) @@ " ^
|
neuper@37950
|
626 |
" (Try (Repeat (Rewrite_Set expand_rootbinoms False))) @@ " ^
|
neuper@37950
|
627 |
" (Try (Repeat (Rewrite_Set make_rooteq False))) @@ " ^
|
neuper@37981
|
628 |
" (Try (Rewrite_Set rooteq_simplify False))) e_e " ^
|
neuper@37981
|
629 |
" in if ((lhs e_e) is_sqrtTerm_in v_v) " ^
|
neuper@37987
|
630 |
" then (SubProblem (RootEq',[normalize,root',univariate,equation], " ^
|
neuper@37985
|
631 |
" [no_met]) [BOOL e_e, REAL v_v]) " ^
|
neuper@37987
|
632 |
" else ((SubProblem (RootEq',[univariate,equation], " ^
|
neuper@37985
|
633 |
" [no_met]) [BOOL e_e, REAL v_v])))"
|
neuper@37950
|
634 |
));
|
neuper@37985
|
635 |
val --------------------------------------------------++++ = "44444";
|
neuper@37950
|
636 |
|
neuper@37950
|
637 |
calclist':= overwritel (!calclist',
|
neuper@37950
|
638 |
[("is_rootTerm_in", ("RootEq.is'_rootTerm'_in",
|
neuper@37950
|
639 |
eval_is_rootTerm_in"")),
|
neuper@37950
|
640 |
("is_sqrtTerm_in", ("RootEq.is'_sqrtTerm'_in",
|
neuper@37950
|
641 |
eval_is_sqrtTerm_in"")),
|
neuper@37950
|
642 |
("is_normSqrtTerm_in", ("RootEq.is_normSqrtTerm_in",
|
neuper@37950
|
643 |
eval_is_normSqrtTerm_in""))
|
neuper@37950
|
644 |
]);(*("", ("", "")),*)
|
neuper@37950
|
645 |
*}
|
neuper@37950
|
646 |
|
neuper@37906
|
647 |
end
|