1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/src/Tools/isac/Knowledge/RootEq.ML Wed Aug 25 16:20:07 2010 +0200
1.3 @@ -0,0 +1,505 @@
1.4 +(*.(c) by Richard Lang, 2003 .*)
1.5 +(* theory collecting all knowledge for RootEquations
1.6 + created by: rlang
1.7 + date: 02.09
1.8 + changed by: rlang
1.9 + last change by: rlang
1.10 + date: 02.11.14
1.11 +*)
1.12 +
1.13 +(* use"Knowledge/RootEq.ML";
1.14 + use"RootEq.ML";
1.15 +
1.16 + use"ROOT.ML";
1.17 + cd"knowledge";
1.18 +
1.19 + remove_thy"RootEq";
1.20 + use_thy"Knowledge/Isac";
1.21 + *)
1.22 +"******* RootEq.ML begin *******";
1.23 +
1.24 +theory' := overwritel (!theory', [("RootEq.thy",RootEq.thy)]);
1.25 +(*-------------------------functions---------------------*)
1.26 +(* true if bdv is under sqrt of a Equation*)
1.27 +fun is_rootTerm_in t v =
1.28 + let
1.29 + fun coeff_in c v = member op = (vars c) v;
1.30 + fun findroot (_ $ _ $ _ $ _) v = raise error("is_rootTerm_in:")
1.31 + (* at the moment there is no term like this, but ....*)
1.32 + | findroot (t as (Const ("Root.nroot",_) $ _ $ t3)) v = coeff_in t3 v
1.33 + | findroot (_ $ t2 $ t3) v = (findroot t2 v) orelse (findroot t3 v)
1.34 + | findroot (t as (Const ("Root.sqrt",_) $ t2)) v = coeff_in t2 v
1.35 + | findroot (_ $ t2) v = (findroot t2 v)
1.36 + | findroot _ _ = false;
1.37 + in
1.38 + findroot t v
1.39 + end;
1.40 +
1.41 + fun is_sqrtTerm_in t v =
1.42 + let
1.43 + fun coeff_in c v = member op = (vars c) v;
1.44 + fun findsqrt (_ $ _ $ _ $ _) v = raise error("is_sqrteqation_in:")
1.45 + (* at the moment there is no term like this, but ....*)
1.46 + | findsqrt (_ $ t1 $ t2) v = (findsqrt t1 v) orelse (findsqrt t2 v)
1.47 + | findsqrt (t as (Const ("Root.sqrt",_) $ a)) v = coeff_in a v
1.48 + | findsqrt (_ $ t1) v = (findsqrt t1 v)
1.49 + | findsqrt _ _ = false;
1.50 + in
1.51 + findsqrt t v
1.52 + end;
1.53 +
1.54 +(* RL: 030518: Is in the rightest subterm of a term a sqrt with bdv,
1.55 +and the subterm ist connected with + or * --> is normalized*)
1.56 + fun is_normSqrtTerm_in t v =
1.57 + let
1.58 + fun coeff_in c v = member op = (vars c) v;
1.59 + fun isnorm (_ $ _ $ _ $ _) v = raise error("is_normSqrtTerm_in:")
1.60 + (* at the moment there is no term like this, but ....*)
1.61 + | isnorm (Const ("op +",_) $ _ $ t2) v = is_sqrtTerm_in t2 v
1.62 + | isnorm (Const ("op *",_) $ _ $ t2) v = is_sqrtTerm_in t2 v
1.63 + | isnorm (Const ("op -",_) $ _ $ _) v = false
1.64 + | isnorm (Const ("HOL.divide",_) $ t1 $ t2) v = (is_sqrtTerm_in t1 v) orelse
1.65 + (is_sqrtTerm_in t2 v)
1.66 + | isnorm (Const ("Root.sqrt",_) $ t1) v = coeff_in t1 v
1.67 + | isnorm (_ $ t1) v = is_sqrtTerm_in t1 v
1.68 + | isnorm _ _ = false;
1.69 + in
1.70 + isnorm t v
1.71 + end;
1.72 +
1.73 +fun eval_is_rootTerm_in _ _ (p as (Const ("RootEq.is'_rootTerm'_in",_) $ t $ v)) _ =
1.74 + if is_rootTerm_in t v then
1.75 + SOME ((term2str p) ^ " = True",
1.76 + Trueprop $ (mk_equality (p, HOLogic.true_const)))
1.77 + else SOME ((term2str p) ^ " = True",
1.78 + Trueprop $ (mk_equality (p, HOLogic.false_const)))
1.79 + | eval_is_rootTerm_in _ _ _ _ = ((*writeln"### nichts matcht";*) NONE);
1.80 +
1.81 +fun eval_is_sqrtTerm_in _ _ (p as (Const ("RootEq.is'_sqrtTerm'_in",_) $ t $ v)) _ =
1.82 + if is_sqrtTerm_in t v then
1.83 + SOME ((term2str p) ^ " = True",
1.84 + Trueprop $ (mk_equality (p, HOLogic.true_const)))
1.85 + else SOME ((term2str p) ^ " = True",
1.86 + Trueprop $ (mk_equality (p, HOLogic.false_const)))
1.87 + | eval_is_sqrtTerm_in _ _ _ _ = ((*writeln"### nichts matcht";*) NONE);
1.88 +
1.89 +fun eval_is_normSqrtTerm_in _ _ (p as (Const ("RootEq.is'_normSqrtTerm'_in",_) $ t $ v)) _ =
1.90 + if is_normSqrtTerm_in t v then
1.91 + SOME ((term2str p) ^ " = True",
1.92 + Trueprop $ (mk_equality (p, HOLogic.true_const)))
1.93 + else SOME ((term2str p) ^ " = True",
1.94 + Trueprop $ (mk_equality (p, HOLogic.false_const)))
1.95 + | eval_is_normSqrtTerm_in _ _ _ _ = ((*writeln"### nichts matcht";*) NONE);
1.96 +
1.97 +(*-------------------------rulse-------------------------*)
1.98 +val RootEq_prls = (*15.10.02:just the following order due to subterm evaluation*)
1.99 + append_rls "RootEq_prls" e_rls
1.100 + [Calc ("Atools.ident",eval_ident "#ident_"),
1.101 + Calc ("Tools.matches",eval_matches ""),
1.102 + Calc ("Tools.lhs" ,eval_lhs ""),
1.103 + Calc ("Tools.rhs" ,eval_rhs ""),
1.104 + Calc ("RootEq.is'_sqrtTerm'_in",eval_is_sqrtTerm_in ""),
1.105 + Calc ("RootEq.is'_rootTerm'_in",eval_is_rootTerm_in ""),
1.106 + Calc ("RootEq.is'_normSqrtTerm'_in",eval_is_normSqrtTerm_in ""),
1.107 + Calc ("op =",eval_equal "#equal_"),
1.108 + Thm ("not_true",num_str not_true),
1.109 + Thm ("not_false",num_str not_false),
1.110 + Thm ("and_true",num_str and_true),
1.111 + Thm ("and_false",num_str and_false),
1.112 + Thm ("or_true",num_str or_true),
1.113 + Thm ("or_false",num_str or_false)
1.114 + ];
1.115 +
1.116 +val RootEq_erls =
1.117 + append_rls "RootEq_erls" Root_erls
1.118 + [Thm ("real_divide_divide2_eq",num_str real_divide_divide2_eq)
1.119 + ];
1.120 +
1.121 +val RootEq_crls =
1.122 + append_rls "RootEq_crls" Root_crls
1.123 + [Thm ("real_divide_divide2_eq",num_str real_divide_divide2_eq)
1.124 + ];
1.125 +
1.126 +val rooteq_srls =
1.127 + append_rls "rooteq_srls" e_rls
1.128 + [Calc ("RootEq.is'_sqrtTerm'_in",eval_is_sqrtTerm_in ""),
1.129 + Calc ("RootEq.is'_normSqrtTerm'_in",eval_is_normSqrtTerm_in ""),
1.130 + Calc ("RootEq.is'_rootTerm'_in",eval_is_rootTerm_in "")
1.131 + ];
1.132 +
1.133 +ruleset' := overwritelthy thy (!ruleset',
1.134 + [("RootEq_erls",RootEq_erls), (*FIXXXME:del with rls.rls'*)
1.135 + ("rooteq_srls",rooteq_srls)
1.136 + ]);
1.137 +
1.138 +(*isolate the bound variable in an sqrt equation; 'bdv' is a meta-constant*)
1.139 + val sqrt_isolate = prep_rls(
1.140 + Rls {id = "sqrt_isolate", preconds = [], rew_ord = ("termlessI",termlessI),
1.141 + erls = RootEq_erls, srls = Erls, calc = [],
1.142 + (*asm_thm = [("sqrt_square_1",""),("sqrt_square_equation_left_1",""),
1.143 + ("sqrt_square_equation_left_2",""),("sqrt_square_equation_left_3",""),
1.144 + ("sqrt_square_equation_left_4",""),("sqrt_square_equation_left_5",""),
1.145 + ("sqrt_square_equation_left_6",""),("sqrt_square_equation_right_1",""),
1.146 + ("sqrt_square_equation_right_2",""),("sqrt_square_equation_right_3",""),
1.147 + ("sqrt_square_equation_right_4",""),("sqrt_square_equation_right_5",""),
1.148 + ("sqrt_square_equation_right_6","")],*)
1.149 + rules = [
1.150 + Thm("sqrt_square_1",num_str sqrt_square_1), (* (sqrt a)^^^2 -> a *)
1.151 + Thm("sqrt_square_2",num_str sqrt_square_2), (* sqrt (a^^^2) -> a *)
1.152 + Thm("sqrt_times_root_1",num_str sqrt_times_root_1), (* sqrt a sqrt b -> sqrt(ab) *)
1.153 + Thm("sqrt_times_root_2",num_str sqrt_times_root_2), (* a sqrt b sqrt c -> a sqrt(bc) *)
1.154 + Thm("sqrt_square_equation_both_1",num_str sqrt_square_equation_both_1),
1.155 + (* (sqrt a + sqrt b = sqrt c + sqrt d) -> (a+2*sqrt(a)*sqrt(b)+b) = c+2*sqrt(c)*sqrt(d)+d) *)
1.156 + Thm("sqrt_square_equation_both_2",num_str sqrt_square_equation_both_2),
1.157 + (* (sqrt a - sqrt b = sqrt c + sqrt d) -> (a-2*sqrt(a)*sqrt(b)+b) = c+2*sqrt(c)*sqrt(d)+d) *)
1.158 + Thm("sqrt_square_equation_both_3",num_str sqrt_square_equation_both_3),
1.159 + (* (sqrt a + sqrt b = sqrt c - sqrt d) -> (a+2*sqrt(a)*sqrt(b)+b) = c-2*sqrt(c)*sqrt(d)+d) *)
1.160 + Thm("sqrt_square_equation_both_4",num_str sqrt_square_equation_both_4),
1.161 + (* (sqrt a - sqrt b = sqrt c - sqrt d) -> (a-2*sqrt(a)*sqrt(b)+b) = c-2*sqrt(c)*sqrt(d)+d) *)
1.162 + Thm("sqrt_isolate_l_add1",num_str sqrt_isolate_l_add1), (* a+b*sqrt(x)=d -> b*sqrt(x) = d-a *)
1.163 + Thm("sqrt_isolate_l_add2",num_str sqrt_isolate_l_add2), (* a+ sqrt(x)=d -> sqrt(x) = d-a *)
1.164 + Thm("sqrt_isolate_l_add3",num_str sqrt_isolate_l_add3), (* a+b*c/sqrt(x)=d->b*c/sqrt(x)=d-a *)
1.165 + Thm("sqrt_isolate_l_add4",num_str sqrt_isolate_l_add4), (* a+c/sqrt(x)=d -> c/sqrt(x) = d-a *)
1.166 + Thm("sqrt_isolate_l_add5",num_str sqrt_isolate_l_add5), (* a+b*c/f*sqrt(x)=d->b*c/f*sqrt(x)=d-a *)
1.167 + Thm("sqrt_isolate_l_add6",num_str sqrt_isolate_l_add6), (* a+c/f*sqrt(x)=d -> c/f*sqrt(x) = d-a *)
1.168 + (*Thm("sqrt_isolate_l_div",num_str sqrt_isolate_l_div),*) (* b*sqrt(x) = d sqrt(x) d/b *)
1.169 + Thm("sqrt_isolate_r_add1",num_str sqrt_isolate_r_add1), (* a= d+e*sqrt(x) -> a-d=e*sqrt(x) *)
1.170 + Thm("sqrt_isolate_r_add2",num_str sqrt_isolate_r_add2), (* a= d+ sqrt(x) -> a-d= sqrt(x) *)
1.171 + Thm("sqrt_isolate_r_add3",num_str sqrt_isolate_r_add3), (* a=d+e*g/sqrt(x)->a-d=e*g/sqrt(x)*)
1.172 + Thm("sqrt_isolate_r_add4",num_str sqrt_isolate_r_add4), (* a= d+g/sqrt(x) -> a-d=g/sqrt(x) *)
1.173 + Thm("sqrt_isolate_r_add5",num_str sqrt_isolate_r_add5), (* a=d+e*g/h*sqrt(x)->a-d=e*g/h*sqrt(x)*)
1.174 + Thm("sqrt_isolate_r_add6",num_str sqrt_isolate_r_add6), (* a= d+g/h*sqrt(x) -> a-d=g/h*sqrt(x) *)
1.175 + (*Thm("sqrt_isolate_r_div",num_str sqrt_isolate_r_div),*) (* a=e*sqrt(x) -> a/e = sqrt(x) *)
1.176 + Thm("sqrt_square_equation_left_1",num_str sqrt_square_equation_left_1),
1.177 + (* sqrt(x)=b -> x=b^2 *)
1.178 + Thm("sqrt_square_equation_left_2",num_str sqrt_square_equation_left_2),
1.179 + (* c*sqrt(x)=b -> c^2*x=b^2 *)
1.180 + Thm("sqrt_square_equation_left_3",num_str sqrt_square_equation_left_3),
1.181 + (* c/sqrt(x)=b -> c^2/x=b^2 *)
1.182 + Thm("sqrt_square_equation_left_4",num_str sqrt_square_equation_left_4),
1.183 + (* c*d/sqrt(x)=b -> c^2*d^2/x=b^2 *)
1.184 + Thm("sqrt_square_equation_left_5",num_str sqrt_square_equation_left_5),
1.185 + (* c/d*sqrt(x)=b -> c^2/d^2x=b^2 *)
1.186 + Thm("sqrt_square_equation_left_6",num_str sqrt_square_equation_left_6),
1.187 + (* c*d/g*sqrt(x)=b -> c^2*d^2/g^2x=b^2 *)
1.188 + Thm("sqrt_square_equation_right_1",num_str sqrt_square_equation_right_1),
1.189 + (* a=sqrt(x) ->a^2=x *)
1.190 + Thm("sqrt_square_equation_right_2",num_str sqrt_square_equation_right_2),
1.191 + (* a=c*sqrt(x) ->a^2=c^2*x *)
1.192 + Thm("sqrt_square_equation_right_3",num_str sqrt_square_equation_right_3),
1.193 + (* a=c/sqrt(x) ->a^2=c^2/x *)
1.194 + Thm("sqrt_square_equation_right_4",num_str sqrt_square_equation_right_4),
1.195 + (* a=c*d/sqrt(x) ->a^2=c^2*d^2/x *)
1.196 + Thm("sqrt_square_equation_right_5",num_str sqrt_square_equation_right_5),
1.197 + (* a=c/e*sqrt(x) ->a^2=c^2/e^2x *)
1.198 + Thm("sqrt_square_equation_right_6",num_str sqrt_square_equation_right_6)
1.199 + (* a=c*d/g*sqrt(x) ->a^2=c^2*d^2/g^2*x *)
1.200 + ],
1.201 + scr = Script ((term_of o the o (parse thy)) "empty_script")
1.202 + }:rls);
1.203 +ruleset' := overwritelthy thy (!ruleset',
1.204 + [("sqrt_isolate",sqrt_isolate)
1.205 + ]);
1.206 +(* -- left 28.08.02--*)
1.207 +(*isolate the bound variable in an sqrt left equation; 'bdv' is a meta-constant*)
1.208 + val l_sqrt_isolate = prep_rls(
1.209 + Rls {id = "l_sqrt_isolate", preconds = [],
1.210 + rew_ord = ("termlessI",termlessI),
1.211 + erls = RootEq_erls, srls = Erls, calc = [],
1.212 + (*asm_thm = [("sqrt_square_1",""),("sqrt_square_equation_left_1",""),
1.213 + ("sqrt_square_equation_left_2",""),("sqrt_square_equation_left_3",""),
1.214 + ("sqrt_square_equation_left_4",""),("sqrt_square_equation_left_5",""),
1.215 + ("sqrt_square_equation_left_6","")],*)
1.216 + rules = [
1.217 + Thm("sqrt_square_1",num_str sqrt_square_1), (* (sqrt a)^^^2 -> a *)
1.218 + Thm("sqrt_square_2",num_str sqrt_square_2), (* sqrt (a^^^2) -> a *)
1.219 + Thm("sqrt_times_root_1",num_str sqrt_times_root_1), (* sqrt a sqrt b -> sqrt(ab) *)
1.220 + Thm("sqrt_times_root_2",num_str sqrt_times_root_2), (* a sqrt b sqrt c -> a sqrt(bc) *)
1.221 + Thm("sqrt_isolate_l_add1",num_str sqrt_isolate_l_add1), (* a+b*sqrt(x)=d -> b*sqrt(x) = d-a *)
1.222 + Thm("sqrt_isolate_l_add2",num_str sqrt_isolate_l_add2), (* a+ sqrt(x)=d -> sqrt(x) = d-a *)
1.223 + Thm("sqrt_isolate_l_add3",num_str sqrt_isolate_l_add3), (* a+b*c/sqrt(x)=d->b*c/sqrt(x)=d-a *)
1.224 + Thm("sqrt_isolate_l_add4",num_str sqrt_isolate_l_add4), (* a+c/sqrt(x)=d -> c/sqrt(x) = d-a *)
1.225 + Thm("sqrt_isolate_l_add5",num_str sqrt_isolate_l_add5), (* a+b*c/f*sqrt(x)=d->b*c/f*sqrt(x)=d-a *)
1.226 + Thm("sqrt_isolate_l_add6",num_str sqrt_isolate_l_add6), (* a+c/f*sqrt(x)=d -> c/f*sqrt(x) = d-a *)
1.227 + (*Thm("sqrt_isolate_l_div",num_str sqrt_isolate_l_div),*) (* b*sqrt(x) = d sqrt(x) d/b *)
1.228 + Thm("sqrt_square_equation_left_1",num_str sqrt_square_equation_left_1),
1.229 + (* sqrt(x)=b -> x=b^2 *)
1.230 + Thm("sqrt_square_equation_left_2",num_str sqrt_square_equation_left_2),
1.231 + (* a*sqrt(x)=b -> a^2*x=b^2*)
1.232 + Thm("sqrt_square_equation_left_3",num_str sqrt_square_equation_left_3),
1.233 + (* c/sqrt(x)=b -> c^2/x=b^2 *)
1.234 + Thm("sqrt_square_equation_left_4",num_str sqrt_square_equation_left_4),
1.235 + (* c*d/sqrt(x)=b -> c^2*d^2/x=b^2 *)
1.236 + Thm("sqrt_square_equation_left_5",num_str sqrt_square_equation_left_5),
1.237 + (* c/d*sqrt(x)=b -> c^2/d^2x=b^2 *)
1.238 + Thm("sqrt_square_equation_left_6",num_str sqrt_square_equation_left_6)
1.239 + (* c*d/g*sqrt(x)=b -> c^2*d^2/g^2x=b^2 *)
1.240 + ],
1.241 + scr = Script ((term_of o the o (parse thy)) "empty_script")
1.242 + }:rls);
1.243 +ruleset' := overwritelthy thy (!ruleset',
1.244 + [("l_sqrt_isolate",l_sqrt_isolate)
1.245 + ]);
1.246 +
1.247 +(* -- right 28.8.02--*)
1.248 +(*isolate the bound variable in an sqrt right equation; 'bdv' is a meta-constant*)
1.249 + val r_sqrt_isolate = prep_rls(
1.250 + Rls {id = "r_sqrt_isolate", preconds = [],
1.251 + rew_ord = ("termlessI",termlessI),
1.252 + erls = RootEq_erls, srls = Erls, calc = [],
1.253 + (*asm_thm = [("sqrt_square_1",""),("sqrt_square_equation_right_1",""),
1.254 + ("sqrt_square_equation_right_2",""),("sqrt_square_equation_right_3",""),
1.255 + ("sqrt_square_equation_right_4",""),("sqrt_square_equation_right_5",""),
1.256 + ("sqrt_square_equation_right_6","")],*)
1.257 + rules = [
1.258 + Thm("sqrt_square_1",num_str sqrt_square_1), (* (sqrt a)^^^2 -> a *)
1.259 + Thm("sqrt_square_2",num_str sqrt_square_2), (* sqrt (a^^^2) -> a *)
1.260 + Thm("sqrt_times_root_1",num_str sqrt_times_root_1), (* sqrt a sqrt b -> sqrt(ab) *)
1.261 + Thm("sqrt_times_root_2",num_str sqrt_times_root_2), (* a sqrt b sqrt c -> a sqrt(bc) *)
1.262 + Thm("sqrt_isolate_r_add1",num_str sqrt_isolate_r_add1), (* a= d+e*sqrt(x) -> a-d=e*sqrt(x) *)
1.263 + Thm("sqrt_isolate_r_add2",num_str sqrt_isolate_r_add2), (* a= d+ sqrt(x) -> a-d= sqrt(x) *)
1.264 + Thm("sqrt_isolate_r_add3",num_str sqrt_isolate_r_add3), (* a=d+e*g/sqrt(x)->a-d=e*g/sqrt(x)*)
1.265 + Thm("sqrt_isolate_r_add4",num_str sqrt_isolate_r_add4), (* a= d+g/sqrt(x) -> a-d=g/sqrt(x) *)
1.266 + Thm("sqrt_isolate_r_add5",num_str sqrt_isolate_r_add5), (* a=d+e*g/h*sqrt(x)->a-d=e*g/h*sqrt(x)*)
1.267 + Thm("sqrt_isolate_r_add6",num_str sqrt_isolate_r_add6), (* a= d+g/h*sqrt(x) -> a-d=g/h*sqrt(x) *)
1.268 + (*Thm("sqrt_isolate_r_div",num_str sqrt_isolate_r_div),*) (* a=e*sqrt(x) -> a/e = sqrt(x) *)
1.269 + Thm("sqrt_square_equation_right_1",num_str sqrt_square_equation_right_1),
1.270 + (* a=sqrt(x) ->a^2=x *)
1.271 + Thm("sqrt_square_equation_right_2",num_str sqrt_square_equation_right_2),
1.272 + (* a=c*sqrt(x) ->a^2=c^2*x *)
1.273 + Thm("sqrt_square_equation_right_3",num_str sqrt_square_equation_right_3),
1.274 + (* a=c/sqrt(x) ->a^2=c^2/x *)
1.275 + Thm("sqrt_square_equation_right_4",num_str sqrt_square_equation_right_4),
1.276 + (* a=c*d/sqrt(x) ->a^2=c^2*d^2/x *)
1.277 + Thm("sqrt_square_equation_right_5",num_str sqrt_square_equation_right_5),
1.278 + (* a=c/e*sqrt(x) ->a^2=c^2/e^2x *)
1.279 + Thm("sqrt_square_equation_right_6",num_str sqrt_square_equation_right_6)
1.280 + (* a=c*d/g*sqrt(x) ->a^2=c^2*d^2/g^2*x *)
1.281 + ],
1.282 + scr = Script ((term_of o the o (parse thy)) "empty_script")
1.283 + }:rls);
1.284 +ruleset' := overwritelthy thy (!ruleset',
1.285 + [("r_sqrt_isolate",r_sqrt_isolate)
1.286 + ]);
1.287 +
1.288 +val rooteq_simplify = prep_rls(
1.289 + Rls {id = "rooteq_simplify",
1.290 + preconds = [], rew_ord = ("termlessI",termlessI),
1.291 + erls = RootEq_erls, srls = Erls, calc = [],
1.292 + (*asm_thm = [("sqrt_square_1","")],*)
1.293 + rules = [Thm ("real_assoc_1",num_str real_assoc_1), (* a+(b+c) = a+b+c *)
1.294 + Thm ("real_assoc_2",num_str real_assoc_2), (* a*(b*c) = a*b*c *)
1.295 + Calc ("op +",eval_binop "#add_"),
1.296 + Calc ("op -",eval_binop "#sub_"),
1.297 + Calc ("op *",eval_binop "#mult_"),
1.298 + Calc ("HOL.divide", eval_cancel "#divide_"),
1.299 + Calc ("Root.sqrt",eval_sqrt "#sqrt_"),
1.300 + Calc ("Atools.pow" ,eval_binop "#power_"),
1.301 + Thm("real_plus_binom_pow2",num_str real_plus_binom_pow2),
1.302 + Thm("real_minus_binom_pow2",num_str real_minus_binom_pow2),
1.303 + Thm("realpow_mul",num_str realpow_mul), (* (a * b)^n = a^n * b^n*)
1.304 + Thm("sqrt_times_root_1",num_str sqrt_times_root_1), (* sqrt b * sqrt c = sqrt(b*c) *)
1.305 + Thm("sqrt_times_root_2",num_str sqrt_times_root_2), (* a * sqrt a * sqrt b = a * sqrt(a*b) *)
1.306 + Thm("sqrt_square_2",num_str sqrt_square_2), (* sqrt (a^^^2) = a *)
1.307 + Thm("sqrt_square_1",num_str sqrt_square_1) (* sqrt a ^^^ 2 = a *)
1.308 + ],
1.309 + scr = Script ((term_of o the o (parse thy)) "empty_script")
1.310 + }:rls);
1.311 + ruleset' := overwritelthy thy (!ruleset',
1.312 + [("rooteq_simplify",rooteq_simplify)
1.313 + ]);
1.314 +
1.315 +(*-------------------------Problem-----------------------*)
1.316 +(*
1.317 +(get_pbt ["root","univariate","equation"]);
1.318 +show_ptyps();
1.319 +*)
1.320 +(* ---------root----------- *)
1.321 +store_pbt
1.322 + (prep_pbt RootEq.thy "pbl_equ_univ_root" [] e_pblID
1.323 + (["root","univariate","equation"],
1.324 + [("#Given" ,["equality e_","solveFor v_"]),
1.325 + ("#Where" ,["(lhs e_) is_rootTerm_in (v_::real) | \
1.326 + \(rhs e_) is_rootTerm_in (v_::real)"]),
1.327 + ("#Find" ,["solutions v_i_"])
1.328 + ],
1.329 + RootEq_prls, SOME "solve (e_::bool, v_)",
1.330 + []));
1.331 +(* ---------sqrt----------- *)
1.332 +store_pbt
1.333 + (prep_pbt RootEq.thy "pbl_equ_univ_root_sq" [] e_pblID
1.334 + (["sq","root","univariate","equation"],
1.335 + [("#Given" ,["equality e_","solveFor v_"]),
1.336 + ("#Where" ,["( ((lhs e_) is_sqrtTerm_in (v_::real)) &\
1.337 + \ ((lhs e_) is_normSqrtTerm_in (v_::real)) ) |\
1.338 + \( ((rhs e_) is_sqrtTerm_in (v_::real)) &\
1.339 + \ ((rhs e_) is_normSqrtTerm_in (v_::real)) )"]),
1.340 + ("#Find" ,["solutions v_i_"])
1.341 + ],
1.342 + RootEq_prls, SOME "solve (e_::bool, v_)",
1.343 + [["RootEq","solve_sq_root_equation"]]));
1.344 +(* ---------normalize----------- *)
1.345 +store_pbt
1.346 + (prep_pbt RootEq.thy "pbl_equ_univ_root_norm" [] e_pblID
1.347 + (["normalize","root","univariate","equation"],
1.348 + [("#Given" ,["equality e_","solveFor v_"]),
1.349 + ("#Where" ,["( ((lhs e_) is_sqrtTerm_in (v_::real)) &\
1.350 + \ Not((lhs e_) is_normSqrtTerm_in (v_::real))) | \
1.351 + \( ((rhs e_) is_sqrtTerm_in (v_::real)) &\
1.352 + \ Not((rhs e_) is_normSqrtTerm_in (v_::real)))"]),
1.353 + ("#Find" ,["solutions v_i_"])
1.354 + ],
1.355 + RootEq_prls, SOME "solve (e_::bool, v_)",
1.356 + [["RootEq","norm_sq_root_equation"]]));
1.357 +
1.358 +(*-------------------------methods-----------------------*)
1.359 +(* ---- root 20.8.02 ---*)
1.360 +store_met
1.361 + (prep_met RootEq.thy "met_rooteq" [] e_metID
1.362 + (["RootEq"],
1.363 + [],
1.364 + {rew_ord'="tless_true",rls'=Atools_erls,calc = [], srls = e_rls, prls=e_rls,
1.365 + crls=RootEq_crls, nrls=norm_Poly(*,
1.366 + asm_rls=[],asm_thm=[]*)}, "empty_script"));
1.367 +(*-- normalize 20.10.02 --*)
1.368 +store_met
1.369 + (prep_met RootEq.thy "met_rooteq_norm" [] e_metID
1.370 + (["RootEq","norm_sq_root_equation"],
1.371 + [("#Given" ,["equality e_","solveFor v_"]),
1.372 + ("#Where" ,["( ((lhs e_) is_sqrtTerm_in (v_::real)) &\
1.373 + \ Not((lhs e_) is_normSqrtTerm_in (v_::real))) | \
1.374 + \( ((rhs e_) is_sqrtTerm_in (v_::real)) &\
1.375 + \ Not((rhs e_) is_normSqrtTerm_in (v_::real)))"]),
1.376 + ("#Find" ,["solutions v_i_"])
1.377 + ],
1.378 + {rew_ord'="termlessI",
1.379 + rls'=RootEq_erls,
1.380 + srls=e_rls,
1.381 + prls=RootEq_prls,
1.382 + calc=[],
1.383 + crls=RootEq_crls, nrls=norm_Poly(*,
1.384 + asm_rls=[],
1.385 + asm_thm=[("sqrt_square_1","")]*)},
1.386 + "Script Norm_sq_root_equation (e_::bool) (v_::real) = \
1.387 + \(let e_ = ((Repeat(Try (Rewrite makex1_x False))) @@ \
1.388 + \ (Try (Repeat (Rewrite_Set expand_rootbinoms False))) @@ \
1.389 + \ (Try (Rewrite_Set rooteq_simplify True)) @@ \
1.390 + \ (Try (Repeat (Rewrite_Set make_rooteq False))) @@ \
1.391 + \ (Try (Rewrite_Set rooteq_simplify True))) e_ \
1.392 + \ in ((SubProblem (RootEq_,[univariate,equation], \
1.393 + \ [no_met]) [bool_ e_, real_ v_])))"
1.394 + ));
1.395 +
1.396 +store_met
1.397 + (prep_met RootEq.thy "met_rooteq_sq" [] e_metID
1.398 + (["RootEq","solve_sq_root_equation"],
1.399 + [("#Given" ,["equality e_","solveFor v_"]),
1.400 + ("#Where" ,["( ((lhs e_) is_sqrtTerm_in (v_::real)) &\
1.401 + \ ((lhs e_) is_normSqrtTerm_in (v_::real)) ) |\
1.402 + \( ((rhs e_) is_sqrtTerm_in (v_::real)) &\
1.403 + \ ((rhs e_) is_normSqrtTerm_in (v_::real)) )"]),
1.404 + ("#Find" ,["solutions v_i_"])
1.405 + ],
1.406 + {rew_ord'="termlessI",
1.407 + rls'=RootEq_erls,
1.408 + srls = rooteq_srls,
1.409 + prls = RootEq_prls,
1.410 + calc = [],
1.411 + crls=RootEq_crls, nrls=norm_Poly(*,
1.412 + asm_rls = [],
1.413 + asm_thm = [("sqrt_square_1",""),("sqrt_square_equation_left_1",""),
1.414 + ("sqrt_square_equation_left_2",""),("sqrt_square_equation_left_3",""),
1.415 + ("sqrt_square_equation_left_4",""),("sqrt_square_equation_left_5",""),
1.416 + ("sqrt_square_equation_left_6",""),("sqrt_square_equation_right_1",""),
1.417 + ("sqrt_square_equation_right_2",""),("sqrt_square_equation_right_3",""),
1.418 + ("sqrt_square_equation_right_4",""),("sqrt_square_equation_right_5",""),
1.419 + ("sqrt_square_equation_right_6","")]*)},
1.420 +"Script Solve_sq_root_equation (e_::bool) (v_::real) = \
1.421 +\(let e_ = \
1.422 +\ ((Try (Rewrite_Set_Inst [(bdv,v_::real)] sqrt_isolate True)) @@ \
1.423 +\ (Try (Rewrite_Set rooteq_simplify True)) @@ \
1.424 +\ (Try (Repeat (Rewrite_Set expand_rootbinoms False))) @@ \
1.425 +\ (Try (Repeat (Rewrite_Set make_rooteq False))) @@ \
1.426 +\ (Try (Rewrite_Set rooteq_simplify True))) e_;\
1.427 +\ (L_::bool list) = \
1.428 +\ (if (((lhs e_) is_sqrtTerm_in v_) | ((rhs e_) is_sqrtTerm_in v_))\
1.429 +\ then (SubProblem (RootEq_,[normalize,root,univariate,equation], \
1.430 +\ [no_met]) [bool_ e_, real_ v_]) \
1.431 +\ else (SubProblem (RootEq_,[univariate,equation], \
1.432 +\ [no_met]) [bool_ e_, real_ v_])) \
1.433 +\ in Check_elementwise L_ {(v_::real). Assumptions})"
1.434 + ));
1.435 +
1.436 +(*-- right 28.08.02 --*)
1.437 +store_met
1.438 + (prep_met RootEq.thy "met_rooteq_sq_right" [] e_metID
1.439 + (["RootEq","solve_right_sq_root_equation"],
1.440 + [("#Given" ,["equality e_","solveFor v_"]),
1.441 + ("#Where" ,["(rhs e_) is_sqrtTerm_in v_"]),
1.442 + ("#Find" ,["solutions v_i_"])
1.443 + ],
1.444 + {rew_ord'="termlessI",
1.445 + rls'=RootEq_erls,
1.446 + srls=e_rls,
1.447 + prls=RootEq_prls,
1.448 + calc=[],
1.449 + crls=RootEq_crls, nrls=norm_Poly(*,
1.450 + asm_rls=[],
1.451 + asm_thm=[("sqrt_square_1",""),("sqrt_square_1",""),("sqrt_square_equation_right_1",""),
1.452 + ("sqrt_square_equation_right_2",""),("sqrt_square_equation_right_3",""),
1.453 + ("sqrt_square_equation_right_4",""),("sqrt_square_equation_right_5",""),
1.454 + ("sqrt_square_equation_right_6","")]*)},
1.455 + "Script Solve_right_sq_root_equation (e_::bool) (v_::real) = \
1.456 + \(let e_ = ((Try (Rewrite_Set_Inst [(bdv,v_::real)] r_sqrt_isolate False)) @@ \
1.457 + \ (Try (Rewrite_Set rooteq_simplify False)) @@ \
1.458 + \ (Try (Repeat (Rewrite_Set expand_rootbinoms False))) @@ \
1.459 + \ (Try (Repeat (Rewrite_Set make_rooteq False))) @@ \
1.460 + \ (Try (Rewrite_Set rooteq_simplify False))) e_\
1.461 + \ in if ((rhs e_) is_sqrtTerm_in v_) \
1.462 + \ then (SubProblem (RootEq_,[normalize,root,univariate,equation], \
1.463 + \ [no_met]) [bool_ e_, real_ v_]) \
1.464 + \ else ((SubProblem (RootEq_,[univariate,equation], \
1.465 + \ [no_met]) [bool_ e_, real_ v_])))"
1.466 + ));
1.467 +
1.468 +(*-- left 28.08.02 --*)
1.469 +store_met
1.470 + (prep_met RootEq.thy "met_rooteq_sq_left" [] e_metID
1.471 + (["RootEq","solve_left_sq_root_equation"],
1.472 + [("#Given" ,["equality e_","solveFor v_"]),
1.473 + ("#Where" ,["(lhs e_) is_sqrtTerm_in v_"]),
1.474 + ("#Find" ,["solutions v_i_"])
1.475 + ],
1.476 + {rew_ord'="termlessI",
1.477 + rls'=RootEq_erls,
1.478 + srls=e_rls,
1.479 + prls=RootEq_prls,
1.480 + calc=[],
1.481 + crls=RootEq_crls, nrls=norm_Poly(*,
1.482 + asm_rls=[],
1.483 + asm_thm=[("sqrt_square_1",""),("sqrt_square_equation_left_1",""),
1.484 + ("sqrt_square_equation_left_2",""),("sqrt_square_equation_left_3",""),
1.485 + ("sqrt_square_equation_left_4",""),("sqrt_square_equation_left_5",""),
1.486 + ("sqrt_square_equation_left_6","")]*)},
1.487 + "Script Solve_left_sq_root_equation (e_::bool) (v_::real) = \
1.488 + \(let e_ = ((Try (Rewrite_Set_Inst [(bdv,v_::real)] l_sqrt_isolate False)) @@ \
1.489 + \ (Try (Rewrite_Set rooteq_simplify False)) @@ \
1.490 + \ (Try (Repeat (Rewrite_Set expand_rootbinoms False))) @@ \
1.491 + \ (Try (Repeat (Rewrite_Set make_rooteq False))) @@ \
1.492 + \ (Try (Rewrite_Set rooteq_simplify False))) e_\
1.493 + \ in if ((lhs e_) is_sqrtTerm_in v_) \
1.494 + \ then (SubProblem (RootEq_,[normalize,root,univariate,equation], \
1.495 + \ [no_met]) [bool_ e_, real_ v_]) \
1.496 + \ else ((SubProblem (RootEq_,[univariate,equation], \
1.497 + \ [no_met]) [bool_ e_, real_ v_])))"
1.498 + ));
1.499 +
1.500 +calclist':= overwritel (!calclist',
1.501 + [("is_rootTerm_in", ("RootEq.is'_rootTerm'_in",
1.502 + eval_is_rootTerm_in"")),
1.503 + ("is_sqrtTerm_in", ("RootEq.is'_sqrtTerm'_in",
1.504 + eval_is_sqrtTerm_in"")),
1.505 + ("is_normSqrtTerm_in", ("RootEq.is_normSqrtTerm_in",
1.506 + eval_is_normSqrtTerm_in""))
1.507 + ]);(*("", ("", "")),*)
1.508 +"******* RootEq.ML end *******";