wneuper/isa: src/Tools/isac/Knowledge/Poly.thy@ede4248a827b (annotated)

neuper@37906	1	(* WN.020812: theorems in the Reals,
neuper@37906	2	necessary for special rule sets, in addition to Isabelle2002.
neuper@37906	3	!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
neuper@37906	4	!!! THIS IS THE _least_ NUMBER OF ADDITIONAL THEOREMS !!!
neuper@37906	5	!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
neuper@37906	6	xxxI contain ^^^ instead of ^ in the respective theorem xxx in 2002
neuper@37906	7	changed by: Richard Lang 020912
neuper@37906	8	*)
neuper@37906	9
neuper@37950	10	theory Poly imports Simplify begin
neuper@37906	11
neuper@37906	12	consts
neuper@37906	13
neuper@37906	14	is'_expanded'_in :: "[real, real] => bool" ("_ is'_expanded'_in _")
neuper@37950	15	is'_poly'_in :: "[real, real] => bool" ("_ is'_poly'_in _") (RL DA )
neuper@37950	16	has'_degree'_in :: "[real, real] => real" ("_ has'_degree'_in _")(RL DA )
neuper@37950	17	is'_polyrat'_in :: "[real, real] => bool" ("_ is'_polyrat'_in _")(RL030626)
neuper@37906	18
neuper@37950	19	is'_multUnordered:: "real => bool" ("_ is'_multUnordered")
neuper@37950	20	is'_addUnordered :: "real => bool" ("_ is'_addUnordered") (WN030618)
neuper@37950	21	is'_polyexp :: "real => bool" ("_ is'_polyexp")
neuper@37906	22
neuper@37906	23	Expand'_binoms
neuper@37950	24	:: "['y,
neuper@37950	25	'y] => 'y"
neuper@37950	26	("((Script Expand'_binoms (_ =))//
neuper@37950	27	(_))" 9)
neuper@37906	28
neuper@37906	29	(-------------------- rules------------------------------------------------)
neuper@52148	30	axiomatization where (*.not contained in Isabelle2002,
neuper@37906	31	stated as axioms, TODO: prove as theorems;
neuper@37906	32	theorem-IDs 'xxxI' with ^^^ instead of ^ in 'xxx' in Isabelle2002.*)
neuper@37906	33
neuper@52148	34	realpow_pow: "(a ^^^ b) ^^^ c = a ^^^ (b * c)" and
neuper@52148	35	realpow_addI: "r ^^^ (n + m) = r ^^^ n * r ^^^ m" and
neuper@52148	36	realpow_addI_assoc_l: "r ^^^ n * (r ^^^ m * s) = r ^^^ (n + m) * s" and
neuper@52148	37	realpow_addI_assoc_r: "s * r ^^^ n * r ^^^ m = s * r ^^^ (n + m)" and
neuper@37906	38
neuper@52148	39	realpow_oneI: "r ^^^ 1 = r" and
neuper@52148	40	realpow_zeroI: "r ^^^ 0 = 1" and
neuper@52148	41	realpow_eq_oneI: "1 ^^^ n = 1" and
neuper@52148	42	realpow_multI: "(r * s) ^^^ n = r ^^^ n * s ^^^ n" and
neuper@37974	43	realpow_multI_poly: "[\| r is_polyexp; s is_polyexp \|] ==>
neuper@52148	44	(r * s) ^^^ n = r ^^^ n * s ^^^ n" and
neuper@52148	45	realpow_minus_oneI: "-1 ^^^ (2 * n) = 1" and
neuper@37906	46
neuper@52148	47	realpow_twoI: "r ^^^ 2 = r * r" and
neuper@52148	48	realpow_twoI_assoc_l: "r * (r * s) = r ^^^ 2 * s" and
neuper@52148	49	realpow_twoI_assoc_r: "s * r * r = s * r ^^^ 2" and
neuper@52148	50	realpow_two_atom: "r is_atom ==> r * r = r ^^^ 2" and
neuper@52148	51	realpow_plus_1: "r * r ^^^ n = r ^^^ (n + 1)" and
neuper@52148	52	realpow_plus_1_assoc_l: "r * (r ^^^ m * s) = r ^^^ (1 + m) * s" and
neuper@52148	53	realpow_plus_1_assoc_l2: "r ^^^ m * (r * s) = r ^^^ (1 + m) * s" and
neuper@52148	54	realpow_plus_1_assoc_r: "s * r * r ^^^ m = s * r ^^^ (1 + m)" and
neuper@52148	55	realpow_plus_1_atom: "r is_atom ==> r * r ^^^ n = r ^^^ (1 + n)" and
neuper@37974	56	realpow_def_atom: "[\| Not (r is_atom); 1 < n \|]
neuper@52148	57	==> r ^^^ n = r * r ^^^ (n + -1)" and
neuper@52148	58	realpow_addI_atom: "r is_atom ==> r ^^^ n * r ^^^ m = r ^^^ (n + m)" and
neuper@37906	59
neuper@37906	60
neuper@52148	61	realpow_minus_even: "n is_even ==> (- r) ^^^ n = r ^^^ n" and
neuper@52148	62	realpow_minus_odd: "Not (n is_even) ==> (- r) ^^^ n = -1 * r ^^^ n" and
neuper@37906	63
neuper@37906	64
neuper@37906	65	(* RL 020914 *)
neuper@52148	66	real_pp_binom_times: "(a + b)(c + d) = ac + ad + bc + b*d" and
neuper@52148	67	real_pm_binom_times: "(a + b)(c - d) = ac - ad + bc - b*d" and
neuper@52148	68	real_mp_binom_times: "(a - b)(c + d) = ac + ad - bc - b*d" and
neuper@52148	69	real_mm_binom_times: "(a - b)(c - d) = ac - ad - bc + b*d" and
neuper@52148	70	real_plus_binom_pow3: "(a + b)^^^3 = a^^^3 + 3a^^^2b + 3ab^^^2 + b^^^3" and
neuper@37974	71	real_plus_binom_pow3_poly: "[\| a is_polyexp; b is_polyexp \|] ==>
neuper@52148	72	(a + b)^^^3 = a^^^3 + 3a^^^2b + 3ab^^^2 + b^^^3" and
neuper@52148	73	real_minus_binom_pow3: "(a - b)^^^3 = a^^^3 - 3a^^^2b + 3ab^^^2 - b^^^3" and
neuper@37974	74	real_minus_binom_pow3_p: "(a + -1 * b)^^^3 = a^^^3 + -3a^^^2b + 3ab^^^2 +
neuper@52148	75	-1*b^^^3" and
neuper@37974	76	(* real_plus_binom_pow: "[\| n is_const; 3 < n \|] ==>
neuper@37950	77	(a + b)^^^n = (a + b) * (a + b)^^^(n - 1)" *)
neuper@37974	78	real_plus_binom_pow4: "(a + b)^^^4 = (a^^^3 + 3a^^^2b + 3ab^^^2 + b^^^3)
neuper@52148	79	*(a + b)" and
neuper@37974	80	real_plus_binom_pow4_poly: "[\| a is_polyexp; b is_polyexp \|] ==>
neuper@37950	81	(a + b)^^^4 = (a^^^3 + 3a^^^2b + 3ab^^^2 + b^^^3)
neuper@52148	82	*(a + b)" and
neuper@37974	83	real_plus_binom_pow5: "(a + b)^^^5 = (a^^^3 + 3a^^^2b + 3ab^^^2 + b^^^3)
neuper@52148	84	(a^^^2 + 2a*b + b^^^2)" and
neuper@37974	85	real_plus_binom_pow5_poly: "[\| a is_polyexp; b is_polyexp \|] ==>
neuper@37950	86	(a + b)^^^5 = (a^^^3 + 3a^^^2b + 3ab^^^2
neuper@52148	87	+ b^^^3)(a^^^2 + 2a*b + b^^^2)" and
neuper@52148	88	real_diff_plus: "a - b = a + -b" (17.3.03: do_NOT_use) and
neuper@52148	89	real_diff_minus: "a - b = a + -1 * b" and
neuper@52148	90	real_plus_binom_times: "(a + b)(a + b) = a^^^2 + 2a*b + b^^^2" and
neuper@52148	91	real_minus_binom_times: "(a - b)(a - b) = a^^^2 - 2a*b + b^^^2" and
neuper@37906	92	(WN071229 changed for Schaerding -----vvv)
neuper@37974	93	(real_plus_binom_pow2: "(a + b)^^^2 = a^^^2 + 2ab + b^^^2")
neuper@52148	94	real_plus_binom_pow2: "(a + b)^^^2 = (a + b) * (a + b)" and
neuper@37906	95	(WN071229 changed for Schaerding -----^^^)
neuper@37974	96	real_plus_binom_pow2_poly: "[\| a is_polyexp; b is_polyexp \|] ==>
neuper@52148	97	(a + b)^^^2 = a^^^2 + 2ab + b^^^2" and
neuper@52148	98	real_minus_binom_pow2: "(a - b)^^^2 = a^^^2 - 2ab + b^^^2" and
neuper@52148	99	real_minus_binom_pow2_p: "(a - b)^^^2 = a^^^2 + -2ab + b^^^2" and
neuper@52148	100	real_plus_minus_binom1: "(a + b)*(a - b) = a^^^2 - b^^^2" and
neuper@52148	101	real_plus_minus_binom1_p: "(a + b)(a - b) = a^^^2 + -1b^^^2" and
neuper@52148	102	real_plus_minus_binom1_p_p: "(a + b)(a + -1 b) = a^^^2 + -1*b^^^2" and
neuper@52148	103	real_plus_minus_binom2: "(a - b)*(a + b) = a^^^2 - b^^^2" and
neuper@52148	104	real_plus_minus_binom2_p: "(a - b)(a + b) = a^^^2 + -1b^^^2" and
neuper@52148	105	real_plus_minus_binom2_p_p: "(a + -1 * b)(a + b) = a^^^2 + -1b^^^2" and
neuper@52148	106	real_plus_binom_times1: "(a + 1b)(a + -1b) = a^^^2 + -1b^^^2" and
neuper@52148	107	real_plus_binom_times2: "(a + -1b)(a + 1b) = a^^^2 + -1b^^^2" and
neuper@37906	108
neuper@37974	109	real_num_collect: "[\| l is_const; m is_const \|] ==>
neuper@52148	110	l * n + m * n = (l + m) * n" and
neuper@37906	111	(* FIXME.MG.0401: replace 'real_num_collect_assoc'
neuper@37906	112	by 'real_num_collect_assoc_l' ... are equal, introduced by MG ! *)
neuper@37974	113	real_num_collect_assoc: "[\| l is_const; m is_const \|] ==>
neuper@52148	114	l * n + (m * n + k) = (l + m) * n + k" and
neuper@37974	115	real_num_collect_assoc_l: "[\| l is_const; m is_const \|] ==>
neuper@37950	116	l * n + (m * n + k) = (l + m)
neuper@52148	117	* n + k" and
neuper@37974	118	real_num_collect_assoc_r: "[\| l is_const; m is_const \|] ==>
neuper@52148	119	(k + m * n) + l * n = k + (l + m) * n" and
neuper@52148	120	real_one_collect: "m is_const ==> n + m * n = (1 + m) * n" and
neuper@37906	121	(* FIXME.MG.0401: replace 'real_one_collect_assoc'
neuper@37906	122	by 'real_one_collect_assoc_l' ... are equal, introduced by MG ! *)
neuper@52148	123	real_one_collect_assoc: "m is_const ==> n + (m * n + k) = (1 + m)* n + k" and
neuper@37906	124
neuper@52148	125	real_one_collect_assoc_l: "m is_const ==> n + (m * n + k) = (1 + m) * n + k" and
neuper@52148	126	real_one_collect_assoc_r: "m is_const ==> (k + n) + m * n = k + (1 + m) * n" and
neuper@37906	127
neuper@37906	128	(* FIXME.MG.0401: replace 'real_mult_2_assoc'
neuper@37906	129	by 'real_mult_2_assoc_l' ... are equal, introduced by MG ! *)
neuper@52148	130	real_mult_2_assoc: "z1 + (z1 + k) = 2 * z1 + k" and
neuper@52148	131	real_mult_2_assoc_l: "z1 + (z1 + k) = 2 * z1 + k" and
neuper@52148	132	real_mult_2_assoc_r: "(k + z1) + z1 = k + 2 * z1" and
neuper@37906	133
neuper@52148	134	real_add_mult_distrib_poly: "w is_polyexp ==> (z1 + z2) * w = z1 * w + z2 * w" and
neuper@37974	135	real_add_mult_distrib2_poly:"w is_polyexp ==> w * (z1 + z2) = w * z1 + w * z2"
neuper@37950	136
neuper@37950	137	text {* remark on 'polynomials'
neuper@37950	138	WN020919
neuper@37950	139	* there are 5 kinds of expanded normalforms *
neuper@37950	140
neuper@37950	141	[1] 'complete polynomial' (Komplettes Polynom), univariate
neuper@37950	142	a_0 + a_1.x^1 +...+ a_n.x^n not (a_n = 0)
neuper@37950	143	not (a_n = 0), some a_i may be zero (DON'T disappear),
neuper@37950	144	variables in monomials lexicographically ordered and complete,
neuper@37950	145	x written as 1*x^1, ...
neuper@37950	146	[2] 'polynomial' (Polynom), univariate and multivariate
neuper@37950	147	a_0 + a_1.x +...+ a_n.x^n not (a_n = 0)
neuper@37950	148	a_0 + a_1.x_1.x_2^n_12...x_m^n_1m +...+ a_n.x_1^n.x_2^n_n2...x_m^n_nm
neuper@37950	149	not (a_n = 0), some a_i may be zero (ie. monomials disappear),
neuper@37950	150	exponents and coefficients equal 1 are not (WN060904.TODO in cancel_p_)shown,
neuper@37950	151	and variables in monomials are lexicographically ordered
neuper@37950	152	examples: [1]: "1 + (-10) * x ^^^ 1 + 25 * x ^^^ 2"
neuper@37950	153	[1]: "11 + 0 * x ^^^ 1 + 1 * x ^^^ 2"
neuper@37950	154	[2]: "x + (-50) * x ^^^ 3"
neuper@37950	155	[2]: "(-1) * x * y ^^^ 2 + 7 * x ^^^ 3"
neuper@37950	156
neuper@37950	157	[3] 'expanded_term' (Ausmultiplizierter Term):
neuper@37950	158	pull out unary minus to binary minus,
neuper@37950	159	as frequently exercised in schools; other conditions for [2] hold however
neuper@37950	160	examples: "a ^^^ 2 - 2 * a * b + b ^^^ 2"
neuper@37950	161	"4 * x ^^^ 2 - 9 * y ^^^ 2"
neuper@37950	162	[4] 'polynomial_in' (Polynom in):
neuper@37950	163	polynomial in 1 variable with arbitrary coefficients
neuper@37950	164	examples: "2 * x + (-50) * x ^^^ 3" (poly in x)
neuper@37950	165	"(u + v) + (2 * u ^^^ 2) * a + (-u) * a ^^^ 2 (poly in a)
neuper@37950	166	[5] 'expanded_in' (Ausmultiplizierter Termin in):
neuper@37950	167	analoguous to [3] with binary minus like [3]
neuper@37950	168	examples: "2 * x - 50 * x ^^^ 3" (expanded in x)
neuper@37950	169	"(u + v) + (2 * u ^^^ 2) * a - u * a ^^^ 2 (expanded in a)
neuper@37950	170	*}
neuper@37950	171
neuper@37950	172	ML {*
neuper@37972	173	val thy = @{theory};
neuper@37972	174
neuper@37950	175	(* is_polyrat_in becomes true, if no bdv is in the denominator of a fraction*)
neuper@37950	176	fun is_polyrat_in t v =
neuper@37950	177	let fun coeff_in c v = member op = (vars c) v;
neuper@38031	178	fun finddivide (_ $ _ $ _ $ _) v = error("is_polyrat_in:")
neuper@37950	179	(* at the moment there is no term like this, but ....*)
neuper@48789	180	\| finddivide (t as (Const ("Fields.inverse_class.divide",_) $ _ $ b)) v =
neuper@37950	181	not(coeff_in b v)
neuper@37950	182	\| finddivide (_ $ t1 $ t2) v =
neuper@37950	183	(finddivide t1 v) orelse (finddivide t2 v)
neuper@37950	184	\| finddivide (_ $ t1) v = (finddivide t1 v)
neuper@37950	185	\| finddivide _ _ = false;
neuper@37950	186	in finddivide t v end;
neuper@37950	187
neuper@37950	188	fun eval_is_polyrat_in _ _(p as (Const ("Poly.is'_polyrat'_in",_) $ t $ v)) _ =
neuper@37950	189	if is_polyrat_in t v
neuper@37950	190	then SOME ((term2str p) ^ " = True",
neuper@48760	191	Trueprop $ (mk_equality (p, @{term True})))
neuper@37950	192	else SOME ((term2str p) ^ " = True",
neuper@48760	193	Trueprop $ (mk_equality (p, @{term False})))
neuper@38015	194	\| eval_is_polyrat_in _ _ _ _ = ((tracing"### no matches";) NONE);
neuper@37950	195
neuper@37950	196	local
neuper@37950	197	(.a 'c is coefficient of v' if v does NOT occur in c.)
neuper@37950	198	fun coeff_in c v = not (member op = (vars c) v);
neuper@37950	199	(* FIXME.WN100826 shift this into test--------------
neuper@37950	200	val v = (term_of o the o (parse thy)) "x";
neuper@37950	201	val t = (term_of o the o (parse thy)) "1";
neuper@37950	202	coeff_in t v;
neuper@37950	203	(val it = true : bool)
neuper@37950	204	val t = (term_of o the o (parse thy)) "a*b+c";
neuper@37950	205	coeff_in t v;
neuper@37950	206	(val it = true : bool)
neuper@37950	207	val t = (term_of o the o (parse thy)) "a*x+c";
neuper@37950	208	coeff_in t v;
neuper@37950	209	(val it = false : bool)
neuper@37950	210	----------------------------------------------------*)
neuper@37950	211	(*. a 'monomial t in variable v' is a term t with
neuper@37950	212	either (1) v NOT existent in t, or (2) v contained in t,
neuper@37950	213	if (1) then degree 0
neuper@37950	214	if (2) then v is a factor on the very right, ev. with exponent.*)
neuper@37950	215	fun factor_right_deg (case 2)
neuper@38034	216	(t as Const ("Groups.times_class.times",_) $ t1 $
neuper@37950	217	(Const ("Atools.pow",_) $ vv $ Free (d,_))) v =
neuper@37950	218	if ((vv = v) andalso (coeff_in t1 v)) then SOME (int_of_str' d) else NONE
neuper@37950	219	\| factor_right_deg (t as Const ("Atools.pow",_) $ vv $ Free (d,_)) v =
neuper@37950	220	if (vv = v) then SOME (int_of_str' d) else NONE
neuper@38034	221	\| factor_right_deg (t as Const ("Groups.times_class.times",_) $ t1 $ vv) v =
neuper@37950	222	if ((vv = v) andalso (coeff_in t1 v))then SOME 1 else NONE
neuper@37950	223	\| factor_right_deg vv v =
neuper@37950	224	if (vv = v) then SOME 1 else NONE;
neuper@37950	225	fun mono_deg_in m v =
neuper@37950	226	if coeff_in m v then (case 1) SOME 0
neuper@37950	227	else factor_right_deg m v;
neuper@37950	228	(* FIXME.WN100826 shift this into test-----------------------------
neuper@37950	229	val v = (term_of o the o (parse thy)) "x";
neuper@37950	230	val t = (term_of o the o (parse thy)) "(ab+c)x^^^7";
neuper@37950	231	mono_deg_in t v;
neuper@37950	232	(val it = SOME 7)
neuper@37950	233	val t = (term_of o the o (parse thy)) "x^^^7";
neuper@37950	234	mono_deg_in t v;
neuper@37950	235	(val it = SOME 7)
neuper@37950	236	val t = (term_of o the o (parse thy)) "(ab+c)x";
neuper@37950	237	mono_deg_in t v;
neuper@37950	238	(val it = SOME 1)
neuper@37950	239	val t = (term_of o the o (parse thy)) "(ab+x)x";
neuper@37950	240	mono_deg_in t v;
neuper@37950	241	(val it = NONE)
neuper@37950	242	val t = (term_of o the o (parse thy)) "x";
neuper@37950	243	mono_deg_in t v;
neuper@37950	244	(val it = SOME 1)
neuper@37950	245	val t = (term_of o the o (parse thy)) "(a*b+c)";
neuper@37950	246	mono_deg_in t v;
neuper@37950	247	(val it = SOME 0)
neuper@37950	248	val t = (term_of o the o (parse thy)) "ab - (ab)x";
neuper@37950	249	mono_deg_in t v;
neuper@37950	250	(val it = NONE)
neuper@37950	251	------------------------------------------------------------------*)
neuper@37950	252	fun expand_deg_in t v =
neuper@38014	253	let fun edi ~1 ~1 (Const ("Groups.plus_class.plus",_) $ t1 $ t2) =
neuper@37950	254	(case mono_deg_in t2 v of (* $ is left associative*)
neuper@37950	255	SOME d' => edi d' d' t1
neuper@37950	256	\| NONE => NONE)
neuper@38014	257	\| edi ~1 ~1 (Const ("Groups.minus_class.minus",_) $ t1 $ t2) =
neuper@37950	258	(case mono_deg_in t2 v of
neuper@37950	259	SOME d' => edi d' d' t1
neuper@37950	260	\| NONE => NONE)
neuper@38014	261	\| edi d dmax (Const ("Groups.minus_class.minus",_) $ t1 $ t2) =
neuper@37950	262	(case mono_deg_in t2 v of
neuper@37950	263	(RL orelse ((d=0) andalso (d'=0)) need to handle 3+4-...4 +x)
neuper@37950	264	SOME d' => if ((d > d') orelse ((d=0) andalso (d'=0)))
neuper@37950	265	then edi d' dmax t1 else NONE
neuper@37950	266	\| NONE => NONE)
neuper@38014	267	\| edi d dmax (Const ("Groups.plus_class.plus",_) $ t1 $ t2) =
neuper@37950	268	(case mono_deg_in t2 v of
neuper@37950	269	(RL orelse ((d=0) andalso (d'=0)) need to handle 3+4-...4 +x)
neuper@37950	270	SOME d' => if ((d > d') orelse ((d=0) andalso (d'=0)))
neuper@37950	271	then edi d' dmax t1 else NONE
neuper@37950	272	\| NONE => NONE)
neuper@37950	273	\| edi ~1 ~1 t = (case mono_deg_in t v of
neuper@37950	274	d as SOME _ => d
neuper@37950	275	\| NONE => NONE)
neuper@37950	276	\| edi d dmax t = (basecase last)
neuper@37950	277	(case mono_deg_in t v of
neuper@37950	278	SOME d' => if ((d > d') orelse ((d=0) andalso (d'=0)))
neuper@37950	279	then SOME dmax else NONE
neuper@37950	280	\| NONE => NONE)
neuper@37950	281	in edi ~1 ~1 t end;
neuper@37950	282	(* FIXME.WN100826 shift this into test-----------------------------
neuper@37950	283	val v = (term_of o the o (parse thy)) "x";
neuper@37950	284	val t = (term_of o the o (parse thy)) "a+b";
neuper@37950	285	expand_deg_in t v;
neuper@37950	286	(val it = SOME 0)
neuper@37950	287	val t = (term_of o the o (parse thy)) "(a+b)*x";
neuper@37950	288	expand_deg_in t v;
neuper@37950	289	(SOME 1)
neuper@37950	290	val t = (term_of o the o (parse thy)) "ab - (a+b)x";
neuper@37950	291	expand_deg_in t v;
neuper@37950	292	(SOME 1)
neuper@37950	293	val t = (term_of o the o (parse thy)) "ab + (a-b)x";
neuper@37950	294	expand_deg_in t v;
neuper@37950	295	(SOME 1)
neuper@37950	296	val t = (term_of o the o (parse thy)) "ab + (a+b)x + x^^^2";
neuper@37950	297	expand_deg_in t v;
neuper@37950	298	-------------------------------------------------------------------*)
neuper@37950	299	fun poly_deg_in t v =
neuper@38014	300	let fun edi ~1 ~1 (Const ("Groups.plus_class.plus",_) $ t1 $ t2) =
neuper@37950	301	(case mono_deg_in t2 v of (* $ is left associative*)
neuper@37950	302	SOME d' => edi d' d' t1
neuper@37950	303	\| NONE => NONE)
neuper@38014	304	\| edi d dmax (Const ("Groups.plus_class.plus",_) $ t1 $ t2) =
neuper@37950	305	(case mono_deg_in t2 v of
neuper@37950	306	(RL orelse ((d=0) andalso (d'=0)) need to handle 3+4-...4 +x)
neuper@37950	307	SOME d' => if ((d > d') orelse ((d=0) andalso (d'=0)))
neuper@37950	308	then edi d' dmax t1 else NONE
neuper@37950	309	\| NONE => NONE)
neuper@37950	310	\| edi ~1 ~1 t = (case mono_deg_in t v of
neuper@37950	311	d as SOME _ => d
neuper@37950	312	\| NONE => NONE)
neuper@37950	313	\| edi d dmax t = (basecase last)
neuper@37950	314	(case mono_deg_in t v of
neuper@37950	315	SOME d' => if ((d > d') orelse ((d=0) andalso (d'=0)))
neuper@37950	316	then SOME dmax else NONE
neuper@37950	317	\| NONE => NONE)
neuper@37950	318	in edi ~1 ~1 t end;
neuper@37950	319	in
neuper@37950	320
neuper@37950	321	fun is_expanded_in t v =
neuper@37950	322	case expand_deg_in t v of SOME _ => true \| NONE => false;
neuper@37950	323	fun is_poly_in t v =
neuper@37950	324	case poly_deg_in t v of SOME _ => true \| NONE => false;
neuper@37950	325	fun has_degree_in t v =
neuper@37950	326	case expand_deg_in t v of SOME d => d \| NONE => ~1;
neuper@37980	327	end;(local)
neuper@37950	328	(* FIXME.WN100826 shift this into test-----------------------------
neuper@37950	329	val v = (term_of o the o (parse thy)) "x";
neuper@37950	330	val t = (term_of o the o (parse thy)) "ab - (a+b)x + x^^^2";
neuper@37950	331	has_degree_in t v;
neuper@37950	332	(val it = 2)
neuper@37950	333	val t = (term_of o the o (parse thy)) "-8 - 2*x + x^^^2";
neuper@37950	334	has_degree_in t v;
neuper@37950	335	(val it = 2)
neuper@37950	336	val t = (term_of o the o (parse thy)) "6 + 13x + 6x^^^2";
neuper@37950	337	has_degree_in t v;
neuper@37950	338	(val it = 2)
neuper@37950	339	-------------------------------------------------------------------*)
neuper@37950	340
neuper@37950	341	(("is_expanded_in", ("Poly.is'_expanded'_in", eval_is_expanded_in "")))
neuper@37950	342	fun eval_is_expanded_in _ _
neuper@37950	343	(p as (Const ("Poly.is'_expanded'_in",_) $ t $ v)) _ =
neuper@37950	344	if is_expanded_in t v
neuper@37950	345	then SOME ((term2str p) ^ " = True",
neuper@48760	346	Trueprop $ (mk_equality (p, @{term True})))
neuper@37950	347	else SOME ((term2str p) ^ " = True",
neuper@48760	348	Trueprop $ (mk_equality (p, @{term False})))
neuper@37950	349	\| eval_is_expanded_in _ _ _ _ = NONE;
neuper@37950	350	(*
neuper@37950	351	val t = (term_of o the o (parse thy)) "(-8 - 2*x + x^^^2) is_expanded_in x";
neuper@37950	352	val SOME (id, t') = eval_is_expanded_in 0 0 t 0;
neuper@37950	353	(val id = "Poly.is'_expanded'_in (-8 - 2 x + x ^^^ 2) x = True"*)
neuper@37950	354	term2str t';
neuper@37950	355	(val it = "Poly.is'_expanded'_in (-8 - 2 x + x ^^^ 2) x = True"*)
neuper@37950	356	*)
neuper@37950	357
neuper@37950	358	(("is_poly_in", ("Poly.is'_poly'_in", eval_is_poly_in "")))
neuper@37950	359	fun eval_is_poly_in _ _
neuper@37950	360	(p as (Const ("Poly.is'_poly'_in",_) $ t $ v)) _ =
neuper@37950	361	if is_poly_in t v
neuper@37950	362	then SOME ((term2str p) ^ " = True",
neuper@48760	363	Trueprop $ (mk_equality (p, @{term True})))
neuper@37950	364	else SOME ((term2str p) ^ " = True",
neuper@48760	365	Trueprop $ (mk_equality (p, @{term False})))
neuper@37950	366	\| eval_is_poly_in _ _ _ _ = NONE;
neuper@37950	367	(*
neuper@37950	368	val t = (term_of o the o (parse thy)) "(8 + 2*x + x^^^2) is_poly_in x";
neuper@37950	369	val SOME (id, t') = eval_is_poly_in 0 0 t 0;
neuper@37950	370	(val id = "Poly.is'_poly'_in (8 + 2 x + x ^^^ 2) x = True"*)
neuper@37950	371	term2str t';
neuper@37950	372	(val it = "Poly.is'_poly'_in (8 + 2 x + x ^^^ 2) x = True"*)
neuper@37950	373	*)
neuper@37950	374
neuper@37950	375	(("has_degree_in", ("Poly.has'_degree'_in", eval_has_degree_in "")))
neuper@37950	376	fun eval_has_degree_in _ _
neuper@37950	377	(p as (Const ("Poly.has'_degree'_in",_) $ t $ v)) _ =
neuper@37950	378	let val d = has_degree_in t v
neuper@37950	379	val d' = term_of_num HOLogic.realT d
neuper@37950	380	in SOME ((term2str p) ^ " = " ^ (string_of_int d),
neuper@37950	381	Trueprop $ (mk_equality (p, d')))
neuper@37950	382	end
neuper@37950	383	\| eval_has_degree_in _ _ _ _ = NONE;
neuper@37950	384	(*
neuper@37950	385	> val t = (term_of o the o (parse thy)) "(-8 - 2*x + x^^^2) has_degree_in x";
neuper@37950	386	> val SOME (id, t') = eval_has_degree_in 0 0 t 0;
neuper@37950	387	val id = "Poly.has'_degree'_in (-8 - 2 * x + x ^^^ 2) x = 2" : string
neuper@37950	388	> term2str t';
neuper@37950	389	val it = "Poly.has'_degree'_in (-8 - 2 * x + x ^^^ 2) x = 2" : string
neuper@37950	390	*)
neuper@37950	391
neuper@37978	392	(..)
neuper@37978	393	val calculate_Poly =
neuper@37978	394	append_rls "calculate_PolyFIXXXME.not.impl." e_rls
neuper@37978	395	[];
neuper@37978	396
neuper@37950	397	(.for evaluation of conditions in rewrite rules.)
neuper@42319	398	val Poly_erls = append_rls "Poly_erls" Atools_erls
neuper@52139	399	[Calc ("HOL.eq", eval_equal "#equal_"),
neuper@52139	400	Thm ("real_unari_minus", num_str @{thm real_unari_minus}),
neuper@52139	401	Calc ("Groups.plus_class.plus", eval_binop "#add_"),
neuper@52139	402	Calc ("Groups.minus_class.minus", eval_binop "#sub_"),
neuper@52139	403	Calc ("Groups.times_class.times", eval_binop "#mult_"),
neuper@52139	404	Calc ("Atools.pow", eval_binop "#power_")];
neuper@37950	405
neuper@52139	406	val poly_crls = append_rls "poly_crls" Atools_crls
neuper@52139	407	[Calc ("HOL.eq", eval_equal "#equal_"),
neuper@52139	408	Thm ("real_unari_minus", num_str @{thm real_unari_minus}),
neuper@52139	409	Calc ("Groups.plus_class.plus", eval_binop "#add_"),
neuper@52139	410	Calc ("Groups.minus_class.minus", eval_binop "#sub_"),
neuper@52139	411	Calc ("Groups.times_class.times", eval_binop "#mult_"),
neuper@52139	412	Calc ("Atools.pow" ,eval_binop "#power_")];
neuper@37950	413
neuper@37950	414	local (. for make_polynomial .)
neuper@37950	415
neuper@37950	416	open Term; (* for type order = EQUAL \| LESS \| GREATER *)
neuper@37950	417
neuper@37950	418	fun pr_ord EQUAL = "EQUAL"
neuper@37950	419	\| pr_ord LESS = "LESS"
neuper@37950	420	\| pr_ord GREATER = "GREATER";
neuper@37950	421
neuper@37950	422	fun dest_hd' (Const (a, T)) = (* ~ term.ML *)
neuper@37950	423	(case a of
neuper@37950	424	"Atools.pow" => ((("\|\|\|\|\|\|\|\|\|\|\|\|\|", 0), T), 0) (WN greatest string)
neuper@37950	425	\| _ => (((a, 0), T), 0))
neuper@37950	426	\| dest_hd' (Free (a, T)) = (((a, 0), T), 1)
neuper@37950	427	\| dest_hd' (Var v) = (v, 2)
neuper@37950	428	\| dest_hd' (Bound i) = ((("", i), dummyT), 3)
neuper@37950	429	\| dest_hd' (Abs (_, T, _)) = ((("", 0), T), 4);
neuper@37950	430
neuper@37950	431	fun get_order_pow (t $ (Free(order,_))) = (* RL FIXXXME:geht zufaellig?WN*)
neuper@37950	432	(case int_of_str (order) of
neuper@37950	433	SOME d => d
neuper@37950	434	\| NONE => 0)
neuper@37950	435	\| get_order_pow _ = 0;
neuper@37950	436
neuper@37950	437	fun size_of_term' (Const(str,_) $ t) =
neuper@37950	438	if "Atools.pow"= str then 1000 + size_of_term' t else 1+size_of_term' t(WN)
neuper@37950	439	\| size_of_term' (Abs (_,_,body)) = 1 + size_of_term' body
neuper@37950	440	\| size_of_term' (f$t) = size_of_term' f + size_of_term' t
neuper@37950	441	\| size_of_term' _ = 1;
neuper@37950	442
neuper@37950	443	fun term_ord' pr thy (Abs (_, T, t), Abs(_, U, u)) = (* ~ term.ML *)
neuper@52070	444	(case term_ord' pr thy (t, u) of EQUAL => Term_Ord.typ_ord (T, U) \| ord => ord)
neuper@37950	445	\| term_ord' pr thy (t, u) =
neuper@52070	446	(if pr then
neuper@52070	447	let
neuper@52070	448	val (f, ts) = strip_comb t and (g, us) = strip_comb u;
neuper@52070	449	val _ = tracing ("t= f@ts= \"" ^ term_to_string''' thy f ^ "\" @ \"[" ^
neuper@52070	450	commas (map (term_to_string''' thy) ts) ^ "]\"");
neuper@52070	451	val _ = tracing("u= g@us= \"" ^ term_to_string''' thy g ^ "\" @ \"[" ^
neuper@52070	452	commas (map (term_to_string''' thy) us) ^ "]\"");
neuper@52070	453	val _ = tracing ("size_of_term(t,u)= (" ^ string_of_int (size_of_term' t) ^ ", " ^
neuper@52070	454	string_of_int (size_of_term' u) ^ ")");
neuper@52070	455	val _ = tracing ("hd_ord(f,g) = " ^ (pr_ord o hd_ord) (f,g));
neuper@52070	456	val _ = tracing ("terms_ord(ts,us) = " ^ (pr_ord o terms_ord str false) (ts, us));
neuper@52070	457	val _ = tracing ("-------");
neuper@52070	458	in () end
neuper@37950	459	else ();
neuper@37950	460	case int_ord (size_of_term' t, size_of_term' u) of
neuper@37950	461	EQUAL =>
neuper@37950	462	let val (f, ts) = strip_comb t and (g, us) = strip_comb u in
neuper@37950	463	(case hd_ord (f, g) of EQUAL => (terms_ord str pr) (ts, us)
neuper@37950	464	\| ord => ord)
neuper@37950	465	end
neuper@37950	466	\| ord => ord)
neuper@37950	467	and hd_ord (f, g) = (* ~ term.ML *)
neuper@37974	468	prod_ord (prod_ord Term_Ord.indexname_ord Term_Ord.typ_ord) int_ord (dest_hd' f, dest_hd' g)
neuper@37950	469	and terms_ord str pr (ts, us) =
neuper@37991	470	list_ord (term_ord' pr (assoc_thy "Isac"))(ts, us);
neuper@52070	471
neuper@37950	472	in
neuper@37950	473
neuper@37950	474	fun ord_make_polynomial (pr:bool) thy (_:subst) tu =
neuper@37950	475	(term_ord' pr thy(***) tu = LESS );
neuper@37950	476
neuper@37950	477	end;(local)
neuper@37950	478
neuper@37950	479
neuper@37950	480	rew_ord' := overwritel (!rew_ord',
neuper@37950	481	[("termlessI", termlessI),
neuper@37950	482	("ord_make_polynomial", ord_make_polynomial false thy)
neuper@37950	483	]);
neuper@37950	484
neuper@37950	485
neuper@37950	486	val expand =
neuper@37974	487	Rls{id = "expand", preconds = [], rew_ord = ("dummy_ord", dummy_ord),
neuper@42451	488	erls = e_rls,srls = Erls, calc = [], errpatts = [],
neuper@52062	489	rules = [Thm ("distrib_right" ,num_str @{thm distrib_right}),
neuper@37950	490	("(z1.0 + z2.0) w = z1.0 * w + z2.0 * w"*)
neuper@52062	491	Thm ("distrib_left",num_str @{thm distrib_left})
neuper@37950	492	("w (z1.0 + z2.0) = w * z1.0 + w * z2.0"*)
neuper@37950	493	], scr = EmptyScr}:rls;
neuper@37950	494
neuper@37950	495	(*----------------- Begin: rulesets for make_polynomial_ -----------------
neuper@37950	496	'rlsIDs' redefined by MG as 'rlsIDs_'
neuper@37950	497	^^^*)
neuper@37950	498
neuper@37980	499	val discard_minus =
neuper@42407	500	Rls {id = "discard_minus", preconds = [], rew_ord = ("dummy_ord", dummy_ord),
neuper@42451	501	erls = e_rls, srls = Erls, calc = [], errpatts = [],
neuper@42407	502	rules =
neuper@42407	503	[Thm ("real_diff_minus", num_str @{thm real_diff_minus}),
neuper@42407	504	("a - b = a + -1 b"*)
neuper@42407	505	Thm ("sym_real_mult_minus1", num_str (@{thm real_mult_minus1} RS @{thm sym}))
neuper@42407	506	(- ?z = "-1 ?z"*)],
neuper@42407	507	scr = EmptyScr}:rls;
neuper@37980	508
neuper@37950	509	val expand_poly_ =
neuper@37950	510	Rls{id = "expand_poly_", preconds = [],
neuper@37950	511	rew_ord = ("dummy_ord", dummy_ord),
neuper@37950	512	erls = e_rls,srls = Erls,
neuper@42451	513	calc = [], errpatts = [],
neuper@42407	514	rules =
neuper@42407	515	[Thm ("real_plus_binom_pow4",num_str @{thm real_plus_binom_pow4}),
neuper@42407	516	("(a + b)^^^4 = ... ")
neuper@42407	517	Thm ("real_plus_binom_pow5",num_str @{thm real_plus_binom_pow5}),
neuper@42407	518	("(a + b)^^^5 = ... ")
neuper@42407	519	Thm ("real_plus_binom_pow3",num_str @{thm real_plus_binom_pow3}),
neuper@42407	520	("(a + b)^^^3 = a^^^3 + 3a^^^2b + 3ab^^^2 + b^^^3" )
neuper@42407	521	(WN071229 changed/removed for Schaerding -----vvv)
neuper@42407	522	(Thm ("real_plus_binom_pow2",num_str @{thm real_plus_binom_pow2}),)
neuper@42407	523	("(a + b)^^^2 = a^^^2 + 2ab + b^^^2")
neuper@42407	524	Thm ("real_plus_binom_pow2",num_str @{thm real_plus_binom_pow2}),
neuper@42407	525	("(a + b)^^^2 = (a + b) (a + b)"*)
neuper@42407	526	(Thm ("real_plus_minus_binom1_p_p", num_str @{thm real_plus_minus_binom1_p_p}),)
neuper@42407	527	("(a + b)(a + -1 * b) = a^^^2 + -1b^^^2")
neuper@42407	528	(Thm ("real_plus_minus_binom2_p_p", num_str @{thm real_plus_minus_binom2_p_p}),)
neuper@42407	529	("(a + -1 b)(a + b) = a^^^2 + -1b^^^2"*)
neuper@42407	530	(WN071229 changed/removed for Schaerding -----^^^)
neuper@37950	531
neuper@52062	532	Thm ("distrib_right" ,num_str @{thm distrib_right}),
neuper@42407	533	("(z1.0 + z2.0) w = z1.0 * w + z2.0 * w"*)
neuper@52062	534	Thm ("distrib_left",num_str @{thm distrib_left}),
neuper@42407	535	("w (z1.0 + z2.0) = w * z1.0 + w * z2.0"*)
neuper@37950	536
neuper@42407	537	Thm ("realpow_multI", num_str @{thm realpow_multI}),
neuper@42407	538	("(r s) ^^^ n = r ^^^ n * s ^^^ n"*)
neuper@42407	539	Thm ("realpow_pow",num_str @{thm realpow_pow})
neuper@42407	540	("(a ^^^ b) ^^^ c = a ^^^ (b c)"*)
neuper@37950	541	], scr = EmptyScr}:rls;
neuper@37950	542
neuper@37950	543	(.the expression contains + - ^ only ?
neuper@37950	544	this is weaker than 'is_polynomial' !.*)
neuper@37950	545	fun is_polyexp (Free _) = true
neuper@38014	546	\| is_polyexp (Const ("Groups.plus_class.plus",_) $ Free _ $ Free _) = true
neuper@38014	547	\| is_polyexp (Const ("Groups.minus_class.minus",_) $ Free _ $ Free _) = true
neuper@38034	548	\| is_polyexp (Const ("Groups.times_class.times",_) $ Free _ $ Free _) = true
neuper@37950	549	\| is_polyexp (Const ("Atools.pow",_) $ Free _ $ Free _) = true
neuper@38014	550	\| is_polyexp (Const ("Groups.plus_class.plus",_) $ t1 $ t2) =
neuper@37950	551	((is_polyexp t1) andalso (is_polyexp t2))
neuper@38014	552	\| is_polyexp (Const ("Groups.minus_class.minus",_) $ t1 $ t2) =
neuper@37950	553	((is_polyexp t1) andalso (is_polyexp t2))
neuper@38034	554	\| is_polyexp (Const ("Groups.times_class.times",_) $ t1 $ t2) =
neuper@37950	555	((is_polyexp t1) andalso (is_polyexp t2))
neuper@37950	556	\| is_polyexp (Const ("Atools.pow",_) $ t1 $ t2) =
neuper@37950	557	((is_polyexp t1) andalso (is_polyexp t2))
neuper@37950	558	\| is_polyexp _ = false;
neuper@37950	559
neuper@37950	560	(("is_polyexp", ("Poly.is'_polyexp", eval_is_polyexp "")))
neuper@37950	561	fun eval_is_polyexp (thmid:string) _
neuper@37950	562	(t as (Const("Poly.is'_polyexp", _) $ arg)) thy =
neuper@37950	563	if is_polyexp arg
neuper@52070	564	then SOME (mk_thmid thmid "" (term_to_string''' thy arg) "",
neuper@52070	565	Trueprop $ (mk_equality (t, @{term True})))
neuper@52070	566	else SOME (mk_thmid thmid "" (term_to_string''' thy arg) "",
neuper@52070	567	Trueprop $ (mk_equality (t, @{term False})))
neuper@37950	568	\| eval_is_polyexp _ _ _ _ = NONE;
neuper@37950	569
neuper@37950	570	val expand_poly_rat_ =
neuper@37950	571	Rls{id = "expand_poly_rat_", preconds = [],
neuper@37950	572	rew_ord = ("dummy_ord", dummy_ord),
neuper@37950	573	erls = append_rls "e_rls-is_polyexp" e_rls
neuper@37950	574	[Calc ("Poly.is'_polyexp", eval_is_polyexp "")
neuper@37950	575	],
neuper@37950	576	srls = Erls,
neuper@42451	577	calc = [], errpatts = [],
neuper@37950	578	rules =
neuper@37969	579	[Thm ("real_plus_binom_pow4_poly", num_str @{thm real_plus_binom_pow4_poly}),
neuper@37950	580	("[\| a is_polyexp; b is_polyexp \|] ==> (a + b)^^^4 = ... ")
neuper@37969	581	Thm ("real_plus_binom_pow5_poly", num_str @{thm real_plus_binom_pow5_poly}),
neuper@37950	582	("[\| a is_polyexp; b is_polyexp \|] ==> (a + b)^^^5 = ... ")
neuper@37969	583	Thm ("real_plus_binom_pow2_poly",num_str @{thm real_plus_binom_pow2_poly}),
neuper@37950	584	(*"[\| a is_polyexp; b is_polyexp \|] ==>
neuper@37950	585	(a + b)^^^2 = a^^^2 + 2ab + b^^^2"*)
neuper@37969	586	Thm ("real_plus_binom_pow3_poly",num_str @{thm real_plus_binom_pow3_poly}),
neuper@37950	587	(*"[\| a is_polyexp; b is_polyexp \|] ==>
neuper@37950	588	(a + b)^^^3 = a^^^3 + 3a^^^2b + 3ab^^^2 + b^^^3" *)
neuper@37969	589	Thm ("real_plus_minus_binom1_p_p",num_str @{thm real_plus_minus_binom1_p_p}),
neuper@37950	590	("(a + b)(a + -1 * b) = a^^^2 + -1b^^^2")
neuper@37969	591	Thm ("real_plus_minus_binom2_p_p",num_str @{thm real_plus_minus_binom2_p_p}),
neuper@37950	592	("(a + -1 b)(a + b) = a^^^2 + -1b^^^2"*)
neuper@37950	593
neuper@37974	594	Thm ("real_add_mult_distrib_poly",
neuper@37974	595	num_str @{thm real_add_mult_distrib_poly}),
neuper@37950	596	("w is_polyexp ==> (z1.0 + z2.0) w = z1.0 * w + z2.0 * w"*)
neuper@37974	597	Thm("real_add_mult_distrib2_poly",
neuper@37974	598	num_str @{thm real_add_mult_distrib2_poly}),
neuper@37950	599	("w is_polyexp ==> w (z1.0 + z2.0) = w * z1.0 + w * z2.0"*)
neuper@37950	600
neuper@37969	601	Thm ("realpow_multI_poly", num_str @{thm realpow_multI_poly}),
neuper@37950	602	(*"[\| r is_polyexp; s is_polyexp \|] ==>
neuper@37950	603	(r * s) ^^^ n = r ^^^ n * s ^^^ n"*)
neuper@37969	604	Thm ("realpow_pow",num_str @{thm realpow_pow})
neuper@37950	605	("(a ^^^ b) ^^^ c = a ^^^ (b c)"*)
neuper@37950	606	], scr = EmptyScr}:rls;
neuper@37950	607
neuper@37950	608	val simplify_power_ =
neuper@37950	609	Rls{id = "simplify_power_", preconds = [],
neuper@37950	610	rew_ord = ("dummy_ord", dummy_ord),
neuper@37950	611	erls = e_rls, srls = Erls,
neuper@42451	612	calc = [], errpatts = [],
neuper@37950	613	rules = [(*MG: Reihenfolge der folgenden 2 Thm muss so bleiben, wegen
neuper@37950	614	a(aa) --> aa^^^2 und nicht a(aa) --> a^^^2a *)
neuper@37969	615	Thm ("sym_realpow_twoI",
neuper@37969	616	num_str (@{thm realpow_twoI} RS @{thm sym})),
neuper@37950	617	("r r = r ^^^ 2"*)
neuper@37969	618	Thm ("realpow_twoI_assoc_l",num_str @{thm realpow_twoI_assoc_l}),
neuper@37950	619	("r (r * s) = r ^^^ 2 * s"*)
neuper@37950	620
neuper@37969	621	Thm ("realpow_plus_1",num_str @{thm realpow_plus_1}),
neuper@37950	622	("r r ^^^ n = r ^^^ (n + 1)"*)
neuper@37969	623	Thm ("realpow_plus_1_assoc_l",
neuper@37969	624	num_str @{thm realpow_plus_1_assoc_l}),
neuper@37950	625	("r (r ^^^ m * s) = r ^^^ (1 + m) * s"*)
neuper@37950	626	(MG 9.7.03: neues Thm wegen a(a(ab)) --> a^^^2(ab) *)
neuper@37969	627	Thm ("realpow_plus_1_assoc_l2",
neuper@37969	628	num_str @{thm realpow_plus_1_assoc_l2}),
neuper@37950	629	("r ^^^ m (r * s) = r ^^^ (1 + m) * s"*)
neuper@37950	630
neuper@37969	631	Thm ("sym_realpow_addI",
neuper@37969	632	num_str (@{thm realpow_addI} RS @{thm sym})),
neuper@37950	633	("r ^^^ n r ^^^ m = r ^^^ (n + m)"*)
neuper@37969	634	Thm ("realpow_addI_assoc_l",num_str @{thm realpow_addI_assoc_l}),
neuper@37950	635	("r ^^^ n (r ^^^ m * s) = r ^^^ (n + m) * s"*)
neuper@37950	636
neuper@37950	637	(* ist in expand_poly - wird hier aber auch gebraucht, wegen:
neuper@37950	638	"r * r = r ^^^ 2" wenn r=a^^^b*)
neuper@37969	639	Thm ("realpow_pow",num_str @{thm realpow_pow})
neuper@37950	640	("(a ^^^ b) ^^^ c = a ^^^ (b c)"*)
neuper@37950	641	], scr = EmptyScr}:rls;
neuper@37950	642
neuper@37950	643	val calc_add_mult_pow_ =
neuper@37950	644	Rls{id = "calc_add_mult_pow_", preconds = [],
neuper@37950	645	rew_ord = ("dummy_ord", dummy_ord),
neuper@37950	646	erls = Atools_erls(erls3.4.03),srls = Erls,
neuper@38014	647	calc = [("PLUS" , ("Groups.plus_class.plus", eval_binop "#add_")),
neuper@38034	648	("TIMES" , ("Groups.times_class.times", eval_binop "#mult_")),
neuper@37950	649	("POWER", ("Atools.pow", eval_binop "#power_"))
neuper@37950	650	],
neuper@42451	651	errpatts = [],
neuper@38014	652	rules = [Calc ("Groups.plus_class.plus", eval_binop "#add_"),
neuper@38034	653	Calc ("Groups.times_class.times", eval_binop "#mult_"),
neuper@37950	654	Calc ("Atools.pow", eval_binop "#power_")
neuper@37950	655	], scr = EmptyScr}:rls;
neuper@37950	656
neuper@37950	657	val reduce_012_mult_ =
neuper@37950	658	Rls{id = "reduce_012_mult_", preconds = [],
neuper@37950	659	rew_ord = ("dummy_ord", dummy_ord),
neuper@37950	660	erls = e_rls,srls = Erls,
neuper@42451	661	calc = [], errpatts = [],
neuper@37950	662	rules = [(* MG: folgende Thm müssen hier stehen bleiben: *)
neuper@37965	663	Thm ("mult_1_right",num_str @{thm mult_1_right}),
neuper@37950	664	("z 1 = z") (wegen "a * b * b^^^(-1) + a"*)
neuper@37969	665	Thm ("realpow_zeroI",num_str @{thm realpow_zeroI}),
neuper@37950	666	("r ^^^ 0 = 1") (wegen "aa^^^(-1)c + b + c")
neuper@37969	667	Thm ("realpow_oneI",num_str @{thm realpow_oneI}),
neuper@37950	668	("r ^^^ 1 = r")
neuper@37974	669	Thm ("realpow_eq_oneI",num_str @{thm realpow_eq_oneI})
neuper@37950	670	("1 ^^^ n = 1")
neuper@37950	671	], scr = EmptyScr}:rls;
neuper@37950	672
neuper@37950	673	val collect_numerals_ =
neuper@37950	674	Rls{id = "collect_numerals_", preconds = [],
neuper@37950	675	rew_ord = ("dummy_ord", dummy_ord),
neuper@37950	676	erls = Atools_erls, srls = Erls,
neuper@38014	677	calc = [("PLUS" , ("Groups.plus_class.plus", eval_binop "#add_"))
neuper@42451	678	], errpatts = [],
neuper@37950	679	rules =
neuper@37969	680	[Thm ("real_num_collect",num_str @{thm real_num_collect}),
neuper@37950	681	("[\| l is_const; m is_const \|]==>l n + m * n = (l + m) * n"*)
neuper@37969	682	Thm ("real_num_collect_assoc_r",num_str @{thm real_num_collect_assoc_r}),
neuper@37950	683	(*"[\| l is_const; m is_const \|] ==> \
neuper@37950	684	\(k + m * n) + l * n = k + (l + m)n")
neuper@37969	685	Thm ("real_one_collect",num_str @{thm real_one_collect}),
neuper@37950	686	("m is_const ==> n + m n = (1 + m) * n"*)
neuper@37969	687	Thm ("real_one_collect_assoc_r",num_str @{thm real_one_collect_assoc_r}),
neuper@37950	688	("m is_const ==> (k + n) + m n = k + (m + 1) * n"*)
neuper@37950	689
neuper@38014	690	Calc ("Groups.plus_class.plus", eval_binop "#add_"),
neuper@37950	691
neuper@37950	692	(*MG: Reihenfolge der folgenden 2 Thm muss so bleiben, wegen
neuper@37950	693	(a+a)+a --> a + 2a --> 3a and not (a+a)+a --> 2a + a )
neuper@37969	694	Thm ("real_mult_2_assoc_r",num_str @{thm real_mult_2_assoc_r}),
neuper@37950	695	("(k + z1) + z1 = k + 2 z1"*)
neuper@37969	696	Thm ("sym_real_mult_2",num_str (@{thm real_mult_2} RS @{thm sym}))
neuper@37950	697	("z1 + z1 = 2 z1"*)
neuper@37950	698	], scr = EmptyScr}:rls;
neuper@37950	699
neuper@37950	700	val reduce_012_ =
neuper@37950	701	Rls{id = "reduce_012_", preconds = [],
neuper@37950	702	rew_ord = ("dummy_ord", dummy_ord),
neuper@42451	703	erls = e_rls,srls = Erls, calc = [], errpatts = [],
neuper@37965	704	rules = [Thm ("mult_1_left",num_str @{thm mult_1_left}),
neuper@37950	705	("1 z = z"*)
neuper@37965	706	Thm ("mult_zero_left",num_str @{thm mult_zero_left}),
neuper@37950	707	("0 z = 0"*)
neuper@37974	708	Thm ("mult_zero_right",num_str @{thm mult_zero_right}),
neuper@37950	709	("z 0 = 0"*)
neuper@37965	710	Thm ("add_0_left",num_str @{thm add_0_left}),
neuper@37950	711	("0 + z = z")
neuper@37965	712	Thm ("add_0_right",num_str @{thm add_0_right}),
neuper@37950	713	("z + 0 = z") (wegen a+b-b --> a+(1-1)b --> a+0 --> a*)
neuper@37950	714
neuper@37969	715	(Thm ("realpow_oneI",num_str @{thm realpow_oneI}))
neuper@37950	716	("?r ^^^ 1 = ?r")
neuper@37965	717	Thm ("divide_zero_left",num_str @{thm divide_zero_left})(WN060914)
neuper@37950	718	("0 / ?x = 0")
neuper@37950	719	], scr = EmptyScr}:rls;
neuper@37950	720
neuper@37979	721	val discard_parentheses1 =
neuper@37979	722	append_rls "discard_parentheses1" e_rls
neuper@48763	723	[Thm ("sym_mult_assoc",
neuper@48763	724	num_str (@{thm mult_assoc} RS @{thm sym}))
neuper@37950	725	("?z1.1 (?z2.1 * ?z3.1) = ?z1.1 * ?z2.1 * ?z3.1"*)
neuper@37974	726	(*Thm ("sym_add_assoc",
neuper@37974	727	num_str (@{thm add_assoc} RS @{thm sym}))*)
neuper@37950	728	("?z1.1 + (?z2.1 + ?z3.1) = ?z1.1 + ?z2.1 + ?z3.1")
neuper@37950	729	];
neuper@37950	730
neuper@37950	731	(----------------- End: rulesets for make_polynomial_ -----------------)
neuper@37950	732
neuper@37950	733	(*MG.0401 ev. for use in rls with ordered rewriting ?
neuper@37950	734	val collect_numerals_left =
neuper@37950	735	Rls{id = "collect_numerals", preconds = [],
neuper@37950	736	rew_ord = ("dummy_ord", dummy_ord),
neuper@37950	737	erls = Atools_erls(erls3.4.03),srls = Erls,
neuper@38014	738	calc = [("PLUS" , ("Groups.plus_class.plus", eval_binop "#add_")),
neuper@38034	739	("TIMES" , ("Groups.times_class.times", eval_binop "#mult_")),
neuper@37950	740	("POWER", ("Atools.pow", eval_binop "#power_"))
neuper@37950	741	],
neuper@42451	742	errpatts = [],
neuper@37969	743	rules = [Thm ("real_num_collect",num_str @{thm real_num_collect}),
neuper@37950	744	("[\| l is_const; m is_const \|]==>l n + m * n = (l + m) * n"*)
neuper@37969	745	Thm ("real_num_collect_assoc",num_str @{thm real_num_collect_assoc}),
neuper@37950	746	(*"[\| l is_const; m is_const \|] ==>
neuper@37950	747	l * n + (m * n + k) = (l + m) * n + k"*)
neuper@37969	748	Thm ("real_one_collect",num_str @{thm real_one_collect}),
neuper@37950	749	("m is_const ==> n + m n = (1 + m) * n"*)
neuper@37969	750	Thm ("real_one_collect_assoc",num_str @{thm real_one_collect_assoc}),
neuper@37950	751	("m is_const ==> n + (m n + k) = (1 + m) * n + k"*)
neuper@37950	752
neuper@38014	753	Calc ("Groups.plus_class.plus", eval_binop "#add_"),
neuper@37950	754
neuper@37950	755	(MG am 2.5.03: 2 Theoreme aus reduce_012 hierher verschoben)
neuper@37969	756	Thm ("sym_real_mult_2",
neuper@37969	757	num_str (@{thm real_mult_2} RS @{thm sym})),
neuper@37950	758	("z1 + z1 = 2 z1"*)
neuper@37969	759	Thm ("real_mult_2_assoc",num_str @{thm real_mult_2_assoc})
neuper@37950	760	("z1 + (z1 + k) = 2 z1 + k"*)
neuper@37950	761	], scr = EmptyScr}:rls;*)
neuper@37950	762
neuper@37950	763	val expand_poly =
neuper@37950	764	Rls{id = "expand_poly", preconds = [],
neuper@37950	765	rew_ord = ("dummy_ord", dummy_ord),
neuper@37950	766	erls = e_rls,srls = Erls,
neuper@42451	767	calc = [], errpatts = [],
neuper@37950	768	(asm_thm = [],)
neuper@52062	769	rules = [Thm ("distrib_right" ,num_str @{thm distrib_right}),
neuper@37950	770	("(z1.0 + z2.0) w = z1.0 * w + z2.0 * w"*)
neuper@52062	771	Thm ("distrib_left",num_str @{thm distrib_left}),
neuper@37950	772	("w (z1.0 + z2.0) = w * z1.0 + w * z2.0"*)
neuper@52062	773	(*Thm ("distrib_right1",num_str @{thm distrib_right}1),
neuper@37950	774	....... 18.3.03 undefined???*)
neuper@37950	775
neuper@37969	776	Thm ("real_plus_binom_pow2",num_str @{thm real_plus_binom_pow2}),
neuper@37950	777	("(a + b)^^^2 = a^^^2 + 2ab + b^^^2")
neuper@37969	778	Thm ("real_minus_binom_pow2_p",num_str @{thm real_minus_binom_pow2_p}),
neuper@37950	779	("(a - b)^^^2 = a^^^2 + -2ab + b^^^2")
neuper@37950	780	Thm ("real_plus_minus_binom1_p",
neuper@37969	781	num_str @{thm real_plus_minus_binom1_p}),
neuper@37950	782	("(a + b)(a - b) = a^^^2 + -1b^^^2")
neuper@37950	783	Thm ("real_plus_minus_binom2_p",
neuper@37969	784	num_str @{thm real_plus_minus_binom2_p}),
neuper@37950	785	("(a - b)(a + b) = a^^^2 + -1b^^^2")
neuper@37950	786
neuper@37965	787	Thm ("minus_minus",num_str @{thm minus_minus}),
neuper@37950	788	("- (- ?z) = ?z")
neuper@37969	789	Thm ("real_diff_minus",num_str @{thm real_diff_minus}),
neuper@37950	790	("a - b = a + -1 b"*)
neuper@37969	791	Thm ("sym_real_mult_minus1",
neuper@37969	792	num_str (@{thm real_mult_minus1} RS @{thm sym}))
neuper@37950	793	(- ?z = "-1 ?z"*)
neuper@37950	794
neuper@37950	795	(*Thm ("real_minus_add_distrib",
neuper@37969	796	num_str @{thm real_minus_add_distrib}),*)
neuper@37950	797	("- (?x + ?y) = - ?x + - ?y")
neuper@37969	798	(Thm ("real_diff_plus",num_str @{thm real_diff_plus}))
neuper@37950	799	("a - b = a + -b")
neuper@37950	800	], scr = EmptyScr}:rls;
neuper@37950	801
neuper@37950	802	val simplify_power =
neuper@37950	803	Rls{id = "simplify_power", preconds = [],
neuper@37950	804	rew_ord = ("dummy_ord", dummy_ord),
neuper@37950	805	erls = e_rls, srls = Erls,
neuper@42451	806	calc = [], errpatts = [],
neuper@37969	807	rules = [Thm ("realpow_multI", num_str @{thm realpow_multI}),
neuper@37950	808	("(r s) ^^^ n = r ^^^ n * s ^^^ n"*)
neuper@37950	809
neuper@37969	810	Thm ("sym_realpow_twoI",
neuper@37969	811	num_str( @{thm realpow_twoI} RS @{thm sym})),
neuper@37950	812	("r1 r1 = r1 ^^^ 2"*)
neuper@37969	813	Thm ("realpow_plus_1",num_str @{thm realpow_plus_1}),
neuper@37950	814	("r r ^^^ n = r ^^^ (n + 1)"*)
neuper@37969	815	Thm ("realpow_pow",num_str @{thm realpow_pow}),
neuper@37950	816	("(a ^^^ b) ^^^ c = a ^^^ (b c)"*)
neuper@37969	817	Thm ("sym_realpow_addI",
neuper@37969	818	num_str (@{thm realpow_addI} RS @{thm sym})),
neuper@37950	819	("r ^^^ n r ^^^ m = r ^^^ (n + m)"*)
neuper@37969	820	Thm ("realpow_oneI",num_str @{thm realpow_oneI}),
neuper@37950	821	("r ^^^ 1 = r")
neuper@37969	822	Thm ("realpow_eq_oneI",num_str @{thm realpow_eq_oneI})
neuper@37950	823	("1 ^^^ n = 1")
neuper@37950	824	], scr = EmptyScr}:rls;
neuper@37950	825	(*MG.0401: termorders for multivariate polys dropped due to principal problems:
neuper@37950	826	(total-degree-)ordering of monoms NOT possible with size_of_term GIVEN*)
neuper@37950	827	val order_add_mult =
neuper@37950	828	Rls{id = "order_add_mult", preconds = [],
neuper@37972	829	rew_ord = ("ord_make_polynomial",ord_make_polynomial false thy),
neuper@37950	830	erls = e_rls,srls = Erls,
neuper@42451	831	calc = [], errpatts = [],
neuper@48763	832	rules = [Thm ("mult_commute",num_str @{thm mult_commute}),
neuper@37950	833	(* z * w = w * z *)
neuper@37969	834	Thm ("real_mult_left_commute",num_str @{thm real_mult_left_commute}),
neuper@37950	835	(z1.0 (z2.0 * z3.0) = z2.0 * (z1.0 * z3.0)*)
neuper@48763	836	Thm ("mult_assoc",num_str @{thm mult_assoc}),
neuper@37950	837	(z1.0 z2.0 * z3.0 = z1.0 * (z2.0 * z3.0)*)
neuper@37965	838	Thm ("add_commute",num_str @{thm add_commute}),
neuper@37950	839	(z + w = w + z)
neuper@37965	840	Thm ("add_left_commute",num_str @{thm add_left_commute}),
neuper@37950	841	(x + (y + z) = y + (x + z))
neuper@37965	842	Thm ("add_assoc",num_str @{thm add_assoc})
neuper@37950	843	(z1.0 + z2.0 + z3.0 = z1.0 + (z2.0 + z3.0))
neuper@37950	844	], scr = EmptyScr}:rls;
neuper@37950	845	(*MG.0401: termorders for multivariate polys dropped due to principal problems:
neuper@37950	846	(total-degree-)ordering of monoms NOT possible with size_of_term GIVEN*)
neuper@37950	847	val order_mult =
neuper@37950	848	Rls{id = "order_mult", preconds = [],
neuper@37972	849	rew_ord = ("ord_make_polynomial",ord_make_polynomial false thy),
neuper@37950	850	erls = e_rls,srls = Erls,
neuper@42451	851	calc = [], errpatts = [],
neuper@48763	852	rules = [Thm ("mult_commute",num_str @{thm mult_commute}),
neuper@37950	853	(* z * w = w * z *)
neuper@37969	854	Thm ("real_mult_left_commute",num_str @{thm real_mult_left_commute}),
neuper@37950	855	(z1.0 (z2.0 * z3.0) = z2.0 * (z1.0 * z3.0)*)
neuper@48763	856	Thm ("mult_assoc",num_str @{thm mult_assoc})
neuper@37950	857	(z1.0 z2.0 * z3.0 = z1.0 * (z2.0 * z3.0)*)
neuper@37950	858	], scr = EmptyScr}:rls;
neuper@42451	859	*}
neuper@42451	860
neuper@42451	861	ML {*
neuper@37950	862	val collect_numerals =
neuper@37950	863	Rls{id = "collect_numerals", preconds = [],
neuper@37950	864	rew_ord = ("dummy_ord", dummy_ord),
neuper@37950	865	erls = Atools_erls(erls3.4.03),srls = Erls,
neuper@38014	866	calc = [("PLUS" , ("Groups.plus_class.plus", eval_binop "#add_")),
neuper@38034	867	("TIMES" , ("Groups.times_class.times", eval_binop "#mult_")),
neuper@37950	868	("POWER", ("Atools.pow", eval_binop "#power_"))
neuper@42451	869	], errpatts = [],
neuper@37969	870	rules = [Thm ("real_num_collect",num_str @{thm real_num_collect}),
neuper@37950	871	("[\| l is_const; m is_const \|]==>l n + m * n = (l + m) * n"*)
neuper@37969	872	Thm ("real_num_collect_assoc",num_str @{thm real_num_collect_assoc}),
neuper@37950	873	(*"[\| l is_const; m is_const \|] ==>
neuper@37950	874	l * n + (m * n + k) = (l + m) * n + k"*)
neuper@37969	875	Thm ("real_one_collect",num_str @{thm real_one_collect}),
neuper@37950	876	("m is_const ==> n + m n = (1 + m) * n"*)
neuper@37969	877	Thm ("real_one_collect_assoc",num_str @{thm real_one_collect_assoc}),
neuper@37950	878	("m is_const ==> k + (n + m n) = k + (1 + m) * n"*)
neuper@38014	879	Calc ("Groups.plus_class.plus", eval_binop "#add_"),
neuper@38034	880	Calc ("Groups.times_class.times", eval_binop "#mult_"),
neuper@37950	881	Calc ("Atools.pow", eval_binop "#power_")
neuper@37950	882	], scr = EmptyScr}:rls;
neuper@37950	883	val reduce_012 =
neuper@37950	884	Rls{id = "reduce_012", preconds = [],
neuper@37950	885	rew_ord = ("dummy_ord", dummy_ord),
neuper@37950	886	erls = e_rls,srls = Erls,
neuper@42451	887	calc = [], errpatts = [],
neuper@37965	888	rules = [Thm ("mult_1_left",num_str @{thm mult_1_left}),
neuper@37950	889	("1 z = z"*)
neuper@37969	890	(Thm ("real_mult_minus1",num_str @{thm real_mult_minus1}),14.3.03)
neuper@37950	891	("-1 z = - z"*)
neuper@37965	892	Thm ("minus_mult_left",
neuper@37974	893	num_str (@{thm minus_mult_left} RS @{thm sym})),
neuper@37950	894	(- (?x ?y) = "- ?x * ?y"*)
neuper@37969	895	(*Thm ("real_minus_mult_cancel",
neuper@37969	896	num_str @{thm real_minus_mult_cancel}),
neuper@37950	897	("- ?x - ?y = ?x * ?y")---)
neuper@37965	898	Thm ("mult_zero_left",num_str @{thm mult_zero_left}),
neuper@37950	899	("0 z = 0"*)
neuper@37965	900	Thm ("add_0_left",num_str @{thm add_0_left}),
neuper@37950	901	("0 + z = z")
neuper@37965	902	Thm ("right_minus",num_str @{thm right_minus}),
neuper@37950	903	("?z + - ?z = 0")
neuper@37969	904	Thm ("sym_real_mult_2",
neuper@37969	905	num_str (@{thm real_mult_2} RS @{thm sym})),
neuper@37950	906	("z1 + z1 = 2 z1"*)
neuper@37969	907	Thm ("real_mult_2_assoc",num_str @{thm real_mult_2_assoc})
neuper@37950	908	("z1 + (z1 + k) = 2 z1 + k"*)
neuper@37950	909	], scr = EmptyScr}:rls;
neuper@52139	910
neuper@37950	911	val discard_parentheses =
neuper@37950	912	append_rls "discard_parentheses" e_rls
neuper@48763	913	[Thm ("sym_mult_assoc",
neuper@48763	914	num_str (@{thm mult_assoc} RS @{thm sym})),
neuper@37974	915	Thm ("sym_add_assoc",
neuper@37974	916	num_str (@{thm add_assoc} RS @{thm sym}))];
neuper@37950	917
neuper@37950	918	val scr_make_polynomial =
neuper@37976	919	"Script Expand_binoms t_t = " ^
neuper@37950	920	"(Repeat " ^
neuper@37950	921	"((Try (Repeat (Rewrite real_diff_minus False))) @@ " ^
neuper@37950	922
neuper@52062	923	" (Try (Repeat (Rewrite distrib_right False))) @@ " ^
neuper@52062	924	" (Try (Repeat (Rewrite distrib_left False))) @@ " ^
neuper@37971	925	" (Try (Repeat (Rewrite left_diff_distrib False))) @@ " ^
neuper@37971	926	" (Try (Repeat (Rewrite right_diff_distrib False))) @@ " ^
neuper@37950	927
neuper@37971	928	" (Try (Repeat (Rewrite mult_1_left False))) @@ " ^
neuper@37971	929	" (Try (Repeat (Rewrite mult_zero_left False))) @@ " ^
neuper@37971	930	" (Try (Repeat (Rewrite add_0_left False))) @@ " ^
neuper@37950	931
neuper@48763	932	" (Try (Repeat (Rewrite mult_commute False))) @@ " ^
neuper@37950	933	" (Try (Repeat (Rewrite real_mult_left_commute False))) @@ " ^
neuper@48763	934	" (Try (Repeat (Rewrite mult_assoc False))) @@ " ^
neuper@37971	935	" (Try (Repeat (Rewrite add_commute False))) @@ " ^
neuper@37971	936	" (Try (Repeat (Rewrite add_left_commute False))) @@ " ^
neuper@37971	937	" (Try (Repeat (Rewrite add_assoc False))) @@ " ^
neuper@37950	938
neuper@37950	939	" (Try (Repeat (Rewrite sym_realpow_twoI False))) @@ " ^
neuper@37950	940	" (Try (Repeat (Rewrite realpow_plus_1 False))) @@ " ^
neuper@37950	941	" (Try (Repeat (Rewrite sym_real_mult_2 False))) @@ " ^
neuper@37950	942	" (Try (Repeat (Rewrite real_mult_2_assoc False))) @@ " ^
neuper@37950	943
neuper@37950	944	" (Try (Repeat (Rewrite real_num_collect False))) @@ " ^
neuper@37950	945	" (Try (Repeat (Rewrite real_num_collect_assoc False))) @@ " ^
neuper@37950	946
neuper@37950	947	" (Try (Repeat (Rewrite real_one_collect False))) @@ " ^
neuper@37950	948	" (Try (Repeat (Rewrite real_one_collect_assoc False))) @@ " ^
neuper@37950	949
neuper@37975	950	" (Try (Repeat (Calculate PLUS ))) @@ " ^
neuper@37975	951	" (Try (Repeat (Calculate TIMES ))) @@ " ^
neuper@37975	952	" (Try (Repeat (Calculate POWER)))) " ^
neuper@37976	953	" t_t)";
neuper@37950	954
neuper@37950	955	(*version used by MG.02/03, overwritten by version AG in 04 below
s1210629013@55444	956	val make_polynomial = prep_rls'(
neuper@37950	957	Seq{id = "make_polynomial", preconds = []:term list,
neuper@37950	958	rew_ord = ("dummy_ord", dummy_ord),
neuper@37950	959	erls = Atools_erls, srls = Erls,
neuper@42451	960	calc = [], errpatts = [],
neuper@37950	961	rules = [Rls_ expand_poly,
neuper@37950	962	Rls_ order_add_mult,
neuper@37950	963	Rls_ simplify_power, (realpow_eq_oneI, eg. x^1 --> x )
neuper@37950	964	Rls_ collect_numerals, (eg. x^(2+ -1) --> x^1 )
neuper@37950	965	Rls_ reduce_012,
neuper@37969	966	Thm ("realpow_oneI",num_str @{thm realpow_oneI}),(in --^)
neuper@37950	967	Rls_ discard_parentheses
neuper@37950	968	],
neuper@37950	969	scr = EmptyScr
neuper@37950	970	}:rls); *)
neuper@37950	971
neuper@37950	972	val scr_expand_binoms =
neuper@37974	973	"Script Expand_binoms t_t =" ^
neuper@37950	974	"(Repeat " ^
neuper@37950	975	"((Try (Repeat (Rewrite real_plus_binom_pow2 False))) @@ " ^
neuper@37950	976	" (Try (Repeat (Rewrite real_plus_binom_times False))) @@ " ^
neuper@37950	977	" (Try (Repeat (Rewrite real_minus_binom_pow2 False))) @@ " ^
neuper@37950	978	" (Try (Repeat (Rewrite real_minus_binom_times False))) @@ " ^
neuper@37950	979	" (Try (Repeat (Rewrite real_plus_minus_binom1 False))) @@ " ^
neuper@37950	980	" (Try (Repeat (Rewrite real_plus_minus_binom2 False))) @@ " ^
neuper@37950	981
neuper@37971	982	" (Try (Repeat (Rewrite mult_1_left False))) @@ " ^
neuper@37971	983	" (Try (Repeat (Rewrite mult_zero_left False))) @@ " ^
neuper@37971	984	" (Try (Repeat (Rewrite add_0_left False))) @@ " ^
neuper@37950	985
neuper@37975	986	" (Try (Repeat (Calculate PLUS ))) @@ " ^
neuper@37975	987	" (Try (Repeat (Calculate TIMES ))) @@ " ^
neuper@37975	988	" (Try (Repeat (Calculate POWER))) @@ " ^
neuper@37950	989
neuper@37950	990	" (Try (Repeat (Rewrite sym_realpow_twoI False))) @@ " ^
neuper@37950	991	" (Try (Repeat (Rewrite realpow_plus_1 False))) @@ " ^
neuper@37950	992	" (Try (Repeat (Rewrite sym_real_mult_2 False))) @@ " ^
neuper@37950	993	" (Try (Repeat (Rewrite real_mult_2_assoc False))) @@ " ^
neuper@37950	994
neuper@37950	995	" (Try (Repeat (Rewrite real_num_collect False))) @@ " ^
neuper@37950	996	" (Try (Repeat (Rewrite real_num_collect_assoc False))) @@ " ^
neuper@37950	997
neuper@37950	998	" (Try (Repeat (Rewrite real_one_collect False))) @@ " ^
neuper@37950	999	" (Try (Repeat (Rewrite real_one_collect_assoc False))) @@ " ^
neuper@37950	1000
neuper@37975	1001	" (Try (Repeat (Calculate PLUS ))) @@ " ^
neuper@37975	1002	" (Try (Repeat (Calculate TIMES ))) @@ " ^
neuper@37975	1003	" (Try (Repeat (Calculate POWER)))) " ^
neuper@37974	1004	" t_t)";
neuper@37974	1005
neuper@37950	1006	val expand_binoms =
neuper@37950	1007	Rls{id = "expand_binoms", preconds = [], rew_ord = ("termlessI",termlessI),
neuper@37950	1008	erls = Atools_erls, srls = Erls,
neuper@38014	1009	calc = [("PLUS" , ("Groups.plus_class.plus", eval_binop "#add_")),
neuper@38034	1010	("TIMES" , ("Groups.times_class.times", eval_binop "#mult_")),
neuper@37950	1011	("POWER", ("Atools.pow", eval_binop "#power_"))
neuper@42451	1012	], errpatts = [],
neuper@37974	1013	rules = [Thm ("real_plus_binom_pow2",
neuper@37974	1014	num_str @{thm real_plus_binom_pow2}),
neuper@37950	1015	("(a + b) ^^^ 2 = a ^^^ 2 + 2 a * b + b ^^^ 2"*)
neuper@37974	1016	Thm ("real_plus_binom_times",
neuper@37974	1017	num_str @{thm real_plus_binom_times}),
neuper@37950	1018	("(a + b)(a + b) = ...*)
neuper@37974	1019	Thm ("real_minus_binom_pow2",
neuper@37974	1020	num_str @{thm real_minus_binom_pow2}),
neuper@37950	1021	("(a - b) ^^^ 2 = a ^^^ 2 - 2 a * b + b ^^^ 2"*)
neuper@37974	1022	Thm ("real_minus_binom_times",
neuper@37974	1023	num_str @{thm real_minus_binom_times}),
neuper@37950	1024	("(a - b)(a - b) = ...*)
neuper@37974	1025	Thm ("real_plus_minus_binom1",
neuper@37974	1026	num_str @{thm real_plus_minus_binom1}),
neuper@37950	1027	("(a + b) (a - b) = a ^^^ 2 - b ^^^ 2"*)
neuper@37974	1028	Thm ("real_plus_minus_binom2",
neuper@37974	1029	num_str @{thm real_plus_minus_binom2}),
neuper@37950	1030	("(a - b) (a + b) = a ^^^ 2 - b ^^^ 2"*)
neuper@37950	1031	(RL 020915)
neuper@37969	1032	Thm ("real_pp_binom_times",num_str @{thm real_pp_binom_times}),
neuper@37950	1033	((a + b)(c + d) = ac + ad + bc + bd*)
neuper@37969	1034	Thm ("real_pm_binom_times",num_str @{thm real_pm_binom_times}),
neuper@37950	1035	((a + b)(c - d) = ac - ad + bc - bd*)
neuper@37969	1036	Thm ("real_mp_binom_times",num_str @{thm real_mp_binom_times}),
neuper@37950	1037	((a - b)(c + d) = ac + ad - bc - bd*)
neuper@37969	1038	Thm ("real_mm_binom_times",num_str @{thm real_mm_binom_times}),
neuper@37950	1039	((a - b)(c - d) = ac - ad - bc + bd*)
neuper@37974	1040	Thm ("realpow_multI",num_str @{thm realpow_multI}),
neuper@37950	1041	((ab)^^^n = a^^^n * b^^^n*)
neuper@37969	1042	Thm ("real_plus_binom_pow3",num_str @{thm real_plus_binom_pow3}),
neuper@37950	1043	(* (a + b)^^^3 = a^^^3 + 3a^^^2b + 3ab^^^2 + b^^^3 *)
neuper@37974	1044	Thm ("real_minus_binom_pow3",
neuper@37974	1045	num_str @{thm real_minus_binom_pow3}),
neuper@37950	1046	(* (a - b)^^^3 = a^^^3 - 3a^^^2b + 3ab^^^2 - b^^^3 *)
neuper@37950	1047
neuper@37950	1048
neuper@52062	1049	(*Thm ("distrib_right" ,num_str @{thm distrib_right}),
neuper@37950	1050	("(z1.0 + z2.0) w = z1.0 * w + z2.0 * w"*)
neuper@52062	1051	Thm ("distrib_left",num_str @{thm distrib_left}),
neuper@37950	1052	("w (z1.0 + z2.0) = w * z1.0 + w * z2.0"*)
neuper@37965	1053	Thm ("left_diff_distrib" ,num_str @{thm left_diff_distrib}),
neuper@37950	1054	("(z1.0 - z2.0) w = z1.0 * w - z2.0 * w"*)
neuper@37982	1055	Thm ("right_diff_distrib",num_str @{thm right_diff_distrib}),
neuper@37950	1056	("w (z1.0 - z2.0) = w * z1.0 - w * z2.0"*)
neuper@37974	1057	*)
neuper@37974	1058	Thm ("mult_1_left",num_str @{thm mult_1_left}),
neuper@37974	1059	("1 z = z"*)
neuper@37974	1060	Thm ("mult_zero_left",num_str @{thm mult_zero_left}),
neuper@37974	1061	("0 z = 0"*)
neuper@37965	1062	Thm ("add_0_left",num_str @{thm add_0_left}),("0 + z = z")
neuper@37950	1063
neuper@38014	1064	Calc ("Groups.plus_class.plus", eval_binop "#add_"),
neuper@38034	1065	Calc ("Groups.times_class.times", eval_binop "#mult_"),
neuper@37950	1066	Calc ("Atools.pow", eval_binop "#power_"),
neuper@48763	1067	(*Thm ("mult_commute",num_str @{thm mult_commute}),
neuper@37974	1068	(AC-rewriting)
neuper@37974	1069	Thm ("real_mult_left_commute",
neuper@37974	1070	num_str @{thm real_mult_left_commute}),
neuper@48763	1071	Thm ("mult_assoc",num_str @{thm mult_assoc}),
neuper@37974	1072	Thm ("add_commute",num_str @{thm add_commute}),
neuper@37974	1073	Thm ("add_left_commute",num_str @{thm add_left_commute}),
neuper@37974	1074	Thm ("add_assoc",num_str @{thm add_assoc}),
neuper@37974	1075	*)
neuper@37969	1076	Thm ("sym_realpow_twoI",
neuper@37969	1077	num_str (@{thm realpow_twoI} RS @{thm sym})),
neuper@37950	1078	("r1 r1 = r1 ^^^ 2"*)
neuper@37969	1079	Thm ("realpow_plus_1",num_str @{thm realpow_plus_1}),
neuper@37950	1080	("r r ^^^ n = r ^^^ (n + 1)"*)
neuper@37974	1081	(*Thm ("sym_real_mult_2",
neuper@37974	1082	num_str (@{thm real_mult_2} RS @{thm sym})),
neuper@37950	1083	("z1 + z1 = 2 z1"))
neuper@37969	1084	Thm ("real_mult_2_assoc",num_str @{thm real_mult_2_assoc}),
neuper@37950	1085	("z1 + (z1 + k) = 2 z1 + k"*)
neuper@37950	1086
neuper@37969	1087	Thm ("real_num_collect",num_str @{thm real_num_collect}),
neuper@37974	1088	("[\| l is_const; m is_const \|] ==>l n + m * n = (l + m) * n"*)
neuper@37974	1089	Thm ("real_num_collect_assoc",
neuper@37974	1090	num_str @{thm real_num_collect_assoc}),
neuper@37974	1091	(*"[\| l is_const; m is_const \|] ==>
neuper@37974	1092	l * n + (m * n + k) = (l + m) * n + k"*)
neuper@37974	1093	Thm ("real_one_collect",num_str @{thm real_one_collect}),
neuper@37950	1094	("m is_const ==> n + m n = (1 + m) * n"*)
neuper@37974	1095	Thm ("real_one_collect_assoc",
neuper@37974	1096	num_str @{thm real_one_collect_assoc}),
neuper@37950	1097	("m is_const ==> k + (n + m n) = k + (1 + m) * n"*)
neuper@37950	1098
neuper@38014	1099	Calc ("Groups.plus_class.plus", eval_binop "#add_"),
neuper@38034	1100	Calc ("Groups.times_class.times", eval_binop "#mult_"),
neuper@37950	1101	Calc ("Atools.pow", eval_binop "#power_")
neuper@37950	1102	],
neuper@48763	1103	scr = Prog ((term_of o the o (parse thy)) scr_expand_binoms)
neuper@37950	1104	}:rls;
neuper@37950	1105
neuper@37950	1106
neuper@37950	1107	(. MG.03: make_polynomial_ ... uses SML-fun for ordering .)
neuper@37950	1108
neuper@37950	1109	(FIXME.0401: make SML-order local to make_polynomial(_) )
neuper@37950	1110	(FIXME.0401: replace 'make_polynomial'(old) by 'make_polynomial_'(MG) )
neuper@37950	1111	(* Polynom --> List von Monomen *)
neuper@38014	1112	fun poly2list (Const ("Groups.plus_class.plus",_) $ t1 $ t2) =
neuper@37950	1113	(poly2list t1) @ (poly2list t2)
neuper@37950	1114	\| poly2list t = [t];
neuper@37950	1115
neuper@37950	1116	(* Monom --> Liste von Variablen *)
neuper@38034	1117	fun monom2list (Const ("Groups.times_class.times",_) $ t1 $ t2) =
neuper@37950	1118	(monom2list t1) @ (monom2list t2)
neuper@37950	1119	\| monom2list t = [t];
neuper@37950	1120
neuper@37950	1121	(* liefert Variablenname (String) einer Variablen und Basis bei Potenz *)
neuper@37950	1122	fun get_basStr (Const ("Atools.pow",_) $ Free (str, _) $ _) = str
neuper@37950	1123	\| get_basStr (Free (str, _)) = str
neuper@37950	1124	\| get_basStr t = "\|\|\|"; (* gross gewichtet; für Brüch ect. *)
neuper@37950	1125	(*\| get_basStr t =
neuper@38031	1126	error("get_basStr: called with t= "^(term2str t));*)
neuper@37950	1127
neuper@37950	1128	(* liefert Hochzahl (String) einer Variablen bzw Gewichtstring (zum Sortieren) *)
neuper@37950	1129	fun get_potStr (Const ("Atools.pow",_) $ Free _ $ Free (str, _)) = str
neuper@37950	1130	\| get_potStr (Const ("Atools.pow",_) $ Free _ $ _ ) = "\|\|\|" (* gross gewichtet *)
neuper@37950	1131	\| get_potStr (Free (str, _)) = "---" (* keine Hochzahl --> kleinst gewichtet *)
neuper@37950	1132	\| get_potStr t = "\|\|\|\|\|\|"; (* gross gewichtet; für Brüch ect. *)
neuper@37950	1133	(*\| get_potStr t =
neuper@38031	1134	error("get_potStr: called with t= "^(term2str t));*)
neuper@37950	1135
neuper@37950	1136	(* Umgekehrte string_ord *)
neuper@37950	1137	val string_ord_rev = rev_order o string_ord;
neuper@37950	1138
neuper@37950	1139	(* Ordnung zum lexikographischen Vergleich zweier Variablen (oder Potenzen)
neuper@37950	1140	innerhalb eines Monomes:
neuper@37950	1141	- zuerst lexikographisch nach Variablenname
neuper@37950	1142	- wenn gleich: nach steigender Potenz *)
neuper@37950	1143	fun var_ord (a,b: term) = prod_ord string_ord string_ord
neuper@37950	1144	((get_basStr a, get_potStr a), (get_basStr b, get_potStr b));
neuper@37950	1145
neuper@37950	1146	(* Ordnung zum lexikographischen Vergleich zweier Variablen (oder Potenzen);
neuper@37950	1147	verwendet zum Sortieren von Monomen mittels Gesamtgradordnung:
neuper@37950	1148	- zuerst lexikographisch nach Variablenname
neuper@37950	1149	- wenn gleich: nach sinkender Potenz*)
neuper@37950	1150	fun var_ord_revPow (a,b: term) = prod_ord string_ord string_ord_rev
neuper@37950	1151	((get_basStr a, get_potStr a), (get_basStr b, get_potStr b));
neuper@37950	1152
neuper@37950	1153
neuper@37950	1154	(* Ordnet ein Liste von Variablen (und Potenzen) lexikographisch *)
neuper@37950	1155	val sort_varList = sort var_ord;
neuper@37950	1156
neuper@37950	1157	(* Entfernet aeussersten Operator (Wurzel) aus einem Term und schreibt
neuper@37950	1158	Argumente in eine Liste *)
neuper@37950	1159	fun args u : term list =
neuper@37950	1160	let fun stripc (f$t, ts) = stripc (f, t::ts)
neuper@37950	1161	\| stripc (t as Free _, ts) = (t::ts)
neuper@37950	1162	\| stripc (_, ts) = ts
neuper@37950	1163	in stripc (u, []) end;
neuper@37950	1164
neuper@37950	1165	(* liefert True, falls der Term (Liste von Termen) nur Zahlen
neuper@37950	1166	(keine Variablen) enthaelt *)
neuper@37950	1167	fun filter_num [] = true
neuper@37950	1168	\| filter_num [Free x] = if (is_num (Free x)) then true
neuper@37950	1169	else false
neuper@37950	1170	\| filter_num ((Free _)::_) = false
neuper@37950	1171	\| filter_num ts =
neuper@37950	1172	(filter_num o (filter_out is_num) o flat o (map args)) ts;
neuper@37950	1173
neuper@37950	1174	(* liefert True, falls der Term nur Zahlen (keine Variablen) enthaelt
neuper@37950	1175	dh. er ist ein numerischer Wert und entspricht einem Koeffizienten *)
neuper@37950	1176	fun is_nums t = filter_num [t];
neuper@37950	1177
neuper@37950	1178	(* Berechnet den Gesamtgrad eines Monoms *)
neuper@37950	1179	local
neuper@37950	1180	fun counter (n, []) = n
neuper@37950	1181	\| counter (n, x :: xs) =
neuper@37950	1182	if (is_nums x) then
neuper@37950	1183	counter (n, xs)
neuper@37950	1184	else
neuper@37950	1185	(case x of
neuper@37950	1186	(Const ("Atools.pow", _) $ Free (str_b, _) $ Free (str_h, T)) =>
neuper@37950	1187	if (is_nums (Free (str_h, T))) then
neuper@37950	1188	counter (n + (the (int_of_str str_h)), xs)
neuper@37950	1189	else counter (n + 1000, xs) (FIXME.MG?!)
neuper@37950	1190	\| (Const ("Atools.pow", _) $ Free (str_b, _) $ _ ) =>
neuper@37950	1191	counter (n + 1000, xs) (FIXME.MG?!)
neuper@37950	1192	\| (Free (str, _)) => counter (n + 1, xs)
neuper@38031	1193	(\| _ => error("monom_degree: called with factor: "^(term2str x))))
neuper@37950	1194	\| _ => counter (n + 10000, xs)) (FIXME.MG?! ... Brüche ect.)
neuper@37950	1195	in
neuper@37950	1196	fun monom_degree l = counter (0, l)
neuper@37980	1197	end;(local)
neuper@37950	1198
neuper@37950	1199	(* wie Ordnung dict_ord (lexicographische Ordnung zweier Listen, mit Vergleich
neuper@37950	1200	der Listen-Elemente mit elem_ord) - Elemente die Bedingung cond erfuellen,
neuper@37950	1201	werden jedoch dabei ignoriert (uebersprungen) *)
neuper@37950	1202	fun dict_cond_ord _ _ ([], []) = EQUAL
neuper@37950	1203	\| dict_cond_ord _ _ ([], _ :: _) = LESS
neuper@37950	1204	\| dict_cond_ord _ _ (_ :: _, []) = GREATER
neuper@37950	1205	\| dict_cond_ord elem_ord cond (x :: xs, y :: ys) =
neuper@37950	1206	(case (cond x, cond y) of
neuper@37950	1207	(false, false) => (case elem_ord (x, y) of
neuper@37950	1208	EQUAL => dict_cond_ord elem_ord cond (xs, ys)
neuper@37950	1209	\| ord => ord)
neuper@37950	1210	\| (false, true) => dict_cond_ord elem_ord cond (x :: xs, ys)
neuper@37950	1211	\| (true, false) => dict_cond_ord elem_ord cond (xs, y :: ys)
neuper@37950	1212	\| (true, true) => dict_cond_ord elem_ord cond (xs, ys) );
neuper@37950	1213
neuper@37950	1214	(* Gesamtgradordnung zum Vergleich von Monomen (Liste von Variablen/Potenzen):
neuper@37950	1215	zuerst nach Gesamtgrad, bei gleichem Gesamtgrad lexikographisch ordnen -
neuper@37950	1216	dabei werden Koeffizienten ignoriert (23a^^^24b gilt wie a^^^2b) )
neuper@37950	1217	fun degree_ord (xs, ys) =
neuper@37950	1218	prod_ord int_ord (dict_cond_ord var_ord_revPow is_nums)
neuper@37950	1219	((monom_degree xs, xs), (monom_degree ys, ys));
neuper@37950	1220
neuper@37950	1221	fun hd_str str = substring (str, 0, 1);
neuper@37950	1222	fun tl_str str = substring (str, 1, (size str) - 1);
neuper@37950	1223
neuper@37950	1224	(* liefert nummerischen Koeffizienten eines Monoms oder NONE *)
neuper@38031	1225	fun get_koeff_of_mon [] = error("get_koeff_of_mon: called with l = []")
neuper@37950	1226	\| get_koeff_of_mon (l as x::xs) = if is_nums x then SOME x
neuper@37950	1227	else NONE;
neuper@37950	1228
neuper@37950	1229	(* wandelt Koeffizient in (zum sortieren geeigneten) String um *)
neuper@37950	1230	fun koeff2ordStr (SOME x) = (case x of
neuper@37950	1231	(Free (str, T)) =>
neuper@37950	1232	if (hd_str str) = "-" then (tl_str str)^"0" (* 3 < -3 *)
neuper@37950	1233	else str
neuper@37950	1234	\| _ => "aaa") (* "num.Ausdruck" --> gross *)
neuper@37950	1235	\| koeff2ordStr NONE = "---"; (* "kein Koeff" --> kleinste *)
neuper@37950	1236
neuper@37950	1237	(* Order zum Vergleich von Koeffizienten (strings):
neuper@37950	1238	"kein Koeff" < "0" < "1" < "-1" < "2" < "-2" < ... < "num.Ausdruck" *)
neuper@37950	1239	fun compare_koeff_ord (xs, ys) =
neuper@37950	1240	string_ord ((koeff2ordStr o get_koeff_of_mon) xs,
neuper@37950	1241	(koeff2ordStr o get_koeff_of_mon) ys);
neuper@37950	1242
neuper@37950	1243	(* Gesamtgradordnung degree_ord + Ordnen nach Koeffizienten falls EQUAL *)
neuper@37950	1244	fun koeff_degree_ord (xs, ys) =
neuper@37950	1245	prod_ord degree_ord compare_koeff_ord ((xs, xs), (ys, ys));
neuper@37950	1246
neuper@37950	1247	(* Ordnet ein Liste von Monomen (Monom = Liste von Variablen) mittels
neuper@37950	1248	Gesamtgradordnung *)
neuper@37950	1249	val sort_monList = sort koeff_degree_ord;
neuper@37950	1250
neuper@37950	1251	(* Alternativ zu degree_ord koennte auch die viel einfachere und
neuper@37950	1252	kuerzere Ordnung simple_ord verwendet werden - ist aber nicht
neuper@37950	1253	fuer unsere Zwecke geeignet!
neuper@37950	1254
neuper@37950	1255	fun simple_ord (al,bl: term list) = dict_ord string_ord
neuper@37950	1256	(map get_basStr al, map get_basStr bl);
neuper@37950	1257
neuper@37950	1258	val sort_monList = sort simple_ord; *)
neuper@37950	1259
neuper@37950	1260	(* aus 2 Variablen wird eine Summe bzw ein Produkt erzeugt
neuper@37950	1261	(mit gewuenschtem Typen T) *)
neuper@38014	1262	fun plus T = Const ("Groups.plus_class.plus", [T,T] ---> T);
neuper@38034	1263	fun mult T = Const ("Groups.times_class.times", [T,T] ---> T);
neuper@37950	1264	fun binop op_ t1 t2 = op_ $ t1 $ t2;
neuper@37950	1265	fun create_prod T (a,b) = binop (mult T) a b;
neuper@37950	1266	fun create_sum T (a,b) = binop (plus T) a b;
neuper@37950	1267
neuper@37950	1268	(* löscht letztes Element einer Liste *)
neuper@37950	1269	fun drop_last l = take ((length l)-1,l);
neuper@37950	1270
neuper@37950	1271	(* Liste von Variablen --> Monom *)
neuper@37950	1272	fun create_monom T vl = foldr (create_prod T) (drop_last vl, last_elem vl);
neuper@37950	1273	(* Bemerkung:
neuper@37950	1274	foldr bewirkt rechtslastige Klammerung des Monoms - ist notwendig, damit zwei
neuper@37950	1275	gleiche Monome zusammengefasst werden können (collect_numerals)!
neuper@37950	1276	zB: 2(x(yz)) + 3(x(yz)) --> (2+3)(x(yz)))
neuper@37950	1277
neuper@37950	1278	(* Liste von Monomen --> Polynom *)
neuper@37950	1279	fun create_polynom T ml = foldl (create_sum T) (hd ml, tl ml);
neuper@37950	1280	(* Bemerkung:
neuper@37950	1281	foldl bewirkt linkslastige Klammerung des Polynoms (der Summanten) -
neuper@37950	1282	bessere Darstellung, da keine Klammern sichtbar!
neuper@37950	1283	(und discard_parentheses in make_polynomial hat weniger zu tun) *)
neuper@37950	1284
neuper@37950	1285	(* sorts the variables (faktors) of an expanded polynomial lexicographical *)
neuper@37950	1286	fun sort_variables t =
neuper@37950	1287	let
neuper@37950	1288	val ll = map monom2list (poly2list t);
neuper@37950	1289	val lls = map sort_varList ll;
neuper@37950	1290	val T = type_of t;
neuper@37950	1291	val ls = map (create_monom T) lls;
neuper@37950	1292	in create_polynom T ls end;
neuper@37950	1293
neuper@37950	1294	(* sorts the monoms of an expanded and variable-sorted polynomial
neuper@37950	1295	by total_degree *)
neuper@37950	1296	fun sort_monoms t =
neuper@37950	1297	let
neuper@37950	1298	val ll = map monom2list (poly2list t);
neuper@37950	1299	val lls = sort_monList ll;
neuper@37950	1300	val T = type_of t;
neuper@37950	1301	val ls = map (create_monom T) lls;
neuper@37950	1302	in create_polynom T ls end;
neuper@37950	1303
neuper@37950	1304	(* auch Klammerung muss übereinstimmen;
neuper@37950	1305	sort_variables klammert Produkte rechtslastig*)
neuper@37950	1306	fun is_multUnordered t = ((is_polyexp t) andalso not (t = sort_variables t));
neuper@37950	1307
neuper@42451	1308	*}
neuper@42451	1309	ML {*
neuper@37950	1310	fun eval_is_multUnordered (thmid:string) _
neuper@37950	1311	(t as (Const("Poly.is'_multUnordered", _) $ arg)) thy =
neuper@37950	1312	if is_multUnordered arg
neuper@52070	1313	then SOME (mk_thmid thmid "" (term_to_string''' thy arg) "",
neuper@52070	1314	Trueprop $ (mk_equality (t, @{term True})))
neuper@52070	1315	else SOME (mk_thmid thmid "" (term_to_string''' thy arg) "",
neuper@52070	1316	Trueprop $ (mk_equality (t, @{term False})))
neuper@37950	1317	\| eval_is_multUnordered _ _ _ _ = NONE;
neuper@37950	1318
neuper@37950	1319	fun attach_form (_:rule list list) (_:term) (_:term) = (still missing)
neuper@37950	1320	[]:(rule * (term * term list)) list;
neuper@37950	1321	fun init_state (_:term) = e_rrlsstate;
neuper@37950	1322	fun locate_rule (_:rule list list) (_:term) (_:rule) =
neuper@37950	1323	([]:(rule * (term * term list)) list);
neuper@37950	1324	fun next_rule (_:rule list list) (_:term) = (NONE:rule option);
neuper@37950	1325	fun normal_form t = SOME (sort_variables t,[]:term list);
neuper@37950	1326
neuper@37950	1327	val order_mult_ =
neuper@37950	1328	Rrls {id = "order_mult_",
neuper@37950	1329	prepat =
neuper@38036	1330	(* ?p matched with the current term gives an environment,
neuper@38037	1331	which evaluates (the instantiated) "?p is_multUnordered" to true *)
neuper@38037	1332	[([parse_patt thy "?p is_multUnordered"],
neuper@38037	1333	parse_patt thy "?p :: real")],
neuper@37950	1334	rew_ord = ("dummy_ord", dummy_ord),
neuper@38037	1335	erls = append_rls "e_rls-is_multUnordered" e_rls
neuper@37976	1336	[Calc ("Poly.is'_multUnordered",
neuper@37976	1337	eval_is_multUnordered "")],
neuper@38036	1338	calc = [("PLUS" , ("Groups.plus_class.plus", eval_binop "#add_")),
neuper@38036	1339	("TIMES" , ("Groups.times_class.times", eval_binop "#mult_")),
neuper@48789	1340	("DIVIDE", ("Fields.inverse_class.divide",
neuper@38036	1341	eval_cancel "#divide_e")),
neuper@37976	1342	("POWER" , ("Atools.pow", eval_binop "#power_"))],
neuper@42451	1343	errpatts = [],
neuper@37950	1344	scr=Rfuns {init_state = init_state,
neuper@37950	1345	normal_form = normal_form,
neuper@37950	1346	locate_rule = locate_rule,
neuper@37950	1347	next_rule = next_rule,
neuper@37950	1348	attach_form = attach_form}};
neuper@37950	1349	val order_mult_rls_ =
neuper@37950	1350	Rls{id = "order_mult_rls_", preconds = [],
neuper@37950	1351	rew_ord = ("dummy_ord", dummy_ord),
neuper@37950	1352	erls = e_rls,srls = Erls,
neuper@42451	1353	calc = [], errpatts = [],
neuper@37950	1354	rules = [Rls_ order_mult_
neuper@37950	1355	], scr = EmptyScr}:rls;
neuper@42451	1356	*}
neuper@42451	1357	ML {*
neuper@37950	1358
neuper@37950	1359	fun is_addUnordered t = ((is_polyexp t) andalso not (t = sort_monoms t));
neuper@37950	1360
neuper@37950	1361	(WN.18.6.03 )
neuper@37950	1362	(("is_addUnordered", ("Poly.is'_addUnordered", eval_is_addUnordered "")))
neuper@37950	1363	fun eval_is_addUnordered (thmid:string) _
neuper@37950	1364	(t as (Const("Poly.is'_addUnordered", _) $ arg)) thy =
neuper@37950	1365	if is_addUnordered arg
neuper@52070	1366	then SOME (mk_thmid thmid "" (term_to_string''' thy arg) "",
neuper@52070	1367	Trueprop $ (mk_equality (t, @{term True})))
neuper@52070	1368	else SOME (mk_thmid thmid "" (term_to_string''' thy arg) "",
neuper@52070	1369	Trueprop $ (mk_equality (t, @{term False})))
neuper@37950	1370	\| eval_is_addUnordered _ _ _ _ = NONE;
neuper@37950	1371
neuper@37950	1372	fun attach_form (_:rule list list) (_:term) (_:term) = (still missing)
neuper@37950	1373	[]:(rule * (term * term list)) list;
neuper@37950	1374	fun init_state (_:term) = e_rrlsstate;
neuper@37950	1375	fun locate_rule (_:rule list list) (_:term) (_:rule) =
neuper@37950	1376	([]:(rule * (term * term list)) list);
neuper@37950	1377	fun next_rule (_:rule list list) (_:term) = (NONE:rule option);
neuper@37950	1378	fun normal_form t = SOME (sort_monoms t,[]:term list);
neuper@37950	1379
neuper@37950	1380	val order_add_ =
neuper@37950	1381	Rrls {id = "order_add_",
neuper@37950	1382	prepat = (*WN.18.6.03 Preconditions und Pattern,
neuper@37950	1383	die beide passen muessen, damit das Rrls angewandt wird*)
neuper@38037	1384	[([parse_patt @{theory} "?p is_addUnordered"],
neuper@38037	1385	parse_patt @{theory} "?p :: real"
neuper@37950	1386	(*WN.18.6.03 also KEIN pattern, dieses erzeugt nur das Environment
neuper@37950	1387	fuer die Evaluation der Precondition "p is_addUnordered"*))],
neuper@37950	1388	rew_ord = ("dummy_ord", dummy_ord),
neuper@37950	1389	erls = append_rls "e_rls-is_addUnordered" e_rls(MG: poly_erls)
neuper@38037	1390	[Calc ("Poly.is'_addUnordered",
neuper@38037	1391	eval_is_addUnordered "")],
neuper@38037	1392	calc = [("PLUS" ,("Groups.plus_class.plus", eval_binop "#add_")),
neuper@38037	1393	("TIMES" ,("Groups.times_class.times", eval_binop "#mult_")),
neuper@48789	1394	("DIVIDE",("Fields.inverse_class.divide",
neuper@38037	1395	eval_cancel "#divide_e")),
neuper@38037	1396	("POWER" ,("Atools.pow" ,eval_binop "#power_"))],
neuper@42451	1397	errpatts = [],
neuper@37950	1398	scr=Rfuns {init_state = init_state,
neuper@37950	1399	normal_form = normal_form,
neuper@37950	1400	locate_rule = locate_rule,
neuper@37950	1401	next_rule = next_rule,
neuper@37950	1402	attach_form = attach_form}};
neuper@37950	1403
neuper@37950	1404	val order_add_rls_ =
neuper@37950	1405	Rls{id = "order_add_rls_", preconds = [],
neuper@37950	1406	rew_ord = ("dummy_ord", dummy_ord),
neuper@37950	1407	erls = e_rls,srls = Erls,
neuper@42451	1408	calc = [], errpatts = [],
neuper@37950	1409	rules = [Rls_ order_add_
neuper@37950	1410	], scr = EmptyScr}:rls;
neuper@42398	1411	*}
neuper@37950	1412
neuper@42398	1413	text {* rule-set make_polynomial also named norm_Poly:
neuper@42398	1414	Rewrite order has not been implemented properly; the order is better in
neuper@42398	1415	make_polynomial_in (coded in SML).
neuper@42398	1416	Notes on state of development:
neuper@42398	1417	\# surprise 2006: test --- norm_Poly NOT COMPLETE ---
neuper@42398	1418	\# migration Isabelle2002 --> 2011 weakened the rule set, see test
neuper@42398	1419	--- Matthias Goldgruber 2003 rewrite orders ---, error "ord_make_polynomial_in #16b"
neuper@42398	1420	*}
neuper@42398	1421	ML {*
neuper@37950	1422	(. see MG-DA.p.52ff .)
neuper@37950	1423	val make_polynomial(*MG.03, overwrites version from above,
neuper@37950	1424	previously 'make_polynomial_'*) =
neuper@37950	1425	Seq {id = "make_polynomial", preconds = []:term list,
neuper@37950	1426	rew_ord = ("dummy_ord", dummy_ord),
neuper@42451	1427	erls = Atools_erls, srls = Erls,calc = [], errpatts = [],
neuper@37980	1428	rules = [Rls_ discard_minus,
neuper@37950	1429	Rls_ expand_poly_,
neuper@38034	1430	Calc ("Groups.times_class.times", eval_binop "#mult_"),
neuper@37950	1431	Rls_ order_mult_rls_,
neuper@37950	1432	Rls_ simplify_power_,
neuper@37950	1433	Rls_ calc_add_mult_pow_,
neuper@37950	1434	Rls_ reduce_012_mult_,
neuper@37950	1435	Rls_ order_add_rls_,
neuper@37950	1436	Rls_ collect_numerals_,
neuper@37950	1437	Rls_ reduce_012_,
neuper@37979	1438	Rls_ discard_parentheses1
neuper@37950	1439	],
neuper@37950	1440	scr = EmptyScr
neuper@37950	1441	}:rls;
neuper@48763	1442	*}
neuper@48763	1443	ML {*
neuper@37950	1444	val norm_Poly(=make_polynomial) =
neuper@37950	1445	Seq {id = "norm_Poly", preconds = []:term list,
neuper@37950	1446	rew_ord = ("dummy_ord", dummy_ord),
neuper@42451	1447	erls = Atools_erls, srls = Erls, calc = [], errpatts = [],
neuper@37980	1448	rules = [Rls_ discard_minus,
neuper@37950	1449	Rls_ expand_poly_,
neuper@38034	1450	Calc ("Groups.times_class.times", eval_binop "#mult_"),
neuper@37950	1451	Rls_ order_mult_rls_,
neuper@37950	1452	Rls_ simplify_power_,
neuper@37950	1453	Rls_ calc_add_mult_pow_,
neuper@37950	1454	Rls_ reduce_012_mult_,
neuper@37950	1455	Rls_ order_add_rls_,
neuper@37950	1456	Rls_ collect_numerals_,
neuper@37950	1457	Rls_ reduce_012_,
neuper@37979	1458	Rls_ discard_parentheses1
neuper@37950	1459	],
neuper@37950	1460	scr = EmptyScr
neuper@37950	1461	}:rls;
neuper@48763	1462	*}
neuper@48763	1463	ML {*
neuper@37979	1464	(* MG:03 Like make_polynomial_ but without Rls_ discard_parentheses1
neuper@37950	1465	and expand_poly_rat_ instead of expand_poly_, see MG-DA.p.56ff*)
neuper@37950	1466	(* MG necessary for termination of norm_Rational(_mg) in Rational.ML*)
neuper@37950	1467	val make_rat_poly_with_parentheses =
neuper@37950	1468	Seq{id = "make_rat_poly_with_parentheses", preconds = []:term list,
neuper@37950	1469	rew_ord = ("dummy_ord", dummy_ord),
neuper@42451	1470	erls = Atools_erls, srls = Erls, calc = [], errpatts = [],
neuper@37980	1471	rules = [Rls_ discard_minus,
neuper@37950	1472	Rls_ expand_poly_rat_,(ignors rationals)
neuper@38034	1473	Calc ("Groups.times_class.times", eval_binop "#mult_"),
neuper@37950	1474	Rls_ order_mult_rls_,
neuper@37950	1475	Rls_ simplify_power_,
neuper@37950	1476	Rls_ calc_add_mult_pow_,
neuper@37950	1477	Rls_ reduce_012_mult_,
neuper@37950	1478	Rls_ order_add_rls_,
neuper@37950	1479	Rls_ collect_numerals_,
neuper@37950	1480	Rls_ reduce_012_
neuper@37979	1481	(Rls_ discard_parentheses1 )
neuper@37950	1482	],
neuper@37950	1483	scr = EmptyScr
neuper@37950	1484	}:rls;
neuper@48763	1485	*}
neuper@48763	1486	ML {*
neuper@37950	1487	(*.a minimal ruleset for reverse rewriting of factions [2];
neuper@37950	1488	compare expand_binoms.*)
neuper@37950	1489	val rev_rew_p =
neuper@42407	1490	Seq{id = "rev_rew_p", preconds = [], rew_ord = ("termlessI",termlessI),
neuper@37950	1491	erls = Atools_erls, srls = Erls,
neuper@38014	1492	calc = [(*("PLUS" , ("Groups.plus_class.plus", eval_binop "#add_")),
neuper@38034	1493	("TIMES" , ("Groups.times_class.times", eval_binop "#mult_")),
neuper@37950	1494	("POWER", ("Atools.pow", eval_binop "#power_"))*)
neuper@42451	1495	], errpatts = [],
neuper@37969	1496	rules = [Thm ("real_plus_binom_times" ,num_str @{thm real_plus_binom_times}),
neuper@37950	1497	("(a + b)(a + b) = a ^ 2 + 2 * a * b + b ^ 2*)
neuper@37969	1498	Thm ("real_plus_binom_times1" ,num_str @{thm real_plus_binom_times1}),
neuper@37950	1499	("(a + 1b)(a + -1b) = a^^^2 + -1b^^^2")
neuper@37969	1500	Thm ("real_plus_binom_times2" ,num_str @{thm real_plus_binom_times2}),
neuper@37950	1501	("(a + -1b)(a + 1b) = a^^^2 + -1b^^^2")
neuper@37950	1502
neuper@37965	1503	Thm ("mult_1_left",num_str @{thm mult_1_left}),("1 z = z"*)
neuper@37950	1504
neuper@52062	1505	Thm ("distrib_right" ,num_str @{thm distrib_right}),
neuper@37950	1506	("(z1.0 + z2.0) w = z1.0 * w + z2.0 * w"*)
neuper@52062	1507	Thm ("distrib_left",num_str @{thm distrib_left}),
neuper@37950	1508	("w (z1.0 + z2.0) = w * z1.0 + w * z2.0"*)
neuper@37950	1509
neuper@48763	1510	Thm ("mult_assoc", num_str @{thm mult_assoc}),
neuper@37950	1511	("?z1.1 ?z2.1 * ?z3. =1 ?z1.1 * (?z2.1 * ?z3.1)"*)
neuper@37950	1512	Rls_ order_mult_rls_,
neuper@37950	1513	(Rls_ order_add_rls_,)
neuper@37950	1514
neuper@38014	1515	Calc ("Groups.plus_class.plus", eval_binop "#add_"),
neuper@38034	1516	Calc ("Groups.times_class.times", eval_binop "#mult_"),
neuper@37950	1517	Calc ("Atools.pow", eval_binop "#power_"),
neuper@37950	1518
neuper@37969	1519	Thm ("sym_realpow_twoI",
neuper@37969	1520	num_str (@{thm realpow_twoI} RS @{thm sym})),
neuper@37950	1521	("r1 r1 = r1 ^^^ 2"*)
neuper@37969	1522	Thm ("sym_real_mult_2",
neuper@37969	1523	num_str (@{thm real_mult_2} RS @{thm sym})),
neuper@37950	1524	("z1 + z1 = 2 z1"*)
neuper@37969	1525	Thm ("real_mult_2_assoc",num_str @{thm real_mult_2_assoc}),
neuper@37950	1526	("z1 + (z1 + k) = 2 z1 + k"*)
neuper@37950	1527
neuper@37969	1528	Thm ("real_num_collect",num_str @{thm real_num_collect}),
neuper@37950	1529	("[\| l is_const; m is_const \|]==>l n + m * n = (l + m) * n"*)
neuper@37969	1530	Thm ("real_num_collect_assoc",num_str @{thm real_num_collect_assoc}),
neuper@37950	1531	(*"[\| l is_const; m is_const \|] ==>
neuper@37950	1532	l * n + (m * n + k) = (l + m) * n + k"*)
neuper@37969	1533	Thm ("real_one_collect",num_str @{thm real_one_collect}),
neuper@37950	1534	("m is_const ==> n + m n = (1 + m) * n"*)
neuper@37969	1535	Thm ("real_one_collect_assoc",num_str @{thm real_one_collect_assoc}),
neuper@37950	1536	("m is_const ==> k + (n + m n) = k + (1 + m) * n"*)
neuper@37950	1537
neuper@37969	1538	Thm ("realpow_multI", num_str @{thm realpow_multI}),
neuper@37950	1539	("(r s) ^^^ n = r ^^^ n * s ^^^ n"*)
neuper@37950	1540
neuper@38014	1541	Calc ("Groups.plus_class.plus", eval_binop "#add_"),
neuper@38034	1542	Calc ("Groups.times_class.times", eval_binop "#mult_"),
neuper@37950	1543	Calc ("Atools.pow", eval_binop "#power_"),
neuper@37950	1544
neuper@37965	1545	Thm ("mult_1_left",num_str @{thm mult_1_left}),("1 z = z"*)
neuper@37965	1546	Thm ("mult_zero_left",num_str @{thm mult_zero_left}),("0 z = 0"*)
neuper@37965	1547	Thm ("add_0_left",num_str @{thm add_0_left})(0 + z = z)
neuper@37950	1548
neuper@37950	1549	(Rls_ order_add_rls_)
neuper@37950	1550	],
neuper@37950	1551
neuper@37950	1552	scr = EmptyScr}:rls;
neuper@48763	1553	*}
neuper@52125	1554
s1210629013@55444	1555	ML {* val prep_rls' = prep_rls @{theory} *}
s1210629013@55444	1556
neuper@52125	1557	setup {* KEStore_Elems.add_rlss
s1210629013@55444	1558	[("norm_Poly", (Context.theory_name @{theory}, prep_rls' norm_Poly)),
s1210629013@55444	1559	("Poly_erls", (Context.theory_name @{theory}, prep_rls' Poly_erls)),(FIXXXME:del with rls.rls')
s1210629013@55444	1560	("expand", (Context.theory_name @{theory}, prep_rls' expand)),
s1210629013@55444	1561	("expand_poly", (Context.theory_name @{theory}, prep_rls' expand_poly)),
s1210629013@55444	1562	("simplify_power", (Context.theory_name @{theory}, prep_rls' simplify_power)),
neuper@52125	1563
s1210629013@55444	1564	("order_add_mult", (Context.theory_name @{theory}, prep_rls' order_add_mult)),
s1210629013@55444	1565	("collect_numerals", (Context.theory_name @{theory}, prep_rls' collect_numerals)),
s1210629013@55444	1566	("collect_numerals_", (Context.theory_name @{theory}, prep_rls' collect_numerals_)),
s1210629013@55444	1567	("reduce_012", (Context.theory_name @{theory}, prep_rls' reduce_012)),
s1210629013@55444	1568	("discard_parentheses", (Context.theory_name @{theory}, prep_rls' discard_parentheses)),
neuper@52125	1569
s1210629013@55444	1570	("make_polynomial", (Context.theory_name @{theory}, prep_rls' make_polynomial)),
s1210629013@55444	1571	("expand_binoms", (Context.theory_name @{theory}, prep_rls' expand_binoms)),
s1210629013@55444	1572	("rev_rew_p", (Context.theory_name @{theory}, prep_rls' rev_rew_p)),
s1210629013@55444	1573	("discard_minus", (Context.theory_name @{theory}, prep_rls' discard_minus)),
s1210629013@55444	1574	("expand_poly_", (Context.theory_name @{theory}, prep_rls' expand_poly_)),
neuper@52125	1575
s1210629013@55444	1576	("expand_poly_rat_", (Context.theory_name @{theory}, prep_rls' expand_poly_rat_)),
s1210629013@55444	1577	("simplify_power_", (Context.theory_name @{theory}, prep_rls' simplify_power_)),
s1210629013@55444	1578	("calc_add_mult_pow_", (Context.theory_name @{theory}, prep_rls' calc_add_mult_pow_)),
s1210629013@55444	1579	("reduce_012_mult_", (Context.theory_name @{theory}, prep_rls' reduce_012_mult_)),
s1210629013@55444	1580	("reduce_012_", (Context.theory_name @{theory}, prep_rls' reduce_012_)),
neuper@52125	1581
s1210629013@55444	1582	("discard_parentheses1", (Context.theory_name @{theory}, prep_rls' discard_parentheses1)),
s1210629013@55444	1583	("order_mult_rls_", (Context.theory_name @{theory}, prep_rls' order_mult_rls_)),
s1210629013@55444	1584	("order_add_rls_", (Context.theory_name @{theory}, prep_rls' order_add_rls_)),
neuper@52125	1585	("make_rat_poly_with_parentheses",
s1210629013@55444	1586	(Context.theory_name @{theory}, prep_rls' make_rat_poly_with_parentheses))] *}
s1210629013@52145	1587	setup {* KEStore_Elems.add_calcs
s1210629013@52145	1588	[("is_polyrat_in", ("Poly.is'_polyrat'_in",
s1210629013@52145	1589	eval_is_polyrat_in "#eval_is_polyrat_in")),
s1210629013@52145	1590	("is_expanded_in", ("Poly.is'_expanded'_in", eval_is_expanded_in "")),
s1210629013@52145	1591	("is_poly_in", ("Poly.is'_poly'_in", eval_is_poly_in "")),
s1210629013@52145	1592	("has_degree_in", ("Poly.has'_degree'_in", eval_has_degree_in "")),
s1210629013@52145	1593	("is_polyexp", ("Poly.is'_polyexp", eval_is_polyexp "")),
s1210629013@52145	1594	("is_multUnordered", ("Poly.is'_multUnordered", eval_is_multUnordered"")),
s1210629013@52145	1595	("is_addUnordered", ("Poly.is'_addUnordered", eval_is_addUnordered ""))] *}
s1210629013@52145	1596
neuper@37950	1597	( problems )
s1210629013@55359	1598	setup {* KEStore_Elems.add_pbts
s1210629013@55339	1599	[(prep_pbt thy "pbl_simp_poly" [] e_pblID
s1210629013@55339	1600	(["polynomial","simplification"],
s1210629013@55339	1601	[("#Given" ,["Term t_t"]),
s1210629013@55339	1602	("#Where" ,["t_t is_polyexp"]),
s1210629013@55339	1603	("#Find" ,["normalform n_n"])],
s1210629013@55339	1604	append_rls "e_rls" e_rls [(for preds in where_)
s1210629013@55339	1605	Calc ("Poly.is'_polyexp", eval_is_polyexp "")],
s1210629013@55339	1606	SOME "Simplify t_t",
s1210629013@55339	1607	[["simplification","for_polynomials"]]))] *}
neuper@37950	1608	( methods )
s1210629013@55373	1609	setup {* KEStore_Elems.add_mets
s1210629013@55373	1610	[prep_met thy "met_simp_poly" [] e_metID
s1210629013@55373	1611	(["simplification","for_polynomials"],
s1210629013@55373	1612	[("#Given" ,["Term t_t"]),
s1210629013@55373	1613	("#Where" ,["t_t is_polyexp"]),
s1210629013@55373	1614	("#Find" ,["normalform n_n"])],
s1210629013@55373	1615	{rew_ord'="tless_true", rls' = e_rls, calc = [], srls = e_rls,
s1210629013@55373	1616	prls = append_rls "simplification_for_polynomials_prls" e_rls
s1210629013@55373	1617	[(for preds in where_)
s1210629013@55373	1618	Calc ("Poly.is'_polyexp",eval_is_polyexp"")],
s1210629013@55373	1619	crls = e_rls, errpats = [], nrls = norm_Poly},
s1210629013@55373	1620	"Script SimplifyScript (t_t::real) = " ^
s1210629013@55373	1621	" ((Rewrite_Set norm_Poly False) t_t)")]
s1210629013@55373	1622	*}
neuper@37950	1623
neuper@37906	1624	end

author	Mathias Lehnfeld <s1210629013@students.fh-hagenberg.at>
	Fri, 13 Jun 2014 10:29:06 +0200
changeset 55444	ede4248a827b
parent 55380	7be2ad0e4acb
child 59107	a65b5af1475f
permissions	-rw-r--r--