neuper@37906
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(* equational systems, minimal -- for use in Biegelinie
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author: Walther Neuper
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050826,
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(c) due to copyright terms
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*)
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theory EqSystem imports Integrate Rational Root begin
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consts
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occur'_exactly'_in ::
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"[real list, real list, 'a] => bool" ("_ from _ occur'_exactly'_in _")
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(*descriptions in the related problems*)
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solveForVars :: "real list => toreall"
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solution :: "bool list => toreall"
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(*the CAS-command, eg. "solveSystem [x+y=1,y=2] [x,y]"*)
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solveSystem :: "[bool list, real list] => bool list"
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(*Script-names*)
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SolveSystemScript :: "[bool list, real list, bool list]
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=> bool list"
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("((Script SolveSystemScript (_ _ =))// (_))" 9)
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axioms
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(*stated as axioms, todo: prove as theorems
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'bdv' is a constant handled on the meta-level
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specifically as a 'bound variable' *)
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commute_0_equality: "(0 = a) = (a = 0)"
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(*WN0510 see simliar rules 'isolate_' 'separate_' (by RL)
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[bdv_1,bdv_2,bdv_3,bdv_4] work also for 2 and 3 bdvs, ugly !*)
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separate_bdvs_add:
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"[| [] from [bdv_1,bdv_2,bdv_3,bdv_4] occur_exactly_in a |]
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==> (a + b = c) = (b = c + -1*a)"
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separate_bdvs0:
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"[| some_of [bdv_1,bdv_2,bdv_3,bdv_4] occur_in b; Not (b=!=0) |]
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==> (a = b) = (a + -1*b = 0)"
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separate_bdvs_add1:
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"[| some_of [bdv_1,bdv_2,bdv_3,bdv_4] occur_in c |]
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==> (a = b + c) = (a + -1*c = b)"
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separate_bdvs_add2:
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"[| Not (some_of [bdv_1,bdv_2,bdv_3,bdv_4] occur_in a) |]
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==> (a + b = c) = (b = -1*a + c)"
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separate_bdvs_mult:
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"[| [] from [bdv_1,bdv_2,bdv_3,bdv_4] occur_exactly_in a; Not (a=!=0) |]
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==>(a * b = c) = (b = c / a)"
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(*requires rew_ord for termination, eg. ord_simplify_Integral;
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works for lists of any length, interestingly !?!*)
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order_system_NxN: "[a,b] = [b,a]"
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ML {*
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val thy = @{theory};
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(** eval functions **)
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(*certain variables of a given list occur _all_ in a term
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args: all: ..variables, which are under consideration (eg. the bound vars)
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vs: variables which must be in t,
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and none of the others in all must be in t
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t: the term under consideration
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*)
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fun occur_exactly_in vs all t =
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let fun occurs_in' a b = occurs_in b a
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in foldl and_ (true, map (occurs_in' t) vs)
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andalso not (foldl or_ (false, map (occurs_in' t)
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(subtract op = vs all)))
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end;
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(*("occur_exactly_in", ("EqSystem.occur'_exactly'_in",
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eval_occur_exactly_in "#eval_occur_exactly_in_"))*)
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fun eval_occur_exactly_in _ "EqSystem.occur'_exactly'_in"
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(p as (Const ("EqSystem.occur'_exactly'_in",_)
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$ vs $ all $ t)) _ =
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if occur_exactly_in (isalist2list vs) (isalist2list all) t
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then SOME ((term2str p) ^ " = True",
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Trueprop $ (mk_equality (p, HOLogic.true_const)))
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else SOME ((term2str p) ^ " = False",
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Trueprop $ (mk_equality (p, HOLogic.false_const)))
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| eval_occur_exactly_in _ _ _ _ = NONE;
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calclist':=
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overwritel (!calclist',
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[("occur_exactly_in",
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("EqSystem.occur'_exactly'_in",
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eval_occur_exactly_in "#eval_occur_exactly_in_"))
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]);
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(** rewrite order 'ord_simplify_System' **)
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(* order wrt. several linear (i.e. without exponents) variables "c","c_2",..
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which leaves the monomials containing c, c_2,... at the end of an Integral
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and puts the c, c_2,... rightmost within a monomial.
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WN050906 this is a quick and dirty adaption of ord_make_polynomial_in,
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which was most adequate, because it uses size_of_term*)
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(**)
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local (*. for simplify_System .*)
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(**)
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open Term; (* for type order = EQUAL | LESS | GREATER *)
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fun pr_ord EQUAL = "EQUAL"
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| pr_ord LESS = "LESS"
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| pr_ord GREATER = "GREATER";
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fun dest_hd' (Const (a, T)) = (((a, 0), T), 0)
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| dest_hd' (Free (ccc, T)) =
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(case Symbol.explode ccc of
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"c"::[] => ((("|||||||||||||||||||||", 0), T), 1)(*greatest string WN*)
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| "c"::"_"::_ => ((("|||||||||||||||||||||", 0), T), 1)
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| _ => (((ccc, 0), T), 1))
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| dest_hd' (Var v) = (v, 2)
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| dest_hd' (Bound i) = ((("", i), dummyT), 3)
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| dest_hd' (Abs (_, T, _)) = ((("", 0), T), 4);
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fun size_of_term' (Free (ccc, _)) =
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(case Symbol.explode ccc of (*WN0510 hack for the bound variables*)
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"c"::[] => 1000
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| "c"::"_"::is => 1000 * ((str2int o implode) is)
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| _ => 1)
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| size_of_term' (Abs (_,_,body)) = 1 + size_of_term' body
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| size_of_term' (f$t) = size_of_term' f + size_of_term' t
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| size_of_term' _ = 1;
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fun term_ord' pr thy (Abs (_, T, t), Abs(_, U, u)) = (* ~ term.ML *)
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(case term_ord' pr thy (t, u) of EQUAL => Term_Ord.typ_ord (T, U) | ord => ord)
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| term_ord' pr thy (t, u) =
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(if pr then
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let
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val (f, ts) = strip_comb t and (g, us) = strip_comb u;
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val _ = tracing ("t= f@ts= \"" ^
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(Print_Mode.setmp [] (Syntax.string_of_term (thy2ctxt thy)) f) ^
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"\" @ \"[" ^
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(commas (map (Print_Mode.setmp [] (Syntax.string_of_term
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(thy2ctxt thy))) ts)) ^ "]\"");
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val _ = tracing ("u= g@us= \"" ^
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(Print_Mode.setmp [] (Syntax.string_of_term (thy2ctxt thy)) g) ^
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"\" @ \"[" ^
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(commas (map (Print_Mode.setmp [] (Syntax.string_of_term
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(thy2ctxt thy))) us)) ^ "]\"");
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val _ = tracing ("size_of_term(t,u)= (" ^
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(string_of_int (size_of_term' t)) ^ ", " ^
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(string_of_int (size_of_term' u)) ^ ")");
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val _ = tracing ("hd_ord(f,g) = " ^ ((pr_ord o hd_ord) (f,g)));
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val _ = tracing ("terms_ord (ts,us) = " ^
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((pr_ord o terms_ord str false) (ts,us)));
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val _=tracing("-------");
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in () end
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else ();
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case int_ord (size_of_term' t, size_of_term' u) of
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EQUAL =>
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let val (f, ts) = strip_comb t and (g, us) = strip_comb u in
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(case hd_ord (f, g) of EQUAL => (terms_ord str pr) (ts, us)
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| ord => ord)
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end
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| ord => ord)
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and hd_ord (f, g) = (* ~ term.ML *)
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prod_ord (prod_ord Term_Ord.indexname_ord Term_Ord.typ_ord) int_ord (dest_hd' f,
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dest_hd' g)
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and terms_ord str pr (ts, us) =
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list_ord (term_ord' pr (assoc_thy "Isac"))(ts, us);
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(**)
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in
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(**)
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(*WN0510 for preliminary use in eval_order_system, see case-study mat-eng.tex
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fun ord_simplify_System_rev (pr:bool) thy subst tu =
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(term_ord' pr thy (Library.swap tu) = LESS);*)
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(*for the rls's*)
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fun ord_simplify_System (pr:bool) thy subst tu =
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(term_ord' pr thy tu = LESS);
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(**)
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end;
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(**)
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rew_ord' := overwritel (!rew_ord',
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[("ord_simplify_System", ord_simplify_System false thy)
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]);
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*}
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ML {*
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(** rulesets **)
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(*.adapted from 'order_add_mult_in' by just replacing the rew_ord.*)
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val order_add_mult_System =
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Rls{id = "order_add_mult_System", preconds = [],
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rew_ord = ("ord_simplify_System",
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ord_simplify_System false (Thy_Info.get_theory "Integrate")),
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erls = e_rls,srls = Erls, calc = [],
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rules = [Thm ("real_mult_commute",num_str @{thm real_mult_commute}),
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(* z * w = w * z *)
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Thm ("real_mult_left_commute",num_str @{thm real_mult_left_commute}),
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(*z1.0 * (z2.0 * z3.0) = z2.0 * (z1.0 * z3.0)*)
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Thm ("real_mult_assoc",num_str @{thm real_mult_assoc}),
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(*z1.0 * z2.0 * z3.0 = z1.0 * (z2.0 * z3.0)*)
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Thm ("add_commute",num_str @{thm add_commute}),
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(*z + w = w + z*)
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Thm ("add_left_commute",num_str @{thm add_left_commute}),
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(*x + (y + z) = y + (x + z)*)
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Thm ("add_assoc",num_str @{thm add_assoc})
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(*z1.0 + z2.0 + z3.0 = z1.0 + (z2.0 + z3.0)*)
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],
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scr = EmptyScr}:rls;
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*}
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ML {*
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(*.adapted from 'norm_Rational' by
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#1 using 'ord_simplify_System' in 'order_add_mult_System'
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#2 NOT using common_nominator_p .*)
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val norm_System_noadd_fractions =
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Rls {id = "norm_System_noadd_fractions", preconds = [],
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rew_ord = ("dummy_ord",dummy_ord),
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erls = norm_rat_erls, srls = Erls, calc = [],
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rules = [(*sequence given by operator precedence*)
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Rls_ discard_minus,
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Rls_ powers,
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Rls_ rat_mult_divide,
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Rls_ expand,
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Rls_ reduce_0_1_2,
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Rls_ (*order_add_mult #1*) order_add_mult_System,
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Rls_ collect_numerals,
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(*Rls_ add_fractions_p, #2*)
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Rls_ cancel_p
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],
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scr = Script ((term_of o the o (parse thy))
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"empty_script")
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}:rls;
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*}
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ML {*
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(*.adapted from 'norm_Rational' by
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*1* using 'ord_simplify_System' in 'order_add_mult_System'.*)
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val norm_System =
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Rls {id = "norm_System", preconds = [],
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rew_ord = ("dummy_ord",dummy_ord),
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erls = norm_rat_erls, srls = Erls, calc = [],
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rules = [(*sequence given by operator precedence*)
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Rls_ discard_minus,
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Rls_ powers,
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Rls_ rat_mult_divide,
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Rls_ expand,
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Rls_ reduce_0_1_2,
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Rls_ (*order_add_mult *1*) order_add_mult_System,
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Rls_ collect_numerals,
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Rls_ add_fractions_p,
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Rls_ cancel_p
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],
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scr = Script ((term_of o the o (parse thy))
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"empty_script")
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}:rls;
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*}
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ML {*
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(*.simplify an equational system BEFORE solving it such that parentheses are
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( ((u0*v0)*w0) + ( ((u1*v1)*w1) * c + ... +((u4*v4)*w4) * c_4 ) )
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ATTENTION: works ONLY for bound variables c, c_1, c_2, c_3, c_4 :ATTENTION
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This is a copy from 'make_ratpoly_in' with respective reductions:
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*0* expand the term, ie. distribute * and / over +
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*1* ord_simplify_System instead of termlessI
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*2* no add_fractions_p (= common_nominator_p_rls !)
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|
263 |
*3* discard_parentheses only for (.*(.*.))
|
neuper@37954
|
264 |
analoguous to simplify_Integral .*)
|
neuper@37954
|
265 |
val simplify_System_parenthesized =
|
neuper@37954
|
266 |
Seq {id = "simplify_System_parenthesized", preconds = []:term list,
|
neuper@37954
|
267 |
rew_ord = ("dummy_ord", dummy_ord),
|
neuper@37954
|
268 |
erls = Atools_erls, srls = Erls, calc = [],
|
neuper@37965
|
269 |
rules = [Thm ("left_distrib",num_str @{thm left_distrib}),
|
neuper@37954
|
270 |
(*"(?z1.0 + ?z2.0) * ?w = ?z1.0 * ?w + ?z2.0 * ?w"*)
|
neuper@37991
|
271 |
Thm ("add_divide_distrib",num_str @{thm add_divide_distrib}),
|
neuper@37954
|
272 |
(*"(?x + ?y) / ?z = ?x / ?z + ?y / ?z"*)
|
neuper@37954
|
273 |
(*^^^^^ *0* ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^*)
|
neuper@37954
|
274 |
Rls_ norm_Rational_noadd_fractions(**2**),
|
neuper@37954
|
275 |
Rls_ (*order_add_mult_in*) norm_System_noadd_fractions (**1**),
|
neuper@37969
|
276 |
Thm ("sym_real_mult_assoc",
|
neuper@37969
|
277 |
num_str (@{thm real_mult_assoc} RS @{thm sym}))
|
neuper@37954
|
278 |
(*Rls_ discard_parentheses *3**),
|
neuper@37954
|
279 |
Rls_ collect_bdv, (*from make_polynomial_in WN051031 welldone?*)
|
neuper@37954
|
280 |
Rls_ separate_bdv2,
|
neuper@38014
|
281 |
Calc ("Rings.inverse_class.divide" ,eval_cancel "#divide_e")
|
neuper@37954
|
282 |
],
|
neuper@37954
|
283 |
scr = EmptyScr}:rls;
|
neuper@37997
|
284 |
*}
|
neuper@37997
|
285 |
ML {*
|
neuper@37954
|
286 |
(*.simplify an equational system AFTER solving it;
|
neuper@37954
|
287 |
This is a copy of 'make_ratpoly_in' with the differences
|
neuper@37954
|
288 |
*1* ord_simplify_System instead of termlessI .*)
|
neuper@37954
|
289 |
(*TODO.WN051031 ^^^^^^^^^^ should be in EACH rls contained *)
|
neuper@37954
|
290 |
val simplify_System =
|
neuper@37954
|
291 |
Seq {id = "simplify_System", preconds = []:term list,
|
neuper@37954
|
292 |
rew_ord = ("dummy_ord", dummy_ord),
|
neuper@37954
|
293 |
erls = Atools_erls, srls = Erls, calc = [],
|
neuper@37954
|
294 |
rules = [Rls_ norm_Rational,
|
neuper@37954
|
295 |
Rls_ (*order_add_mult_in*) norm_System (**1**),
|
neuper@37954
|
296 |
Rls_ discard_parentheses,
|
neuper@37954
|
297 |
Rls_ collect_bdv, (*from make_polynomial_in WN051031 welldone?*)
|
neuper@37954
|
298 |
Rls_ separate_bdv2,
|
neuper@38014
|
299 |
Calc ("Rings.inverse_class.divide" ,eval_cancel "#divide_e")
|
neuper@37954
|
300 |
],
|
neuper@37954
|
301 |
scr = EmptyScr}:rls;
|
neuper@37906
|
302 |
(*
|
neuper@37954
|
303 |
val simplify_System =
|
neuper@37954
|
304 |
append_rls "simplify_System" simplify_System_parenthesized
|
neuper@37974
|
305 |
[Thm ("sym_add_assoc",
|
neuper@37974
|
306 |
num_str (@{thm add_assoc} RS @{thm sym}))];
|
neuper@37954
|
307 |
*)
|
neuper@37997
|
308 |
*}
|
neuper@37997
|
309 |
ML {*
|
neuper@37954
|
310 |
val isolate_bdvs =
|
neuper@37954
|
311 |
Rls {id="isolate_bdvs", preconds = [],
|
neuper@37954
|
312 |
rew_ord = ("e_rew_ord", e_rew_ord),
|
neuper@37954
|
313 |
erls = append_rls "erls_isolate_bdvs" e_rls
|
neuper@37954
|
314 |
[(Calc ("EqSystem.occur'_exactly'_in",
|
neuper@37954
|
315 |
eval_occur_exactly_in
|
neuper@37954
|
316 |
"#eval_occur_exactly_in_"))
|
neuper@37954
|
317 |
],
|
neuper@37954
|
318 |
srls = Erls, calc = [],
|
neuper@37997
|
319 |
rules =
|
neuper@37997
|
320 |
[Thm ("commute_0_equality", num_str @{thm commute_0_equality}),
|
neuper@37997
|
321 |
Thm ("separate_bdvs_add", num_str @{thm separate_bdvs_add}),
|
neuper@37997
|
322 |
Thm ("separate_bdvs_mult", num_str @{thm separate_bdvs_mult})],
|
neuper@37954
|
323 |
scr = EmptyScr};
|
neuper@37997
|
324 |
*}
|
neuper@37997
|
325 |
ML {*
|
neuper@37954
|
326 |
val isolate_bdvs_4x4 =
|
neuper@37954
|
327 |
Rls {id="isolate_bdvs_4x4", preconds = [],
|
neuper@37954
|
328 |
rew_ord = ("e_rew_ord", e_rew_ord),
|
neuper@37954
|
329 |
erls = append_rls
|
neuper@37954
|
330 |
"erls_isolate_bdvs_4x4" e_rls
|
neuper@37954
|
331 |
[Calc ("EqSystem.occur'_exactly'_in",
|
neuper@37954
|
332 |
eval_occur_exactly_in "#eval_occur_exactly_in_"),
|
neuper@37954
|
333 |
Calc ("Atools.ident",eval_ident "#ident_"),
|
neuper@37954
|
334 |
Calc ("Atools.some'_occur'_in",
|
neuper@37954
|
335 |
eval_some_occur_in "#some_occur_in_"),
|
neuper@37969
|
336 |
Thm ("not_true",num_str @{thm not_true}),
|
neuper@37969
|
337 |
Thm ("not_false",num_str @{thm not_false})
|
neuper@37954
|
338 |
],
|
neuper@37954
|
339 |
srls = Erls, calc = [],
|
neuper@37997
|
340 |
rules = [Thm ("commute_0_equality", num_str @{thm commute_0_equality}),
|
neuper@37969
|
341 |
Thm ("separate_bdvs0", num_str @{thm separate_bdvs0}),
|
neuper@37969
|
342 |
Thm ("separate_bdvs_add1", num_str @{thm separate_bdvs_add1}),
|
neuper@37969
|
343 |
Thm ("separate_bdvs_add1", num_str @{thm separate_bdvs_add2}),
|
neuper@37969
|
344 |
Thm ("separate_bdvs_mult", num_str @{thm separate_bdvs_mult})
|
neuper@37969
|
345 |
], scr = EmptyScr};
|
neuper@37954
|
346 |
|
neuper@37997
|
347 |
*}
|
neuper@37997
|
348 |
ML {*
|
neuper@37997
|
349 |
|
neuper@37954
|
350 |
(*.order the equations in a system such, that a triangular system (if any)
|
neuper@37954
|
351 |
appears as [..c_4 = .., ..., ..., ..c_1 + ..c_2 + ..c_3 ..c_4 = ..].*)
|
neuper@37954
|
352 |
val order_system =
|
neuper@37954
|
353 |
Rls {id="order_system", preconds = [],
|
neuper@37954
|
354 |
rew_ord = ("ord_simplify_System",
|
neuper@37954
|
355 |
ord_simplify_System false thy),
|
neuper@37954
|
356 |
erls = Erls, srls = Erls, calc = [],
|
neuper@37969
|
357 |
rules = [Thm ("order_system_NxN", num_str @{thm order_system_NxN})
|
neuper@37954
|
358 |
],
|
neuper@37954
|
359 |
scr = EmptyScr};
|
neuper@37954
|
360 |
|
neuper@37954
|
361 |
val prls_triangular =
|
neuper@37954
|
362 |
Rls {id="prls_triangular", preconds = [],
|
neuper@37954
|
363 |
rew_ord = ("e_rew_ord", e_rew_ord),
|
neuper@37954
|
364 |
erls = Rls {id="erls_prls_triangular", preconds = [],
|
neuper@37954
|
365 |
rew_ord = ("e_rew_ord", e_rew_ord),
|
neuper@37954
|
366 |
erls = Erls, srls = Erls, calc = [],
|
neuper@37997
|
367 |
rules = [(*for precond NTH_CONS ...*)
|
neuper@38045
|
368 |
Calc ("Orderings.ord_class.less",eval_equ "#less_"),
|
neuper@38014
|
369 |
Calc ("Groups.plus_class.plus", eval_binop "#add_")
|
neuper@37954
|
370 |
(*immediately repeated rewrite pushes
|
neuper@37954
|
371 |
'+' into precondition !*)
|
neuper@37954
|
372 |
],
|
neuper@37954
|
373 |
scr = EmptyScr},
|
neuper@37954
|
374 |
srls = Erls, calc = [],
|
neuper@37997
|
375 |
rules = [Thm ("NTH_CONS",num_str @{thm NTH_CONS}),
|
neuper@38014
|
376 |
Calc ("Groups.plus_class.plus", eval_binop "#add_"),
|
neuper@37997
|
377 |
Thm ("NTH_NIL",num_str @{thm NTH_NIL}),
|
neuper@37969
|
378 |
Thm ("tl_Cons",num_str @{thm tl_Cons}),
|
neuper@37969
|
379 |
Thm ("tl_Nil",num_str @{thm tl_Nil}),
|
neuper@37954
|
380 |
Calc ("EqSystem.occur'_exactly'_in",
|
neuper@37954
|
381 |
eval_occur_exactly_in
|
neuper@37954
|
382 |
"#eval_occur_exactly_in_")
|
neuper@37954
|
383 |
],
|
neuper@37954
|
384 |
scr = EmptyScr};
|
neuper@37997
|
385 |
*}
|
neuper@37997
|
386 |
ML {*
|
neuper@37954
|
387 |
|
neuper@37954
|
388 |
(*WN060914 quickly created for 4x4;
|
neuper@37954
|
389 |
more similarity to prls_triangular desirable*)
|
neuper@37954
|
390 |
val prls_triangular4 =
|
neuper@37954
|
391 |
Rls {id="prls_triangular4", preconds = [],
|
neuper@37954
|
392 |
rew_ord = ("e_rew_ord", e_rew_ord),
|
neuper@37954
|
393 |
erls = Rls {id="erls_prls_triangular4", preconds = [],
|
neuper@37954
|
394 |
rew_ord = ("e_rew_ord", e_rew_ord),
|
neuper@37954
|
395 |
erls = Erls, srls = Erls, calc = [],
|
neuper@37997
|
396 |
rules = [(*for precond NTH_CONS ...*)
|
neuper@38045
|
397 |
Calc ("Orderings.ord_class.less",eval_equ "#less_"),
|
neuper@38014
|
398 |
Calc ("Groups.plus_class.plus", eval_binop "#add_")
|
neuper@37954
|
399 |
(*immediately repeated rewrite pushes
|
neuper@37954
|
400 |
'+' into precondition !*)
|
neuper@37954
|
401 |
],
|
neuper@37954
|
402 |
scr = EmptyScr},
|
neuper@37954
|
403 |
srls = Erls, calc = [],
|
neuper@37997
|
404 |
rules = [Thm ("NTH_CONS",num_str @{thm NTH_CONS}),
|
neuper@38014
|
405 |
Calc ("Groups.plus_class.plus", eval_binop "#add_"),
|
neuper@37997
|
406 |
Thm ("NTH_NIL",num_str @{thm NTH_NIL}),
|
neuper@37969
|
407 |
Thm ("tl_Cons",num_str @{thm tl_Cons}),
|
neuper@37969
|
408 |
Thm ("tl_Nil",num_str @{thm tl_Nil}),
|
neuper@37954
|
409 |
Calc ("EqSystem.occur'_exactly'_in",
|
neuper@37954
|
410 |
eval_occur_exactly_in
|
neuper@37954
|
411 |
"#eval_occur_exactly_in_")
|
neuper@37954
|
412 |
],
|
neuper@37954
|
413 |
scr = EmptyScr};
|
neuper@37997
|
414 |
*}
|
neuper@37997
|
415 |
ML {*
|
neuper@37954
|
416 |
|
neuper@37954
|
417 |
ruleset' :=
|
neuper@37967
|
418 |
overwritelthy @{theory}
|
neuper@37954
|
419 |
(!ruleset',
|
neuper@37954
|
420 |
[("simplify_System_parenthesized", prep_rls simplify_System_parenthesized),
|
neuper@37954
|
421 |
("simplify_System", prep_rls simplify_System),
|
neuper@37954
|
422 |
("isolate_bdvs", prep_rls isolate_bdvs),
|
neuper@37954
|
423 |
("isolate_bdvs_4x4", prep_rls isolate_bdvs_4x4),
|
neuper@37954
|
424 |
("order_system", prep_rls order_system),
|
neuper@37954
|
425 |
("order_add_mult_System", prep_rls order_add_mult_System),
|
neuper@37954
|
426 |
("norm_System_noadd_fractions", prep_rls norm_System_noadd_fractions),
|
neuper@37954
|
427 |
("norm_System", prep_rls norm_System)
|
neuper@37954
|
428 |
]);
|
neuper@37997
|
429 |
*}
|
neuper@37997
|
430 |
ML {*
|
neuper@37954
|
431 |
|
neuper@37954
|
432 |
|
neuper@37954
|
433 |
(** problems **)
|
neuper@37954
|
434 |
|
neuper@37954
|
435 |
store_pbt
|
neuper@37972
|
436 |
(prep_pbt thy "pbl_equsys" [] e_pblID
|
neuper@37954
|
437 |
(["system"],
|
neuper@37997
|
438 |
[("#Given" ,["equalities e_s", "solveForVars v_s"]),
|
neuper@37997
|
439 |
("#Find" ,["solution ss'''"](*''' is copy-named*))
|
neuper@37954
|
440 |
],
|
neuper@37954
|
441 |
append_rls "e_rls" e_rls [(*for preds in where_*)],
|
neuper@37997
|
442 |
SOME "solveSystem e_s v_s",
|
neuper@37954
|
443 |
[]));
|
neuper@37954
|
444 |
store_pbt
|
neuper@37972
|
445 |
(prep_pbt thy "pbl_equsys_lin" [] e_pblID
|
neuper@37954
|
446 |
(["linear", "system"],
|
neuper@37997
|
447 |
[("#Given" ,["equalities e_s", "solveForVars v_s"]),
|
neuper@37954
|
448 |
(*TODO.WN050929 check linearity*)
|
neuper@37997
|
449 |
("#Find" ,["solution ss'''"])
|
neuper@37954
|
450 |
],
|
neuper@37954
|
451 |
append_rls "e_rls" e_rls [(*for preds in where_*)],
|
neuper@37997
|
452 |
SOME "solveSystem e_s v_s",
|
neuper@37954
|
453 |
[]));
|
neuper@37954
|
454 |
store_pbt
|
neuper@37972
|
455 |
(prep_pbt thy "pbl_equsys_lin_2x2" [] e_pblID
|
neuper@37954
|
456 |
(["2x2", "linear", "system"],
|
neuper@37954
|
457 |
(*~~~~~~~~~~~~~~~~~~~~~~~~~*)
|
neuper@37997
|
458 |
[("#Given" ,["equalities e_s", "solveForVars v_s"]),
|
neuper@37997
|
459 |
("#Where" ,["LENGTH (e_s:: bool list) = 2", "LENGTH v_s = 2"]),
|
neuper@37997
|
460 |
("#Find" ,["solution ss'''"])
|
neuper@37954
|
461 |
],
|
neuper@37954
|
462 |
append_rls "prls_2x2_linear_system" e_rls
|
neuper@37997
|
463 |
[Thm ("LENGTH_CONS",num_str @{thm LENGTH_CONS}),
|
neuper@37997
|
464 |
Thm ("LENGTH_NIL",num_str @{thm LENGTH_NIL}),
|
neuper@38014
|
465 |
Calc ("Groups.plus_class.plus", eval_binop "#add_"),
|
neuper@37954
|
466 |
Calc ("op =",eval_equal "#equal_")
|
neuper@37954
|
467 |
],
|
neuper@37997
|
468 |
SOME "solveSystem e_s v_s",
|
neuper@37954
|
469 |
[]));
|
neuper@37997
|
470 |
*}
|
neuper@37997
|
471 |
ML {*
|
neuper@37954
|
472 |
store_pbt
|
neuper@37972
|
473 |
(prep_pbt thy "pbl_equsys_lin_2x2_tri" [] e_pblID
|
neuper@37954
|
474 |
(["triangular", "2x2", "linear", "system"],
|
neuper@37997
|
475 |
[("#Given" ,["equalities e_s", "solveForVars v_s"]),
|
neuper@37954
|
476 |
("#Where" ,
|
neuper@37998
|
477 |
["(tl v_s) from v_s occur_exactly_in (NTH 1 (e_s::bool list))",
|
neuper@37998
|
478 |
" v_s from v_s occur_exactly_in (NTH 2 (e_s::bool list))"]),
|
neuper@37997
|
479 |
("#Find" ,["solution ss'''"])
|
neuper@37954
|
480 |
],
|
neuper@37954
|
481 |
prls_triangular,
|
neuper@37997
|
482 |
SOME "solveSystem e_s v_s",
|
neuper@37954
|
483 |
[["EqSystem","top_down_substitution","2x2"]]));
|
neuper@37954
|
484 |
store_pbt
|
neuper@37972
|
485 |
(prep_pbt thy "pbl_equsys_lin_2x2_norm" [] e_pblID
|
neuper@37954
|
486 |
(["normalize", "2x2", "linear", "system"],
|
neuper@37997
|
487 |
[("#Given" ,["equalities e_s", "solveForVars v_s"]),
|
neuper@37997
|
488 |
("#Find" ,["solution ss'''"])
|
neuper@37954
|
489 |
],
|
neuper@37954
|
490 |
append_rls "e_rls" e_rls [(*for preds in where_*)],
|
neuper@37997
|
491 |
SOME "solveSystem e_s v_s",
|
neuper@37954
|
492 |
[["EqSystem","normalize","2x2"]]));
|
neuper@37954
|
493 |
store_pbt
|
neuper@37972
|
494 |
(prep_pbt thy "pbl_equsys_lin_3x3" [] e_pblID
|
neuper@37954
|
495 |
(["3x3", "linear", "system"],
|
neuper@37954
|
496 |
(*~~~~~~~~~~~~~~~~~~~~~~~~~*)
|
neuper@37997
|
497 |
[("#Given" ,["equalities e_s", "solveForVars v_s"]),
|
neuper@37997
|
498 |
("#Where" ,["LENGTH (e_s:: bool list) = 3", "LENGTH v_s = 3"]),
|
neuper@37997
|
499 |
("#Find" ,["solution ss'''"])
|
neuper@37954
|
500 |
],
|
neuper@37954
|
501 |
append_rls "prls_3x3_linear_system" e_rls
|
neuper@37997
|
502 |
[Thm ("LENGTH_CONS",num_str @{thm LENGTH_CONS}),
|
neuper@37997
|
503 |
Thm ("LENGTH_NIL",num_str @{thm LENGTH_NIL}),
|
neuper@38014
|
504 |
Calc ("Groups.plus_class.plus", eval_binop "#add_"),
|
neuper@37954
|
505 |
Calc ("op =",eval_equal "#equal_")
|
neuper@37954
|
506 |
],
|
neuper@37997
|
507 |
SOME "solveSystem e_s v_s",
|
neuper@37954
|
508 |
[]));
|
neuper@37954
|
509 |
store_pbt
|
neuper@37972
|
510 |
(prep_pbt thy "pbl_equsys_lin_4x4" [] e_pblID
|
neuper@37954
|
511 |
(["4x4", "linear", "system"],
|
neuper@37954
|
512 |
(*~~~~~~~~~~~~~~~~~~~~~~~~~*)
|
neuper@37997
|
513 |
[("#Given" ,["equalities e_s", "solveForVars v_s"]),
|
neuper@37997
|
514 |
("#Where" ,["LENGTH (e_s:: bool list) = 4", "LENGTH v_s = 4"]),
|
neuper@37997
|
515 |
("#Find" ,["solution ss'''"])
|
neuper@37954
|
516 |
],
|
neuper@37954
|
517 |
append_rls "prls_4x4_linear_system" e_rls
|
neuper@37997
|
518 |
[Thm ("LENGTH_CONS",num_str @{thm LENGTH_CONS}),
|
neuper@37997
|
519 |
Thm ("LENGTH_NIL",num_str @{thm LENGTH_NIL}),
|
neuper@38014
|
520 |
Calc ("Groups.plus_class.plus", eval_binop "#add_"),
|
neuper@37954
|
521 |
Calc ("op =",eval_equal "#equal_")
|
neuper@37954
|
522 |
],
|
neuper@37997
|
523 |
SOME "solveSystem e_s v_s",
|
neuper@37954
|
524 |
[]));
|
neuper@37997
|
525 |
*}
|
neuper@37997
|
526 |
ML {*
|
neuper@37954
|
527 |
store_pbt
|
neuper@37972
|
528 |
(prep_pbt thy "pbl_equsys_lin_4x4_tri" [] e_pblID
|
neuper@37954
|
529 |
(["triangular", "4x4", "linear", "system"],
|
neuper@37997
|
530 |
[("#Given" ,["equalities e_s", "solveForVars v_s"]),
|
neuper@37954
|
531 |
("#Where" , (*accepts missing variables up to diagional form*)
|
neuper@37997
|
532 |
["(NTH 1 (v_s::real list)) occurs_in (NTH 1 (e_s::bool list))",
|
neuper@37997
|
533 |
"(NTH 2 (v_s::real list)) occurs_in (NTH 2 (e_s::bool list))",
|
neuper@37997
|
534 |
"(NTH 3 (v_s::real list)) occurs_in (NTH 3 (e_s::bool list))",
|
neuper@37997
|
535 |
"(NTH 4 (v_s::real list)) occurs_in (NTH 4 (e_s::bool list))"
|
neuper@37954
|
536 |
]),
|
neuper@37997
|
537 |
("#Find" ,["solution ss'''"])
|
neuper@37954
|
538 |
],
|
neuper@37954
|
539 |
append_rls "prls_tri_4x4_lin_sys" prls_triangular
|
neuper@37954
|
540 |
[Calc ("Atools.occurs'_in",eval_occurs_in "")],
|
neuper@37997
|
541 |
SOME "solveSystem e_s v_s",
|
neuper@37954
|
542 |
[["EqSystem","top_down_substitution","4x4"]]));
|
neuper@37997
|
543 |
*}
|
neuper@37997
|
544 |
ML {*
|
neuper@37954
|
545 |
store_pbt
|
neuper@37972
|
546 |
(prep_pbt thy "pbl_equsys_lin_4x4_norm" [] e_pblID
|
neuper@37954
|
547 |
(["normalize", "4x4", "linear", "system"],
|
neuper@37997
|
548 |
[("#Given" ,["equalities e_s", "solveForVars v_s"]),
|
neuper@37997
|
549 |
(*LENGTH is checked 1 level above*)
|
neuper@37997
|
550 |
("#Find" ,["solution ss'''"])
|
neuper@37954
|
551 |
],
|
neuper@37954
|
552 |
append_rls "e_rls" e_rls [(*for preds in where_*)],
|
neuper@37997
|
553 |
SOME "solveSystem e_s v_s",
|
neuper@37954
|
554 |
[["EqSystem","normalize","4x4"]]));
|
neuper@37954
|
555 |
|
neuper@37954
|
556 |
|
neuper@37954
|
557 |
(* show_ptyps();
|
neuper@37954
|
558 |
*)
|
neuper@37954
|
559 |
|
neuper@37997
|
560 |
*}
|
neuper@37997
|
561 |
ML {*
|
neuper@37954
|
562 |
(** methods **)
|
neuper@37954
|
563 |
|
neuper@37954
|
564 |
store_met
|
neuper@37972
|
565 |
(prep_met thy "met_eqsys" [] e_metID
|
neuper@37954
|
566 |
(["EqSystem"],
|
neuper@37954
|
567 |
[],
|
neuper@37954
|
568 |
{rew_ord'="tless_true", rls' = Erls, calc = [],
|
neuper@37954
|
569 |
srls = Erls, prls = Erls, crls = Erls, nrls = Erls},
|
neuper@37954
|
570 |
"empty_script"
|
neuper@37954
|
571 |
));
|
neuper@37954
|
572 |
store_met
|
neuper@37972
|
573 |
(prep_met thy "met_eqsys_topdown" [] e_metID
|
neuper@37954
|
574 |
(["EqSystem","top_down_substitution"],
|
neuper@37954
|
575 |
[],
|
neuper@37954
|
576 |
{rew_ord'="tless_true", rls' = Erls, calc = [],
|
neuper@37954
|
577 |
srls = Erls, prls = Erls, crls = Erls, nrls = Erls},
|
neuper@37954
|
578 |
"empty_script"
|
neuper@37954
|
579 |
));
|
neuper@37997
|
580 |
*}
|
neuper@37997
|
581 |
ML {*
|
neuper@37954
|
582 |
store_met
|
neuper@37972
|
583 |
(prep_met thy "met_eqsys_topdown_2x2" [] e_metID
|
neuper@37954
|
584 |
(["EqSystem","top_down_substitution","2x2"],
|
neuper@37997
|
585 |
[("#Given" ,["equalities e_s", "solveForVars v_s"]),
|
neuper@37954
|
586 |
("#Where" ,
|
neuper@37998
|
587 |
["(tl v_s) from v_s occur_exactly_in (NTH 1 (e_s::bool list))",
|
neuper@37998
|
588 |
" v_s from v_s occur_exactly_in (NTH 2 (e_s::bool list))"]),
|
neuper@37997
|
589 |
("#Find" ,["solution ss'''"])
|
neuper@37954
|
590 |
],
|
neuper@37954
|
591 |
{rew_ord'="ord_simplify_System", rls' = Erls, calc = [],
|
neuper@37954
|
592 |
srls = append_rls "srls_top_down_2x2" e_rls
|
neuper@37969
|
593 |
[Thm ("hd_thm",num_str @{thm hd_thm}),
|
neuper@37969
|
594 |
Thm ("tl_Cons",num_str @{thm tl_Cons}),
|
neuper@37969
|
595 |
Thm ("tl_Nil",num_str @{thm tl_Nil})
|
neuper@37954
|
596 |
],
|
neuper@37954
|
597 |
prls = prls_triangular, crls = Erls, nrls = Erls},
|
neuper@37997
|
598 |
"Script SolveSystemScript (e_s::bool list) (v_s::real list) = " ^
|
neuper@37997
|
599 |
" (let e_1 = Take (hd e_s); " ^
|
neuper@37997
|
600 |
" e_1 = ((Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]" ^
|
neuper@37954
|
601 |
" isolate_bdvs False)) @@ " ^
|
neuper@37995
|
602 |
" (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]" ^
|
neuper@37997
|
603 |
" simplify_System False))) e_1; " ^
|
neuper@37997
|
604 |
" e_2 = Take (hd (tl e_s)); " ^
|
neuper@37997
|
605 |
" e_2 = ((Substitute [e_1]) @@ " ^
|
neuper@37995
|
606 |
" (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]" ^
|
neuper@37954
|
607 |
" simplify_System_parenthesized False)) @@ " ^
|
neuper@37995
|
608 |
" (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]" ^
|
neuper@37954
|
609 |
" isolate_bdvs False)) @@ " ^
|
neuper@37995
|
610 |
" (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]" ^
|
neuper@37997
|
611 |
" simplify_System False))) e_2; " ^
|
neuper@37997
|
612 |
" e__s = Take [e_1, e_2] " ^
|
neuper@37997
|
613 |
" in (Try (Rewrite_Set order_system False)) e__s)"
|
neuper@37954
|
614 |
(*---------------------------------------------------------------------------
|
neuper@37997
|
615 |
this script does NOT separate the equations as above,
|
neuper@37954
|
616 |
but it does not yet work due to preliminary script-interpreter,
|
neuper@37954
|
617 |
see eqsystem.sml 'script [EqSystem,top_down_substitution,2x2] Vers.2'
|
neuper@37954
|
618 |
|
neuper@37997
|
619 |
"Script SolveSystemScript (e_s::bool list) (v_s::real list) = " ^
|
neuper@37997
|
620 |
" (let e__s = Take e_s; " ^
|
neuper@37997
|
621 |
" e_1 = hd e__s; " ^
|
neuper@37997
|
622 |
" e_2 = hd (tl e__s); " ^
|
neuper@37997
|
623 |
" e__s = [e_1, Substitute [e_1] e_2] " ^
|
neuper@37995
|
624 |
" in ((Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]" ^
|
neuper@37954
|
625 |
" simplify_System_parenthesized False)) @@ " ^
|
neuper@37995
|
626 |
" (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))] " ^
|
neuper@37954
|
627 |
" isolate_bdvs False)) @@ " ^
|
neuper@37995
|
628 |
" (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]" ^
|
neuper@37997
|
629 |
" simplify_System False))) e__s)"
|
neuper@37954
|
630 |
---------------------------------------------------------------------------*)
|
neuper@37954
|
631 |
));
|
neuper@37997
|
632 |
*}
|
neuper@37997
|
633 |
ML {*
|
neuper@37954
|
634 |
store_met
|
neuper@37972
|
635 |
(prep_met thy "met_eqsys_norm" [] e_metID
|
neuper@37954
|
636 |
(["EqSystem","normalize"],
|
neuper@37954
|
637 |
[],
|
neuper@37954
|
638 |
{rew_ord'="tless_true", rls' = Erls, calc = [],
|
neuper@37954
|
639 |
srls = Erls, prls = Erls, crls = Erls, nrls = Erls},
|
neuper@37954
|
640 |
"empty_script"
|
neuper@37954
|
641 |
));
|
neuper@37998
|
642 |
*}
|
neuper@37998
|
643 |
ML {*
|
neuper@37954
|
644 |
store_met
|
neuper@37972
|
645 |
(prep_met thy "met_eqsys_norm_2x2" [] e_metID
|
neuper@37954
|
646 |
(["EqSystem","normalize","2x2"],
|
neuper@37997
|
647 |
[("#Given" ,["equalities e_s", "solveForVars v_s"]),
|
neuper@37997
|
648 |
("#Find" ,["solution ss'''"])],
|
neuper@37954
|
649 |
{rew_ord'="tless_true", rls' = Erls, calc = [],
|
neuper@37954
|
650 |
srls = append_rls "srls_normalize_2x2" e_rls
|
neuper@37969
|
651 |
[Thm ("hd_thm",num_str @{thm hd_thm}),
|
neuper@37969
|
652 |
Thm ("tl_Cons",num_str @{thm tl_Cons}),
|
neuper@37969
|
653 |
Thm ("tl_Nil",num_str @{thm tl_Nil})
|
neuper@37954
|
654 |
],
|
neuper@37954
|
655 |
prls = Erls, crls = Erls, nrls = Erls},
|
neuper@37997
|
656 |
"Script SolveSystemScript (e_s::bool list) (v_s::real list) = " ^
|
neuper@37997
|
657 |
" (let e__s = ((Try (Rewrite_Set norm_Rational False)) @@ " ^
|
neuper@37995
|
658 |
" (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]" ^
|
neuper@37954
|
659 |
" simplify_System_parenthesized False)) @@ " ^
|
neuper@37995
|
660 |
" (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]" ^
|
neuper@37954
|
661 |
" isolate_bdvs False)) @@ " ^
|
neuper@37995
|
662 |
" (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]" ^
|
neuper@37954
|
663 |
" simplify_System_parenthesized False)) @@ " ^
|
neuper@37997
|
664 |
" (Try (Rewrite_Set order_system False))) e_s " ^
|
neuper@37998
|
665 |
" in (SubProblem (EqSystem',[linear,system],[no_met]) " ^
|
neuper@37997
|
666 |
" [BOOL_LIST e__s, REAL_LIST v_s]))"
|
neuper@37954
|
667 |
));
|
neuper@37954
|
668 |
|
neuper@37998
|
669 |
*}
|
neuper@37998
|
670 |
ML {*
|
neuper@37997
|
671 |
(*this is for NTH only*)
|
neuper@37954
|
672 |
val srls = Rls {id="srls_normalize_4x4",
|
neuper@37954
|
673 |
preconds = [],
|
neuper@37954
|
674 |
rew_ord = ("termlessI",termlessI),
|
neuper@37954
|
675 |
erls = append_rls "erls_in_srls_IntegrierenUnd.." e_rls
|
neuper@37997
|
676 |
[(*for asm in NTH_CONS ...*)
|
neuper@38045
|
677 |
Calc ("Orderings.ord_class.less",eval_equ "#less_"),
|
neuper@37997
|
678 |
(*2nd NTH_CONS pushes n+-1 into asms*)
|
neuper@38014
|
679 |
Calc("Groups.plus_class.plus", eval_binop "#add_")
|
neuper@37954
|
680 |
],
|
neuper@37954
|
681 |
srls = Erls, calc = [],
|
neuper@37997
|
682 |
rules = [Thm ("NTH_CONS",num_str @{thm NTH_CONS}),
|
neuper@38014
|
683 |
Calc("Groups.plus_class.plus", eval_binop "#add_"),
|
neuper@37997
|
684 |
Thm ("NTH_NIL",num_str @{thm NTH_NIL})],
|
neuper@37954
|
685 |
scr = EmptyScr};
|
neuper@37954
|
686 |
store_met
|
neuper@37972
|
687 |
(prep_met thy "met_eqsys_norm_4x4" [] e_metID
|
neuper@37954
|
688 |
(["EqSystem","normalize","4x4"],
|
neuper@37997
|
689 |
[("#Given" ,["equalities e_s", "solveForVars v_s"]),
|
neuper@37997
|
690 |
("#Find" ,["solution ss'''"])],
|
neuper@37954
|
691 |
{rew_ord'="tless_true", rls' = Erls, calc = [],
|
neuper@37954
|
692 |
srls = append_rls "srls_normalize_4x4" srls
|
neuper@37969
|
693 |
[Thm ("hd_thm",num_str @{thm hd_thm}),
|
neuper@37969
|
694 |
Thm ("tl_Cons",num_str @{thm tl_Cons}),
|
neuper@37969
|
695 |
Thm ("tl_Nil",num_str @{thm tl_Nil})
|
neuper@37954
|
696 |
],
|
neuper@37954
|
697 |
prls = Erls, crls = Erls, nrls = Erls},
|
neuper@37954
|
698 |
(*GOON met ["EqSystem","normalize","4x4"] @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@*)
|
neuper@37997
|
699 |
"Script SolveSystemScript (e_s::bool list) (v_s::real list) = " ^
|
neuper@37997
|
700 |
" (let e__s = " ^
|
neuper@37954
|
701 |
" ((Try (Rewrite_Set norm_Rational False)) @@ " ^
|
neuper@37954
|
702 |
" (Repeat (Rewrite commute_0_equality False)) @@ " ^
|
neuper@37997
|
703 |
" (Try (Rewrite_Set_Inst [(bdv_1, NTH 1 v_s),(bdv_2, NTH 2 v_s ), " ^
|
neuper@37997
|
704 |
" (bdv_3, NTH 3 v_s),(bdv_3, NTH 4 v_s )] " ^
|
neuper@37954
|
705 |
" simplify_System_parenthesized False)) @@ " ^
|
neuper@37997
|
706 |
" (Try (Rewrite_Set_Inst [(bdv_1, NTH 1 v_s),(bdv_2, NTH 2 v_s ), " ^
|
neuper@37997
|
707 |
" (bdv_3, NTH 3 v_s),(bdv_3, NTH 4 v_s )] " ^
|
neuper@37954
|
708 |
" isolate_bdvs_4x4 False)) @@ " ^
|
neuper@37997
|
709 |
" (Try (Rewrite_Set_Inst [(bdv_1, NTH 1 v_s),(bdv_2, NTH 2 v_s ), " ^
|
neuper@37997
|
710 |
" (bdv_3, NTH 3 v_s),(bdv_3, NTH 4 v_s )] " ^
|
neuper@37954
|
711 |
" simplify_System_parenthesized False)) @@ " ^
|
neuper@37997
|
712 |
" (Try (Rewrite_Set order_system False))) e_s " ^
|
neuper@37998
|
713 |
" in (SubProblem (EqSystem',[linear,system],[no_met]) " ^
|
neuper@37997
|
714 |
" [BOOL_LIST e__s, REAL_LIST v_s]))"
|
neuper@37954
|
715 |
));
|
neuper@37954
|
716 |
store_met
|
neuper@37972
|
717 |
(prep_met thy "met_eqsys_topdown_4x4" [] e_metID
|
neuper@37954
|
718 |
(["EqSystem","top_down_substitution","4x4"],
|
neuper@37997
|
719 |
[("#Given" ,["equalities e_s", "solveForVars v_s"]),
|
neuper@37954
|
720 |
("#Where" , (*accepts missing variables up to diagonal form*)
|
neuper@37997
|
721 |
["(NTH 1 (v_s::real list)) occurs_in (NTH 1 (e_s::bool list))",
|
neuper@37997
|
722 |
"(NTH 2 (v_s::real list)) occurs_in (NTH 2 (e_s::bool list))",
|
neuper@37997
|
723 |
"(NTH 3 (v_s::real list)) occurs_in (NTH 3 (e_s::bool list))",
|
neuper@37997
|
724 |
"(NTH 4 (v_s::real list)) occurs_in (NTH 4 (e_s::bool list))"
|
neuper@37954
|
725 |
]),
|
neuper@37997
|
726 |
("#Find" ,["solution ss'''"])
|
neuper@37954
|
727 |
],
|
neuper@37954
|
728 |
{rew_ord'="ord_simplify_System", rls' = Erls, calc = [],
|
neuper@37954
|
729 |
srls = append_rls "srls_top_down_4x4" srls [],
|
neuper@37954
|
730 |
prls = append_rls "prls_tri_4x4_lin_sys" prls_triangular
|
neuper@37954
|
731 |
[Calc ("Atools.occurs'_in",eval_occurs_in "")],
|
neuper@37954
|
732 |
crls = Erls, nrls = Erls},
|
neuper@37954
|
733 |
(*FIXXXXME.WN060916: this script works ONLY for exp 7.79 @@@@@@@@@@@@@@@@@@@@*)
|
neuper@37997
|
734 |
"Script SolveSystemScript (e_s::bool list) (v_s::real list) = " ^
|
neuper@37997
|
735 |
" (let e_1 = NTH 1 e_s; " ^
|
neuper@37997
|
736 |
" e_2 = Take (NTH 2 e_s); " ^
|
neuper@37997
|
737 |
" e_2 = ((Substitute [e_1]) @@ " ^
|
neuper@37997
|
738 |
" (Try (Rewrite_Set_Inst [(bdv_1,NTH 1 v_s),(bdv_2,NTH 2 v_s)," ^
|
neuper@37997
|
739 |
" (bdv_3,NTH 3 v_s),(bdv_4,NTH 4 v_s)]" ^
|
neuper@37954
|
740 |
" simplify_System_parenthesized False)) @@ " ^
|
neuper@37997
|
741 |
" (Try (Rewrite_Set_Inst [(bdv_1,NTH 1 v_s),(bdv_2,NTH 2 v_s)," ^
|
neuper@37997
|
742 |
" (bdv_3,NTH 3 v_s),(bdv_4,NTH 4 v_s)]" ^
|
neuper@37954
|
743 |
" isolate_bdvs False)) @@ " ^
|
neuper@37997
|
744 |
" (Try (Rewrite_Set_Inst [(bdv_1,NTH 1 v_s),(bdv_2,NTH 2 v_s)," ^
|
neuper@37997
|
745 |
" (bdv_3,NTH 3 v_s),(bdv_4,NTH 4 v_s)]" ^
|
neuper@37997
|
746 |
" norm_Rational False))) e_2 " ^
|
neuper@37997
|
747 |
" in [e_1, e_2, NTH 3 e_s, NTH 4 e_s])"
|
neuper@37954
|
748 |
));
|
neuper@37954
|
749 |
*}
|
neuper@37954
|
750 |
|
neuper@37906
|
751 |
end |