wneuper/isa: src/Tools/isac/Knowledge/Poly.thy@c0fe04973189 (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"
wneuper@59334	26	("((Script Expand'_binoms (_ =))// (_))" 9)
neuper@37906	27
neuper@37906	28	(-------------------- rules------------------------------------------------)
neuper@52148	29	axiomatization where (*.not contained in Isabelle2002,
neuper@37906	30	stated as axioms, TODO: prove as theorems;
neuper@37906	31	theorem-IDs 'xxxI' with ^^^ instead of ^ in 'xxx' in Isabelle2002.*)
neuper@37906	32
neuper@52148	33	realpow_pow: "(a ^^^ b) ^^^ c = a ^^^ (b * c)" and
neuper@52148	34	realpow_addI: "r ^^^ (n + m) = r ^^^ n * r ^^^ m" and
neuper@52148	35	realpow_addI_assoc_l: "r ^^^ n * (r ^^^ m * s) = r ^^^ (n + m) * s" and
neuper@52148	36	realpow_addI_assoc_r: "s * r ^^^ n * r ^^^ m = s * r ^^^ (n + m)" and
neuper@37906	37
neuper@52148	38	realpow_oneI: "r ^^^ 1 = r" and
neuper@52148	39	realpow_zeroI: "r ^^^ 0 = 1" and
neuper@52148	40	realpow_eq_oneI: "1 ^^^ n = 1" and
neuper@52148	41	realpow_multI: "(r * s) ^^^ n = r ^^^ n * s ^^^ n" and
neuper@37974	42	realpow_multI_poly: "[\| r is_polyexp; s is_polyexp \|] ==>
neuper@52148	43	(r * s) ^^^ n = r ^^^ n * s ^^^ n" and
wneuper@59189	44	realpow_minus_oneI: "(- 1) ^^^ (2 * n) = 1" and
neuper@37906	45
neuper@52148	46	realpow_twoI: "r ^^^ 2 = r * r" and
neuper@52148	47	realpow_twoI_assoc_l: "r * (r * s) = r ^^^ 2 * s" and
neuper@52148	48	realpow_twoI_assoc_r: "s * r * r = s * r ^^^ 2" and
neuper@52148	49	realpow_two_atom: "r is_atom ==> r * r = r ^^^ 2" and
neuper@52148	50	realpow_plus_1: "r * r ^^^ n = r ^^^ (n + 1)" and
neuper@52148	51	realpow_plus_1_assoc_l: "r * (r ^^^ m * s) = r ^^^ (1 + m) * s" and
neuper@52148	52	realpow_plus_1_assoc_l2: "r ^^^ m * (r * s) = r ^^^ (1 + m) * s" and
neuper@52148	53	realpow_plus_1_assoc_r: "s * r * r ^^^ m = s * r ^^^ (1 + m)" and
neuper@52148	54	realpow_plus_1_atom: "r is_atom ==> r * r ^^^ n = r ^^^ (1 + n)" and
neuper@37974	55	realpow_def_atom: "[\| Not (r is_atom); 1 < n \|]
neuper@52148	56	==> r ^^^ n = r * r ^^^ (n + -1)" and
neuper@52148	57	realpow_addI_atom: "r is_atom ==> r ^^^ n * r ^^^ m = r ^^^ (n + m)" and
neuper@37906	58
neuper@37906	59
neuper@52148	60	realpow_minus_even: "n is_even ==> (- r) ^^^ n = r ^^^ n" and
neuper@52148	61	realpow_minus_odd: "Not (n is_even) ==> (- r) ^^^ n = -1 * r ^^^ n" and
neuper@37906	62
neuper@37906	63
neuper@37906	64	(* RL 020914 *)
neuper@52148	65	real_pp_binom_times: "(a + b)(c + d) = ac + ad + bc + b*d" and
neuper@52148	66	real_pm_binom_times: "(a + b)(c - d) = ac - ad + bc - b*d" and
neuper@52148	67	real_mp_binom_times: "(a - b)(c + d) = ac + ad - bc - b*d" and
neuper@52148	68	real_mm_binom_times: "(a - b)(c - d) = ac - ad - bc + b*d" and
neuper@52148	69	real_plus_binom_pow3: "(a + b)^^^3 = a^^^3 + 3a^^^2b + 3ab^^^2 + b^^^3" and
neuper@37974	70	real_plus_binom_pow3_poly: "[\| a is_polyexp; b is_polyexp \|] ==>
neuper@52148	71	(a + b)^^^3 = a^^^3 + 3a^^^2b + 3ab^^^2 + b^^^3" and
neuper@52148	72	real_minus_binom_pow3: "(a - b)^^^3 = a^^^3 - 3a^^^2b + 3ab^^^2 - b^^^3" and
neuper@37974	73	real_minus_binom_pow3_p: "(a + -1 * b)^^^3 = a^^^3 + -3a^^^2b + 3ab^^^2 +
neuper@52148	74	-1*b^^^3" and
neuper@37974	75	(* real_plus_binom_pow: "[\| n is_const; 3 < n \|] ==>
neuper@37950	76	(a + b)^^^n = (a + b) * (a + b)^^^(n - 1)" *)
neuper@37974	77	real_plus_binom_pow4: "(a + b)^^^4 = (a^^^3 + 3a^^^2b + 3ab^^^2 + b^^^3)
neuper@52148	78	*(a + b)" and
neuper@37974	79	real_plus_binom_pow4_poly: "[\| a is_polyexp; b is_polyexp \|] ==>
neuper@37950	80	(a + b)^^^4 = (a^^^3 + 3a^^^2b + 3ab^^^2 + b^^^3)
neuper@52148	81	*(a + b)" and
neuper@37974	82	real_plus_binom_pow5: "(a + b)^^^5 = (a^^^3 + 3a^^^2b + 3ab^^^2 + b^^^3)
neuper@52148	83	(a^^^2 + 2a*b + b^^^2)" and
neuper@37974	84	real_plus_binom_pow5_poly: "[\| a is_polyexp; b is_polyexp \|] ==>
neuper@37950	85	(a + b)^^^5 = (a^^^3 + 3a^^^2b + 3ab^^^2
neuper@52148	86	+ b^^^3)(a^^^2 + 2a*b + b^^^2)" and
neuper@52148	87	real_diff_plus: "a - b = a + -b" (17.3.03: do_NOT_use) and
neuper@52148	88	real_diff_minus: "a - b = a + -1 * b" and
neuper@52148	89	real_plus_binom_times: "(a + b)(a + b) = a^^^2 + 2a*b + b^^^2" and
neuper@52148	90	real_minus_binom_times: "(a - b)(a - b) = a^^^2 - 2a*b + b^^^2" and
neuper@37906	91	(WN071229 changed for Schaerding -----vvv)
neuper@37974	92	(real_plus_binom_pow2: "(a + b)^^^2 = a^^^2 + 2ab + b^^^2")
neuper@52148	93	real_plus_binom_pow2: "(a + b)^^^2 = (a + b) * (a + b)" and
neuper@37906	94	(WN071229 changed for Schaerding -----^^^)
neuper@37974	95	real_plus_binom_pow2_poly: "[\| a is_polyexp; b is_polyexp \|] ==>
neuper@52148	96	(a + b)^^^2 = a^^^2 + 2ab + b^^^2" and
neuper@52148	97	real_minus_binom_pow2: "(a - b)^^^2 = a^^^2 - 2ab + b^^^2" and
neuper@52148	98	real_minus_binom_pow2_p: "(a - b)^^^2 = a^^^2 + -2ab + b^^^2" and
neuper@52148	99	real_plus_minus_binom1: "(a + b)*(a - b) = a^^^2 - b^^^2" and
neuper@52148	100	real_plus_minus_binom1_p: "(a + b)(a - b) = a^^^2 + -1b^^^2" and
neuper@52148	101	real_plus_minus_binom1_p_p: "(a + b)(a + -1 b) = a^^^2 + -1*b^^^2" and
neuper@52148	102	real_plus_minus_binom2: "(a - b)*(a + b) = a^^^2 - b^^^2" and
neuper@52148	103	real_plus_minus_binom2_p: "(a - b)(a + b) = a^^^2 + -1b^^^2" and
neuper@52148	104	real_plus_minus_binom2_p_p: "(a + -1 * b)(a + b) = a^^^2 + -1b^^^2" and
neuper@52148	105	real_plus_binom_times1: "(a + 1b)(a + -1b) = a^^^2 + -1b^^^2" and
neuper@52148	106	real_plus_binom_times2: "(a + -1b)(a + 1b) = a^^^2 + -1b^^^2" and
neuper@37906	107
neuper@37974	108	real_num_collect: "[\| l is_const; m is_const \|] ==>
neuper@52148	109	l * n + m * n = (l + m) * n" and
neuper@37906	110	(* FIXME.MG.0401: replace 'real_num_collect_assoc'
neuper@37906	111	by 'real_num_collect_assoc_l' ... are equal, introduced by MG ! *)
neuper@37974	112	real_num_collect_assoc: "[\| l is_const; m is_const \|] ==>
neuper@52148	113	l * n + (m * n + k) = (l + m) * n + k" and
neuper@37974	114	real_num_collect_assoc_l: "[\| l is_const; m is_const \|] ==>
neuper@37950	115	l * n + (m * n + k) = (l + m)
neuper@52148	116	* n + k" and
neuper@37974	117	real_num_collect_assoc_r: "[\| l is_const; m is_const \|] ==>
neuper@52148	118	(k + m * n) + l * n = k + (l + m) * n" and
neuper@52148	119	real_one_collect: "m is_const ==> n + m * n = (1 + m) * n" and
neuper@37906	120	(* FIXME.MG.0401: replace 'real_one_collect_assoc'
neuper@37906	121	by 'real_one_collect_assoc_l' ... are equal, introduced by MG ! *)
neuper@52148	122	real_one_collect_assoc: "m is_const ==> n + (m * n + k) = (1 + m)* n + k" and
neuper@37906	123
neuper@52148	124	real_one_collect_assoc_l: "m is_const ==> n + (m * n + k) = (1 + m) * n + k" and
neuper@52148	125	real_one_collect_assoc_r: "m is_const ==> (k + n) + m * n = k + (1 + m) * n" and
neuper@37906	126
neuper@37906	127	(* FIXME.MG.0401: replace 'real_mult_2_assoc'
neuper@37906	128	by 'real_mult_2_assoc_l' ... are equal, introduced by MG ! *)
neuper@52148	129	real_mult_2_assoc: "z1 + (z1 + k) = 2 * z1 + k" and
neuper@52148	130	real_mult_2_assoc_l: "z1 + (z1 + k) = 2 * z1 + k" and
neuper@52148	131	real_mult_2_assoc_r: "(k + z1) + z1 = k + 2 * z1" and
neuper@37906	132
neuper@52148	133	real_add_mult_distrib_poly: "w is_polyexp ==> (z1 + z2) * w = z1 * w + z2 * w" and
neuper@37974	134	real_add_mult_distrib2_poly:"w is_polyexp ==> w * (z1 + z2) = w * z1 + w * z2"
neuper@37950	135
neuper@37950	136	text {* remark on 'polynomials'
neuper@37950	137	WN020919
neuper@37950	138	* there are 5 kinds of expanded normalforms *
neuper@37950	139
neuper@37950	140	[1] 'complete polynomial' (Komplettes Polynom), univariate
neuper@37950	141	a_0 + a_1.x^1 +...+ a_n.x^n not (a_n = 0)
neuper@37950	142	not (a_n = 0), some a_i may be zero (DON'T disappear),
neuper@37950	143	variables in monomials lexicographically ordered and complete,
neuper@37950	144	x written as 1*x^1, ...
neuper@37950	145	[2] 'polynomial' (Polynom), univariate and multivariate
neuper@37950	146	a_0 + a_1.x +...+ a_n.x^n not (a_n = 0)
neuper@37950	147	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	148	not (a_n = 0), some a_i may be zero (ie. monomials disappear),
neuper@37950	149	exponents and coefficients equal 1 are not (WN060904.TODO in cancel_p_)shown,
neuper@37950	150	and variables in monomials are lexicographically ordered
neuper@37950	151	examples: [1]: "1 + (-10) * x ^^^ 1 + 25 * x ^^^ 2"
neuper@37950	152	[1]: "11 + 0 * x ^^^ 1 + 1 * x ^^^ 2"
neuper@37950	153	[2]: "x + (-50) * x ^^^ 3"
neuper@37950	154	[2]: "(-1) * x * y ^^^ 2 + 7 * x ^^^ 3"
neuper@37950	155
neuper@37950	156	[3] 'expanded_term' (Ausmultiplizierter Term):
neuper@37950	157	pull out unary minus to binary minus,
neuper@37950	158	as frequently exercised in schools; other conditions for [2] hold however
neuper@37950	159	examples: "a ^^^ 2 - 2 * a * b + b ^^^ 2"
neuper@37950	160	"4 * x ^^^ 2 - 9 * y ^^^ 2"
neuper@37950	161	[4] 'polynomial_in' (Polynom in):
neuper@37950	162	polynomial in 1 variable with arbitrary coefficients
neuper@37950	163	examples: "2 * x + (-50) * x ^^^ 3" (poly in x)
neuper@37950	164	"(u + v) + (2 * u ^^^ 2) * a + (-u) * a ^^^ 2 (poly in a)
neuper@37950	165	[5] 'expanded_in' (Ausmultiplizierter Termin in):
neuper@37950	166	analoguous to [3] with binary minus like [3]
neuper@37950	167	examples: "2 * x - 50 * x ^^^ 3" (expanded in x)
neuper@37950	168	"(u + v) + (2 * u ^^^ 2) * a - u * a ^^^ 2 (expanded in a)
neuper@37950	169	*}
neuper@37950	170
neuper@37950	171	ML {*
neuper@37972	172	val thy = @{theory};
neuper@37972	173
neuper@37950	174	(* is_polyrat_in becomes true, if no bdv is in the denominator of a fraction*)
neuper@37950	175	fun is_polyrat_in t v =
wneuper@59389	176	let fun coeff_in c v = member op = (TermC.vars c) v;
neuper@38031	177	fun finddivide (_ $ _ $ _ $ _) v = error("is_polyrat_in:")
neuper@37950	178	(* at the moment there is no term like this, but ....*)
wneuper@59360	179	\| finddivide (t as (Const ("Rings.divide_class.divide",_) $ _ $ b)) v =
neuper@37950	180	not(coeff_in b v)
neuper@37950	181	\| finddivide (_ $ t1 $ t2) v =
neuper@37950	182	(finddivide t1 v) orelse (finddivide t2 v)
neuper@37950	183	\| finddivide (_ $ t1) v = (finddivide t1 v)
neuper@37950	184	\| finddivide _ _ = false;
neuper@37950	185	in finddivide t v end;
neuper@37950	186
neuper@37950	187	fun eval_is_polyrat_in _ _(p as (Const ("Poly.is'_polyrat'_in",_) $ t $ v)) _ =
neuper@37950	188	if is_polyrat_in t v
wneuper@59416	189	then SOME ((Rule.term2str p) ^ " = True",
wneuper@59390	190	HOLogic.Trueprop $ (TermC.mk_equality (p, @{term True})))
wneuper@59416	191	else SOME ((Rule.term2str p) ^ " = True",
wneuper@59390	192	HOLogic.Trueprop $ (TermC.mk_equality (p, @{term False})))
neuper@38015	193	\| eval_is_polyrat_in _ _ _ _ = ((tracing"### no matches";) NONE);
neuper@37950	194
neuper@37950	195	local
neuper@37950	196	(.a 'c is coefficient of v' if v does NOT occur in c.)
wneuper@59389	197	fun coeff_in c v = not (member op = (TermC.vars c) v);
neuper@37950	198	(* FIXME.WN100826 shift this into test--------------
wneuper@59186	199	val v = (Thm.term_of o the o (parse thy)) "x";
wneuper@59186	200	val t = (Thm.term_of o the o (parse thy)) "1";
neuper@37950	201	coeff_in t v;
neuper@37950	202	(val it = true : bool)
wneuper@59186	203	val t = (Thm.term_of o the o (parse thy)) "a*b+c";
neuper@37950	204	coeff_in t v;
neuper@37950	205	(val it = true : bool)
wneuper@59186	206	val t = (Thm.term_of o the o (parse thy)) "a*x+c";
neuper@37950	207	coeff_in t v;
neuper@37950	208	(val it = false : bool)
neuper@37950	209	----------------------------------------------------*)
neuper@37950	210	(*. a 'monomial t in variable v' is a term t with
neuper@37950	211	either (1) v NOT existent in t, or (2) v contained in t,
neuper@37950	212	if (1) then degree 0
neuper@37950	213	if (2) then v is a factor on the very right, ev. with exponent.*)
neuper@37950	214	fun factor_right_deg (case 2)
neuper@38034	215	(t as Const ("Groups.times_class.times",_) $ t1 $
neuper@37950	216	(Const ("Atools.pow",_) $ vv $ Free (d,_))) v =
wneuper@59390	217	if ((vv = v) andalso (coeff_in t1 v)) then SOME (TermC.int_of_str d) else NONE
neuper@37950	218	\| factor_right_deg (t as Const ("Atools.pow",_) $ vv $ Free (d,_)) v =
wneuper@59390	219	if (vv = v) then SOME (TermC.int_of_str d) else NONE
neuper@38034	220	\| factor_right_deg (t as Const ("Groups.times_class.times",_) $ t1 $ vv) v =
neuper@37950	221	if ((vv = v) andalso (coeff_in t1 v))then SOME 1 else NONE
neuper@37950	222	\| factor_right_deg vv v =
neuper@37950	223	if (vv = v) then SOME 1 else NONE;
neuper@37950	224	fun mono_deg_in m v =
neuper@37950	225	if coeff_in m v then (case 1) SOME 0
neuper@37950	226	else factor_right_deg m v;
neuper@37950	227	(* FIXME.WN100826 shift this into test-----------------------------
wneuper@59186	228	val v = (Thm.term_of o the o (parse thy)) "x";
wneuper@59186	229	val t = (Thm.term_of o the o (parse thy)) "(ab+c)x^^^7";
neuper@37950	230	mono_deg_in t v;
neuper@37950	231	(val it = SOME 7)
wneuper@59186	232	val t = (Thm.term_of o the o (parse thy)) "x^^^7";
neuper@37950	233	mono_deg_in t v;
neuper@37950	234	(val it = SOME 7)
wneuper@59186	235	val t = (Thm.term_of o the o (parse thy)) "(ab+c)x";
neuper@37950	236	mono_deg_in t v;
neuper@37950	237	(val it = SOME 1)
wneuper@59186	238	val t = (Thm.term_of o the o (parse thy)) "(ab+x)x";
neuper@37950	239	mono_deg_in t v;
neuper@37950	240	(val it = NONE)
wneuper@59186	241	val t = (Thm.term_of o the o (parse thy)) "x";
neuper@37950	242	mono_deg_in t v;
neuper@37950	243	(val it = SOME 1)
wneuper@59186	244	val t = (Thm.term_of o the o (parse thy)) "(a*b+c)";
neuper@37950	245	mono_deg_in t v;
neuper@37950	246	(val it = SOME 0)
wneuper@59186	247	val t = (Thm.term_of o the o (parse thy)) "ab - (ab)x";
neuper@37950	248	mono_deg_in t v;
neuper@37950	249	(val it = NONE)
neuper@37950	250	------------------------------------------------------------------*)
neuper@37950	251	fun expand_deg_in t v =
neuper@38014	252	let fun edi ~1 ~1 (Const ("Groups.plus_class.plus",_) $ t1 $ t2) =
neuper@37950	253	(case mono_deg_in t2 v of (* $ is left associative*)
neuper@37950	254	SOME d' => edi d' d' t1
neuper@37950	255	\| NONE => NONE)
neuper@38014	256	\| edi ~1 ~1 (Const ("Groups.minus_class.minus",_) $ t1 $ t2) =
neuper@37950	257	(case mono_deg_in t2 v of
neuper@37950	258	SOME d' => edi d' d' t1
neuper@37950	259	\| NONE => NONE)
neuper@38014	260	\| edi d dmax (Const ("Groups.minus_class.minus",_) $ t1 $ t2) =
neuper@37950	261	(case mono_deg_in t2 v of
neuper@37950	262	(RL orelse ((d=0) andalso (d'=0)) need to handle 3+4-...4 +x)
neuper@37950	263	SOME d' => if ((d > d') orelse ((d=0) andalso (d'=0)))
neuper@37950	264	then edi d' dmax t1 else NONE
neuper@37950	265	\| NONE => NONE)
neuper@38014	266	\| edi d dmax (Const ("Groups.plus_class.plus",_) $ t1 $ t2) =
neuper@37950	267	(case mono_deg_in t2 v of
neuper@37950	268	(RL orelse ((d=0) andalso (d'=0)) need to handle 3+4-...4 +x)
neuper@37950	269	SOME d' => if ((d > d') orelse ((d=0) andalso (d'=0)))
neuper@37950	270	then edi d' dmax t1 else NONE
neuper@37950	271	\| NONE => NONE)
neuper@37950	272	\| edi ~1 ~1 t = (case mono_deg_in t v of
neuper@37950	273	d as SOME _ => d
neuper@37950	274	\| NONE => NONE)
neuper@37950	275	\| edi d dmax t = (basecase last)
neuper@37950	276	(case mono_deg_in t v of
neuper@37950	277	SOME d' => if ((d > d') orelse ((d=0) andalso (d'=0)))
neuper@37950	278	then SOME dmax else NONE
neuper@37950	279	\| NONE => NONE)
neuper@37950	280	in edi ~1 ~1 t end;
neuper@37950	281	(* FIXME.WN100826 shift this into test-----------------------------
wneuper@59186	282	val v = (Thm.term_of o the o (parse thy)) "x";
wneuper@59186	283	val t = (Thm.term_of o the o (parse thy)) "a+b";
neuper@37950	284	expand_deg_in t v;
neuper@37950	285	(val it = SOME 0)
wneuper@59186	286	val t = (Thm.term_of o the o (parse thy)) "(a+b)*x";
neuper@37950	287	expand_deg_in t v;
neuper@37950	288	(SOME 1)
wneuper@59186	289	val t = (Thm.term_of o the o (parse thy)) "ab - (a+b)x";
neuper@37950	290	expand_deg_in t v;
neuper@37950	291	(SOME 1)
wneuper@59186	292	val t = (Thm.term_of o the o (parse thy)) "ab + (a-b)x";
neuper@37950	293	expand_deg_in t v;
neuper@37950	294	(SOME 1)
wneuper@59186	295	val t = (Thm.term_of o the o (parse thy)) "ab + (a+b)x + x^^^2";
neuper@37950	296	expand_deg_in t v;
neuper@37950	297	-------------------------------------------------------------------*)
neuper@37950	298	fun poly_deg_in t v =
neuper@38014	299	let fun edi ~1 ~1 (Const ("Groups.plus_class.plus",_) $ t1 $ t2) =
neuper@37950	300	(case mono_deg_in t2 v of (* $ is left associative*)
neuper@37950	301	SOME d' => edi d' d' t1
neuper@37950	302	\| NONE => NONE)
neuper@38014	303	\| edi d dmax (Const ("Groups.plus_class.plus",_) $ t1 $ t2) =
neuper@37950	304	(case mono_deg_in t2 v of
neuper@37950	305	(RL orelse ((d=0) andalso (d'=0)) need to handle 3+4-...4 +x)
neuper@37950	306	SOME d' => if ((d > d') orelse ((d=0) andalso (d'=0)))
neuper@37950	307	then edi d' dmax t1 else NONE
neuper@37950	308	\| NONE => NONE)
neuper@37950	309	\| edi ~1 ~1 t = (case mono_deg_in t v of
neuper@37950	310	d as SOME _ => d
neuper@37950	311	\| NONE => NONE)
neuper@37950	312	\| edi d dmax t = (basecase last)
neuper@37950	313	(case mono_deg_in t v of
neuper@37950	314	SOME d' => if ((d > d') orelse ((d=0) andalso (d'=0)))
neuper@37950	315	then SOME dmax else NONE
neuper@37950	316	\| NONE => NONE)
neuper@37950	317	in edi ~1 ~1 t end;
neuper@37950	318	in
neuper@37950	319
neuper@37950	320	fun is_expanded_in t v =
neuper@37950	321	case expand_deg_in t v of SOME _ => true \| NONE => false;
neuper@37950	322	fun is_poly_in t v =
neuper@37950	323	case poly_deg_in t v of SOME _ => true \| NONE => false;
neuper@37950	324	fun has_degree_in t v =
neuper@37950	325	case expand_deg_in t v of SOME d => d \| NONE => ~1;
neuper@37980	326	end;(local)
neuper@37950	327	(* FIXME.WN100826 shift this into test-----------------------------
wneuper@59186	328	val v = (Thm.term_of o the o (parse thy)) "x";
wneuper@59186	329	val t = (Thm.term_of o the o (parse thy)) "ab - (a+b)x + x^^^2";
neuper@37950	330	has_degree_in t v;
neuper@37950	331	(val it = 2)
wneuper@59186	332	val t = (Thm.term_of o the o (parse thy)) "-8 - 2*x + x^^^2";
neuper@37950	333	has_degree_in t v;
neuper@37950	334	(val it = 2)
wneuper@59186	335	val t = (Thm.term_of o the o (parse thy)) "6 + 13x + 6x^^^2";
neuper@37950	336	has_degree_in t v;
neuper@37950	337	(val it = 2)
neuper@37950	338	-------------------------------------------------------------------*)
neuper@37950	339
neuper@37950	340	(("is_expanded_in", ("Poly.is'_expanded'_in", eval_is_expanded_in "")))
neuper@37950	341	fun eval_is_expanded_in _ _
neuper@37950	342	(p as (Const ("Poly.is'_expanded'_in",_) $ t $ v)) _ =
neuper@37950	343	if is_expanded_in t v
wneuper@59416	344	then SOME ((Rule.term2str p) ^ " = True",
wneuper@59390	345	HOLogic.Trueprop $ (TermC.mk_equality (p, @{term True})))
wneuper@59416	346	else SOME ((Rule.term2str p) ^ " = True",
wneuper@59390	347	HOLogic.Trueprop $ (TermC.mk_equality (p, @{term False})))
neuper@37950	348	\| eval_is_expanded_in _ _ _ _ = NONE;
neuper@37950	349	(*
wneuper@59186	350	val t = (Thm.term_of o the o (parse thy)) "(-8 - 2*x + x^^^2) is_expanded_in x";
neuper@37950	351	val SOME (id, t') = eval_is_expanded_in 0 0 t 0;
neuper@37950	352	(val id = "Poly.is'_expanded'_in (-8 - 2 x + x ^^^ 2) x = True"*)
wneuper@59416	353	Rule.term2str t';
neuper@37950	354	(val it = "Poly.is'_expanded'_in (-8 - 2 x + x ^^^ 2) x = True"*)
neuper@37950	355	*)
neuper@37950	356
neuper@37950	357	(("is_poly_in", ("Poly.is'_poly'_in", eval_is_poly_in "")))
neuper@37950	358	fun eval_is_poly_in _ _
neuper@37950	359	(p as (Const ("Poly.is'_poly'_in",_) $ t $ v)) _ =
neuper@37950	360	if is_poly_in t v
wneuper@59416	361	then SOME ((Rule.term2str p) ^ " = True",
wneuper@59390	362	HOLogic.Trueprop $ (TermC.mk_equality (p, @{term True})))
wneuper@59416	363	else SOME ((Rule.term2str p) ^ " = True",
wneuper@59390	364	HOLogic.Trueprop $ (TermC.mk_equality (p, @{term False})))
neuper@37950	365	\| eval_is_poly_in _ _ _ _ = NONE;
neuper@37950	366	(*
wneuper@59186	367	val t = (Thm.term_of o the o (parse thy)) "(8 + 2*x + x^^^2) is_poly_in x";
neuper@37950	368	val SOME (id, t') = eval_is_poly_in 0 0 t 0;
neuper@37950	369	(val id = "Poly.is'_poly'_in (8 + 2 x + x ^^^ 2) x = True"*)
wneuper@59416	370	Rule.term2str t';
neuper@37950	371	(val it = "Poly.is'_poly'_in (8 + 2 x + x ^^^ 2) x = True"*)
neuper@37950	372	*)
neuper@37950	373
neuper@37950	374	(("has_degree_in", ("Poly.has'_degree'_in", eval_has_degree_in "")))
neuper@37950	375	fun eval_has_degree_in _ _
neuper@37950	376	(p as (Const ("Poly.has'_degree'_in",_) $ t $ v)) _ =
neuper@37950	377	let val d = has_degree_in t v
wneuper@59389	378	val d' = TermC.term_of_num HOLogic.realT d
wneuper@59416	379	in SOME ((Rule.term2str p) ^ " = " ^ (string_of_int d),
wneuper@59390	380	HOLogic.Trueprop $ (TermC.mk_equality (p, d')))
neuper@37950	381	end
neuper@37950	382	\| eval_has_degree_in _ _ _ _ = NONE;
neuper@37950	383	(*
wneuper@59186	384	> val t = (Thm.term_of o the o (parse thy)) "(-8 - 2*x + x^^^2) has_degree_in x";
neuper@37950	385	> val SOME (id, t') = eval_has_degree_in 0 0 t 0;
neuper@37950	386	val id = "Poly.has'_degree'_in (-8 - 2 * x + x ^^^ 2) x = 2" : string
wneuper@59416	387	> Rule.term2str t';
neuper@37950	388	val it = "Poly.has'_degree'_in (-8 - 2 * x + x ^^^ 2) x = 2" : string
neuper@37950	389	*)
neuper@37950	390
neuper@37978	391	(..)
neuper@37978	392	val calculate_Poly =
wneuper@59416	393	Rule.append_rls "calculate_PolyFIXXXME.not.impl." Rule.e_rls
neuper@37978	394	[];
neuper@37978	395
neuper@37950	396	(.for evaluation of conditions in rewrite rules.)
wneuper@59416	397	val Poly_erls = Rule.append_rls "Poly_erls" Atools_erls
wneuper@59416	398	[Rule.Calc ("HOL.eq", eval_equal "#equal_"),
wneuper@59416	399	Rule.Thm ("real_unari_minus", TermC.num_str @{thm real_unari_minus}),
wneuper@59416	400	Rule.Calc ("Groups.plus_class.plus", eval_binop "#add_"),
wneuper@59416	401	Rule.Calc ("Groups.minus_class.minus", eval_binop "#sub_"),
wneuper@59416	402	Rule.Calc ("Groups.times_class.times", eval_binop "#mult_"),
wneuper@59416	403	Rule.Calc ("Atools.pow", eval_binop "#power_")];
neuper@37950	404
wneuper@59416	405	val poly_crls = Rule.append_rls "poly_crls" Atools_crls
wneuper@59416	406	[Rule.Calc ("HOL.eq", eval_equal "#equal_"),
wneuper@59416	407	Rule.Thm ("real_unari_minus", TermC.num_str @{thm real_unari_minus}),
wneuper@59416	408	Rule.Calc ("Groups.plus_class.plus", eval_binop "#add_"),
wneuper@59416	409	Rule.Calc ("Groups.minus_class.minus", eval_binop "#sub_"),
wneuper@59416	410	Rule.Calc ("Groups.times_class.times", eval_binop "#mult_"),
wneuper@59416	411	Rule.Calc ("Atools.pow" ,eval_binop "#power_")];
neuper@37950	412
neuper@37950	413	local (. for make_polynomial .)
neuper@37950	414
neuper@37950	415	open Term; (* for type order = EQUAL \| LESS \| GREATER *)
neuper@37950	416
neuper@37950	417	fun pr_ord EQUAL = "EQUAL"
neuper@37950	418	\| pr_ord LESS = "LESS"
neuper@37950	419	\| pr_ord GREATER = "GREATER";
neuper@37950	420
neuper@37950	421	fun dest_hd' (Const (a, T)) = (* ~ term.ML *)
neuper@37950	422	(case a of
neuper@37950	423	"Atools.pow" => ((("\|\|\|\|\|\|\|\|\|\|\|\|\|", 0), T), 0) (WN greatest string)
neuper@37950	424	\| _ => (((a, 0), T), 0))
neuper@37950	425	\| dest_hd' (Free (a, T)) = (((a, 0), T), 1)
neuper@37950	426	\| dest_hd' (Var v) = (v, 2)
neuper@37950	427	\| dest_hd' (Bound i) = ((("", i), dummyT), 3)
neuper@37950	428	\| dest_hd' (Abs (_, T, _)) = ((("", 0), T), 4);
neuper@37950	429
neuper@37950	430	fun get_order_pow (t $ (Free(order,_))) = (* RL FIXXXME:geht zufaellig?WN*)
wneuper@59390	431	(case TermC.int_of_str_opt (order) of
neuper@37950	432	SOME d => d
neuper@37950	433	\| NONE => 0)
neuper@37950	434	\| get_order_pow _ = 0;
neuper@37950	435
neuper@37950	436	fun size_of_term' (Const(str,_) $ t) =
neuper@37950	437	if "Atools.pow"= str then 1000 + size_of_term' t else 1+size_of_term' t(WN)
neuper@37950	438	\| size_of_term' (Abs (_,_,body)) = 1 + size_of_term' body
neuper@37950	439	\| size_of_term' (f$t) = size_of_term' f + size_of_term' t
neuper@37950	440	\| size_of_term' _ = 1;
neuper@37950	441
neuper@37950	442	fun term_ord' pr thy (Abs (_, T, t), Abs(_, U, u)) = (* ~ term.ML *)
neuper@52070	443	(case term_ord' pr thy (t, u) of EQUAL => Term_Ord.typ_ord (T, U) \| ord => ord)
neuper@37950	444	\| term_ord' pr thy (t, u) =
neuper@52070	445	(if pr then
neuper@52070	446	let
neuper@52070	447	val (f, ts) = strip_comb t and (g, us) = strip_comb u;
wneuper@59416	448	val _ = tracing ("t= f@ts= \"" ^ Rule.term_to_string''' thy f ^ "\" @ \"[" ^
wneuper@59416	449	commas (map (Rule.term_to_string''' thy) ts) ^ "]\"");
wneuper@59416	450	val _ = tracing("u= g@us= \"" ^ Rule.term_to_string''' thy g ^ "\" @ \"[" ^
wneuper@59416	451	commas (map (Rule.term_to_string''' thy) us) ^ "]\"");
neuper@52070	452	val _ = tracing ("size_of_term(t,u)= (" ^ string_of_int (size_of_term' t) ^ ", " ^
neuper@52070	453	string_of_int (size_of_term' u) ^ ")");
neuper@52070	454	val _ = tracing ("hd_ord(f,g) = " ^ (pr_ord o hd_ord) (f,g));
neuper@52070	455	val _ = tracing ("terms_ord(ts,us) = " ^ (pr_ord o terms_ord str false) (ts, us));
neuper@52070	456	val _ = tracing ("-------");
neuper@52070	457	in () end
neuper@37950	458	else ();
neuper@37950	459	case int_ord (size_of_term' t, size_of_term' u) of
neuper@37950	460	EQUAL =>
neuper@37950	461	let val (f, ts) = strip_comb t and (g, us) = strip_comb u in
neuper@37950	462	(case hd_ord (f, g) of EQUAL => (terms_ord str pr) (ts, us)
neuper@37950	463	\| ord => ord)
neuper@37950	464	end
neuper@37950	465	\| ord => ord)
neuper@37950	466	and hd_ord (f, g) = (* ~ term.ML *)
neuper@37974	467	prod_ord (prod_ord Term_Ord.indexname_ord Term_Ord.typ_ord) int_ord (dest_hd' f, dest_hd' g)
neuper@37950	468	and terms_ord str pr (ts, us) =
wneuper@59406	469	list_ord (term_ord' pr (Celem.assoc_thy "Isac"))(ts, us);
neuper@52070	470
neuper@37950	471	in
neuper@37950	472
wneuper@59416	473	fun ord_make_polynomial (pr:bool) thy (_: Rule.subst) tu =
neuper@37950	474	(term_ord' pr thy(***) tu = LESS );
neuper@37950	475
neuper@37950	476	end;(local)
neuper@37950	477
neuper@37950	478
wneuper@59416	479	Rule.rew_ord' := overwritel (! Rule.rew_ord',
neuper@37950	480	[("termlessI", termlessI),
neuper@37950	481	("ord_make_polynomial", ord_make_polynomial false thy)
neuper@37950	482	]);
neuper@37950	483
neuper@37950	484
neuper@37950	485	val expand =
wneuper@59416	486	Rule.Rls {id = "expand", preconds = [], rew_ord = ("dummy_ord", Rule.dummy_ord),
wneuper@59416	487	erls = Rule.e_rls,srls = Rule.Erls, calc = [], errpatts = [],
wneuper@59416	488	rules = [Rule.Thm ("distrib_right" , TermC.num_str @{thm distrib_right}),
neuper@37950	489	("(z1.0 + z2.0) w = z1.0 * w + z2.0 * w"*)
wneuper@59416	490	Rule.Thm ("distrib_left", TermC.num_str @{thm distrib_left})
neuper@37950	491	("w (z1.0 + z2.0) = w * z1.0 + w * z2.0"*)
wneuper@59416	492	], scr = Rule.EmptyScr};
neuper@37950	493
neuper@37950	494	(*----------------- Begin: rulesets for make_polynomial_ -----------------
neuper@37950	495	'rlsIDs' redefined by MG as 'rlsIDs_'
neuper@37950	496	^^^*)
neuper@37950	497
neuper@37980	498	val discard_minus =
wneuper@59416	499	Rule.Rls {id = "discard_minus", preconds = [], rew_ord = ("dummy_ord", Rule.dummy_ord),
wneuper@59416	500	erls = Rule.e_rls, srls = Rule.Erls, calc = [], errpatts = [],
neuper@42407	501	rules =
wneuper@59416	502	[Rule.Thm ("real_diff_minus", TermC.num_str @{thm real_diff_minus}),
neuper@42407	503	("a - b = a + -1 b"*)
wneuper@59416	504	Rule.Thm ("sym_real_mult_minus1", TermC.num_str (@{thm real_mult_minus1} RS @{thm sym}))
neuper@42407	505	(- ?z = "-1 ?z"*)],
wneuper@59416	506	scr = Rule.EmptyScr};
neuper@37980	507
neuper@37950	508	val expand_poly_ =
wneuper@59416	509	Rule.Rls{id = "expand_poly_", preconds = [],
wneuper@59416	510	rew_ord = ("dummy_ord", Rule.dummy_ord),
wneuper@59416	511	erls = Rule.e_rls,srls = Rule.Erls,
neuper@42451	512	calc = [], errpatts = [],
neuper@42407	513	rules =
wneuper@59416	514	[Rule.Thm ("real_plus_binom_pow4", TermC.num_str @{thm real_plus_binom_pow4}),
neuper@42407	515	("(a + b)^^^4 = ... ")
wneuper@59416	516	Rule.Thm ("real_plus_binom_pow5",TermC.num_str @{thm real_plus_binom_pow5}),
neuper@42407	517	("(a + b)^^^5 = ... ")
wneuper@59416	518	Rule.Thm ("real_plus_binom_pow3",TermC.num_str @{thm real_plus_binom_pow3}),
neuper@42407	519	("(a + b)^^^3 = a^^^3 + 3a^^^2b + 3ab^^^2 + b^^^3" )
neuper@42407	520	(WN071229 changed/removed for Schaerding -----vvv)
wneuper@59416	521	(Rule.Thm ("real_plus_binom_pow2",TermC.num_str @{thm real_plus_binom_pow2}),)
neuper@42407	522	("(a + b)^^^2 = a^^^2 + 2ab + b^^^2")
wneuper@59416	523	Rule.Thm ("real_plus_binom_pow2",TermC.num_str @{thm real_plus_binom_pow2}),
neuper@42407	524	("(a + b)^^^2 = (a + b) (a + b)"*)
wneuper@59416	525	(Rule.Thm ("real_plus_minus_binom1_p_p", TermC.num_str @{thm real_plus_minus_binom1_p_p}),)
neuper@42407	526	("(a + b)(a + -1 * b) = a^^^2 + -1b^^^2")
wneuper@59416	527	(Rule.Thm ("real_plus_minus_binom2_p_p", TermC.num_str @{thm real_plus_minus_binom2_p_p}),)
neuper@42407	528	("(a + -1 b)(a + b) = a^^^2 + -1b^^^2"*)
neuper@42407	529	(WN071229 changed/removed for Schaerding -----^^^)
neuper@37950	530
wneuper@59416	531	Rule.Thm ("distrib_right" ,TermC.num_str @{thm distrib_right}),
neuper@42407	532	("(z1.0 + z2.0) w = z1.0 * w + z2.0 * w"*)
wneuper@59416	533	Rule.Thm ("distrib_left",TermC.num_str @{thm distrib_left}),
neuper@42407	534	("w (z1.0 + z2.0) = w * z1.0 + w * z2.0"*)
neuper@37950	535
wneuper@59416	536	Rule.Thm ("realpow_multI", TermC.num_str @{thm realpow_multI}),
neuper@42407	537	("(r s) ^^^ n = r ^^^ n * s ^^^ n"*)
wneuper@59416	538	Rule.Thm ("realpow_pow",TermC.num_str @{thm realpow_pow})
neuper@42407	539	("(a ^^^ b) ^^^ c = a ^^^ (b c)"*)
wneuper@59416	540	], scr = Rule.EmptyScr};
neuper@37950	541
neuper@37950	542	(.the expression contains + - ^ only ?
neuper@37950	543	this is weaker than 'is_polynomial' !.*)
neuper@37950	544	fun is_polyexp (Free _) = true
neuper@38014	545	\| is_polyexp (Const ("Groups.plus_class.plus",_) $ Free _ $ Free _) = true
neuper@38014	546	\| is_polyexp (Const ("Groups.minus_class.minus",_) $ Free _ $ Free _) = true
neuper@38034	547	\| is_polyexp (Const ("Groups.times_class.times",_) $ Free _ $ Free _) = true
neuper@37950	548	\| is_polyexp (Const ("Atools.pow",_) $ Free _ $ Free _) = true
neuper@38014	549	\| is_polyexp (Const ("Groups.plus_class.plus",_) $ t1 $ t2) =
neuper@37950	550	((is_polyexp t1) andalso (is_polyexp t2))
neuper@38014	551	\| is_polyexp (Const ("Groups.minus_class.minus",_) $ t1 $ t2) =
neuper@37950	552	((is_polyexp t1) andalso (is_polyexp t2))
neuper@38034	553	\| is_polyexp (Const ("Groups.times_class.times",_) $ t1 $ t2) =
neuper@37950	554	((is_polyexp t1) andalso (is_polyexp t2))
neuper@37950	555	\| is_polyexp (Const ("Atools.pow",_) $ t1 $ t2) =
neuper@37950	556	((is_polyexp t1) andalso (is_polyexp t2))
neuper@37950	557	\| is_polyexp _ = false;
neuper@37950	558
neuper@37950	559	(("is_polyexp", ("Poly.is'_polyexp", eval_is_polyexp "")))
neuper@37950	560	fun eval_is_polyexp (thmid:string) _
neuper@37950	561	(t as (Const("Poly.is'_polyexp", _) $ arg)) thy =
neuper@37950	562	if is_polyexp arg
wneuper@59416	563	then SOME (TermC.mk_thmid thmid (Rule.term_to_string''' thy arg) "",
wneuper@59390	564	HOLogic.Trueprop $ (TermC.mk_equality (t, @{term True})))
wneuper@59416	565	else SOME (TermC.mk_thmid thmid (Rule.term_to_string''' thy arg) "",
wneuper@59390	566	HOLogic.Trueprop $ (TermC.mk_equality (t, @{term False})))
neuper@37950	567	\| eval_is_polyexp _ _ _ _ = NONE;
neuper@37950	568
neuper@37950	569	val expand_poly_rat_ =
wneuper@59416	570	Rule.Rls{id = "expand_poly_rat_", preconds = [],
wneuper@59416	571	rew_ord = ("dummy_ord", Rule.dummy_ord),
wneuper@59416	572	erls = Rule.append_rls "Rule.e_rls-is_polyexp" Rule.e_rls
wneuper@59416	573	[Rule.Calc ("Poly.is'_polyexp", eval_is_polyexp "")
neuper@37950	574	],
wneuper@59416	575	srls = Rule.Erls,
neuper@42451	576	calc = [], errpatts = [],
neuper@37950	577	rules =
wneuper@59416	578	[Rule.Thm ("real_plus_binom_pow4_poly", TermC.num_str @{thm real_plus_binom_pow4_poly}),
neuper@37950	579	("[\| a is_polyexp; b is_polyexp \|] ==> (a + b)^^^4 = ... ")
wneuper@59416	580	Rule.Thm ("real_plus_binom_pow5_poly", TermC.num_str @{thm real_plus_binom_pow5_poly}),
neuper@37950	581	("[\| a is_polyexp; b is_polyexp \|] ==> (a + b)^^^5 = ... ")
wneuper@59416	582	Rule.Thm ("real_plus_binom_pow2_poly",TermC.num_str @{thm real_plus_binom_pow2_poly}),
neuper@37950	583	(*"[\| a is_polyexp; b is_polyexp \|] ==>
neuper@37950	584	(a + b)^^^2 = a^^^2 + 2ab + b^^^2"*)
wneuper@59416	585	Rule.Thm ("real_plus_binom_pow3_poly",TermC.num_str @{thm real_plus_binom_pow3_poly}),
neuper@37950	586	(*"[\| a is_polyexp; b is_polyexp \|] ==>
neuper@37950	587	(a + b)^^^3 = a^^^3 + 3a^^^2b + 3ab^^^2 + b^^^3" *)
wneuper@59416	588	Rule.Thm ("real_plus_minus_binom1_p_p",TermC.num_str @{thm real_plus_minus_binom1_p_p}),
neuper@37950	589	("(a + b)(a + -1 * b) = a^^^2 + -1b^^^2")
wneuper@59416	590	Rule.Thm ("real_plus_minus_binom2_p_p",TermC.num_str @{thm real_plus_minus_binom2_p_p}),
neuper@37950	591	("(a + -1 b)(a + b) = a^^^2 + -1b^^^2"*)
neuper@37950	592
wneuper@59416	593	Rule.Thm ("real_add_mult_distrib_poly",
wneuper@59389	594	TermC.num_str @{thm real_add_mult_distrib_poly}),
neuper@37950	595	("w is_polyexp ==> (z1.0 + z2.0) w = z1.0 * w + z2.0 * w"*)
wneuper@59416	596	Rule.Thm("real_add_mult_distrib2_poly",
wneuper@59389	597	TermC.num_str @{thm real_add_mult_distrib2_poly}),
neuper@37950	598	("w is_polyexp ==> w (z1.0 + z2.0) = w * z1.0 + w * z2.0"*)
neuper@37950	599
wneuper@59416	600	Rule.Thm ("realpow_multI_poly", TermC.num_str @{thm realpow_multI_poly}),
neuper@37950	601	(*"[\| r is_polyexp; s is_polyexp \|] ==>
neuper@37950	602	(r * s) ^^^ n = r ^^^ n * s ^^^ n"*)
wneuper@59416	603	Rule.Thm ("realpow_pow",TermC.num_str @{thm realpow_pow})
neuper@37950	604	("(a ^^^ b) ^^^ c = a ^^^ (b c)"*)
wneuper@59416	605	], scr = Rule.EmptyScr};
neuper@37950	606
neuper@37950	607	val simplify_power_ =
wneuper@59416	608	Rule.Rls{id = "simplify_power_", preconds = [],
wneuper@59416	609	rew_ord = ("dummy_ord", Rule.dummy_ord),
wneuper@59416	610	erls = Rule.e_rls, srls = Rule.Erls,
neuper@42451	611	calc = [], errpatts = [],
wneuper@59416	612	rules = [(*MG: Reihenfolge der folgenden 2 Rule.Thm muss so bleiben, wegen
neuper@37950	613	a(aa) --> aa^^^2 und nicht a(aa) --> a^^^2a *)
wneuper@59416	614	Rule.Thm ("sym_realpow_twoI",
wneuper@59389	615	TermC.num_str (@{thm realpow_twoI} RS @{thm sym})),
neuper@37950	616	("r r = r ^^^ 2"*)
wneuper@59416	617	Rule.Thm ("realpow_twoI_assoc_l",TermC.num_str @{thm realpow_twoI_assoc_l}),
neuper@37950	618	("r (r * s) = r ^^^ 2 * s"*)
neuper@37950	619
wneuper@59416	620	Rule.Thm ("realpow_plus_1",TermC.num_str @{thm realpow_plus_1}),
neuper@37950	621	("r r ^^^ n = r ^^^ (n + 1)"*)
wneuper@59416	622	Rule.Thm ("realpow_plus_1_assoc_l",
wneuper@59389	623	TermC.num_str @{thm realpow_plus_1_assoc_l}),
neuper@37950	624	("r (r ^^^ m * s) = r ^^^ (1 + m) * s"*)
wneuper@59416	625	(MG 9.7.03: neues Rule.Thm wegen a(a(ab)) --> a^^^2(ab) *)
wneuper@59416	626	Rule.Thm ("realpow_plus_1_assoc_l2",
wneuper@59389	627	TermC.num_str @{thm realpow_plus_1_assoc_l2}),
neuper@37950	628	("r ^^^ m (r * s) = r ^^^ (1 + m) * s"*)
neuper@37950	629
wneuper@59416	630	Rule.Thm ("sym_realpow_addI",
wneuper@59389	631	TermC.num_str (@{thm realpow_addI} RS @{thm sym})),
neuper@37950	632	("r ^^^ n r ^^^ m = r ^^^ (n + m)"*)
wneuper@59416	633	Rule.Thm ("realpow_addI_assoc_l",TermC.num_str @{thm realpow_addI_assoc_l}),
neuper@37950	634	("r ^^^ n (r ^^^ m * s) = r ^^^ (n + m) * s"*)
neuper@37950	635
neuper@37950	636	(* ist in expand_poly - wird hier aber auch gebraucht, wegen:
neuper@37950	637	"r * r = r ^^^ 2" wenn r=a^^^b*)
wneuper@59416	638	Rule.Thm ("realpow_pow",TermC.num_str @{thm realpow_pow})
neuper@37950	639	("(a ^^^ b) ^^^ c = a ^^^ (b c)"*)
wneuper@59416	640	], scr = Rule.EmptyScr};
neuper@37950	641
neuper@37950	642	val calc_add_mult_pow_ =
wneuper@59416	643	Rule.Rls{id = "calc_add_mult_pow_", preconds = [],
wneuper@59416	644	rew_ord = ("dummy_ord", Rule.dummy_ord),
wneuper@59416	645	erls = Atools_erls(erls3.4.03),srls = Rule.Erls,
neuper@38014	646	calc = [("PLUS" , ("Groups.plus_class.plus", eval_binop "#add_")),
neuper@38034	647	("TIMES" , ("Groups.times_class.times", eval_binop "#mult_")),
neuper@37950	648	("POWER", ("Atools.pow", eval_binop "#power_"))
neuper@37950	649	],
neuper@42451	650	errpatts = [],
wneuper@59416	651	rules = [Rule.Calc ("Groups.plus_class.plus", eval_binop "#add_"),
wneuper@59416	652	Rule.Calc ("Groups.times_class.times", eval_binop "#mult_"),
wneuper@59416	653	Rule.Calc ("Atools.pow", eval_binop "#power_")
wneuper@59416	654	], scr = Rule.EmptyScr};
neuper@37950	655
neuper@37950	656	val reduce_012_mult_ =
wneuper@59416	657	Rule.Rls{id = "reduce_012_mult_", preconds = [],
wneuper@59416	658	rew_ord = ("dummy_ord", Rule.dummy_ord),
wneuper@59416	659	erls = Rule.e_rls,srls = Rule.Erls,
neuper@42451	660	calc = [], errpatts = [],
wneuper@59416	661	rules = [(* MG: folgende Rule.Thm müssen hier stehen bleiben: *)
wneuper@59416	662	Rule.Thm ("mult_1_right",TermC.num_str @{thm mult_1_right}),
neuper@37950	663	("z 1 = z") (wegen "a * b * b^^^(-1) + a"*)
wneuper@59416	664	Rule.Thm ("realpow_zeroI",TermC.num_str @{thm realpow_zeroI}),
neuper@37950	665	("r ^^^ 0 = 1") (wegen "aa^^^(-1)c + b + c")
wneuper@59416	666	Rule.Thm ("realpow_oneI",TermC.num_str @{thm realpow_oneI}),
neuper@37950	667	("r ^^^ 1 = r")
wneuper@59416	668	Rule.Thm ("realpow_eq_oneI",TermC.num_str @{thm realpow_eq_oneI})
neuper@37950	669	("1 ^^^ n = 1")
wneuper@59416	670	], scr = Rule.EmptyScr};
neuper@37950	671
neuper@37950	672	val collect_numerals_ =
wneuper@59416	673	Rule.Rls{id = "collect_numerals_", preconds = [],
wneuper@59416	674	rew_ord = ("dummy_ord", Rule.dummy_ord),
wneuper@59416	675	erls = Atools_erls, srls = Rule.Erls,
neuper@38014	676	calc = [("PLUS" , ("Groups.plus_class.plus", eval_binop "#add_"))
neuper@42451	677	], errpatts = [],
neuper@37950	678	rules =
wneuper@59416	679	[Rule.Thm ("real_num_collect",TermC.num_str @{thm real_num_collect}),
neuper@37950	680	("[\| l is_const; m is_const \|]==>l n + m * n = (l + m) * n"*)
wneuper@59416	681	Rule.Thm ("real_num_collect_assoc_r",TermC.num_str @{thm real_num_collect_assoc_r}),
neuper@37950	682	(*"[\| l is_const; m is_const \|] ==> \
neuper@37950	683	\(k + m * n) + l * n = k + (l + m)n")
wneuper@59416	684	Rule.Thm ("real_one_collect",TermC.num_str @{thm real_one_collect}),
neuper@37950	685	("m is_const ==> n + m n = (1 + m) * n"*)
wneuper@59416	686	Rule.Thm ("real_one_collect_assoc_r",TermC.num_str @{thm real_one_collect_assoc_r}),
neuper@37950	687	("m is_const ==> (k + n) + m n = k + (m + 1) * n"*)
neuper@37950	688
wneuper@59416	689	Rule.Calc ("Groups.plus_class.plus", eval_binop "#add_"),
neuper@37950	690
wneuper@59416	691	(*MG: Reihenfolge der folgenden 2 Rule.Thm muss so bleiben, wegen
neuper@37950	692	(a+a)+a --> a + 2a --> 3a and not (a+a)+a --> 2a + a )
wneuper@59416	693	Rule.Thm ("real_mult_2_assoc_r",TermC.num_str @{thm real_mult_2_assoc_r}),
neuper@37950	694	("(k + z1) + z1 = k + 2 z1"*)
wneuper@59416	695	Rule.Thm ("sym_real_mult_2",TermC.num_str (@{thm real_mult_2} RS @{thm sym}))
neuper@37950	696	("z1 + z1 = 2 z1"*)
wneuper@59416	697	], scr = Rule.EmptyScr};
neuper@37950	698
neuper@37950	699	val reduce_012_ =
wneuper@59416	700	Rule.Rls{id = "reduce_012_", preconds = [],
wneuper@59416	701	rew_ord = ("dummy_ord", Rule.dummy_ord),
wneuper@59416	702	erls = Rule.e_rls,srls = Rule.Erls, calc = [], errpatts = [],
wneuper@59416	703	rules = [Rule.Thm ("mult_1_left",TermC.num_str @{thm mult_1_left}),
neuper@37950	704	("1 z = z"*)
wneuper@59416	705	Rule.Thm ("mult_zero_left",TermC.num_str @{thm mult_zero_left}),
neuper@37950	706	("0 z = 0"*)
wneuper@59416	707	Rule.Thm ("mult_zero_right",TermC.num_str @{thm mult_zero_right}),
neuper@37950	708	("z 0 = 0"*)
wneuper@59416	709	Rule.Thm ("add_0_left",TermC.num_str @{thm add_0_left}),
neuper@37950	710	("0 + z = z")
wneuper@59416	711	Rule.Thm ("add_0_right",TermC.num_str @{thm add_0_right}),
neuper@37950	712	("z + 0 = z") (wegen a+b-b --> a+(1-1)b --> a+0 --> a*)
neuper@37950	713
wneuper@59416	714	(Rule.Thm ("realpow_oneI",TermC.num_str @{thm realpow_oneI}))
neuper@37950	715	("?r ^^^ 1 = ?r")
wneuper@59416	716	Rule.Thm ("division_ring_divide_zero",TermC.num_str @{thm division_ring_divide_zero})
neuper@37950	717	("0 / ?x = 0")
wneuper@59416	718	], scr = Rule.EmptyScr};
neuper@37950	719
neuper@37979	720	val discard_parentheses1 =
wneuper@59416	721	Rule.append_rls "discard_parentheses1" Rule.e_rls
wneuper@59416	722	[Rule.Thm ("sym_mult_assoc",
wneuper@59389	723	TermC.num_str (@{thm mult.assoc} RS @{thm sym}))
neuper@37950	724	("?z1.1 (?z2.1 * ?z3.1) = ?z1.1 * ?z2.1 * ?z3.1"*)
wneuper@59416	725	(*Rule.Thm ("sym_add_assoc",
wneuper@59389	726	TermC.num_str (@{thm add_assoc} RS @{thm sym}))*)
neuper@37950	727	("?z1.1 + (?z2.1 + ?z3.1) = ?z1.1 + ?z2.1 + ?z3.1")
neuper@37950	728	];
neuper@37950	729
neuper@37950	730	(----------------- End: rulesets for make_polynomial_ -----------------)
neuper@37950	731
neuper@37950	732	(*MG.0401 ev. for use in rls with ordered rewriting ?
neuper@37950	733	val collect_numerals_left =
wneuper@59416	734	Rule.Rls{id = "collect_numerals", preconds = [],
wneuper@59416	735	rew_ord = ("dummy_ord", Rule.dummy_ord),
wneuper@59416	736	erls = Atools_erls(erls3.4.03),srls = Rule.Erls,
neuper@38014	737	calc = [("PLUS" , ("Groups.plus_class.plus", eval_binop "#add_")),
neuper@38034	738	("TIMES" , ("Groups.times_class.times", eval_binop "#mult_")),
neuper@37950	739	("POWER", ("Atools.pow", eval_binop "#power_"))
neuper@37950	740	],
neuper@42451	741	errpatts = [],
wneuper@59416	742	rules = [Rule.Thm ("real_num_collect",TermC.num_str @{thm real_num_collect}),
neuper@37950	743	("[\| l is_const; m is_const \|]==>l n + m * n = (l + m) * n"*)
wneuper@59416	744	Rule.Thm ("real_num_collect_assoc",TermC.num_str @{thm real_num_collect_assoc}),
neuper@37950	745	(*"[\| l is_const; m is_const \|] ==>
neuper@37950	746	l * n + (m * n + k) = (l + m) * n + k"*)
wneuper@59416	747	Rule.Thm ("real_one_collect",TermC.num_str @{thm real_one_collect}),
neuper@37950	748	("m is_const ==> n + m n = (1 + m) * n"*)
wneuper@59416	749	Rule.Thm ("real_one_collect_assoc",TermC.num_str @{thm real_one_collect_assoc}),
neuper@37950	750	("m is_const ==> n + (m n + k) = (1 + m) * n + k"*)
neuper@37950	751
wneuper@59416	752	Rule.Calc ("Groups.plus_class.plus", eval_binop "#add_"),
neuper@37950	753
neuper@37950	754	(MG am 2.5.03: 2 Theoreme aus reduce_012 hierher verschoben)
wneuper@59416	755	Rule.Thm ("sym_real_mult_2",
wneuper@59389	756	TermC.num_str (@{thm real_mult_2} RS @{thm sym})),
neuper@37950	757	("z1 + z1 = 2 z1"*)
wneuper@59416	758	Rule.Thm ("real_mult_2_assoc",TermC.num_str @{thm real_mult_2_assoc})
neuper@37950	759	("z1 + (z1 + k) = 2 z1 + k"*)
wneuper@59416	760	], scr = Rule.EmptyScr};*)
neuper@37950	761
neuper@37950	762	val expand_poly =
wneuper@59416	763	Rule.Rls{id = "expand_poly", preconds = [],
wneuper@59416	764	rew_ord = ("dummy_ord", Rule.dummy_ord),
wneuper@59416	765	erls = Rule.e_rls,srls = Rule.Erls,
neuper@42451	766	calc = [], errpatts = [],
neuper@37950	767	(asm_thm = [],)
wneuper@59416	768	rules = [Rule.Thm ("distrib_right" ,TermC.num_str @{thm distrib_right}),
neuper@37950	769	("(z1.0 + z2.0) w = z1.0 * w + z2.0 * w"*)
wneuper@59416	770	Rule.Thm ("distrib_left",TermC.num_str @{thm distrib_left}),
neuper@37950	771	("w (z1.0 + z2.0) = w * z1.0 + w * z2.0"*)
wneuper@59416	772	(*Rule.Thm ("distrib_right1",TermC.num_str @{thm distrib_right}1),
neuper@37950	773	....... 18.3.03 undefined???*)
neuper@37950	774
wneuper@59416	775	Rule.Thm ("real_plus_binom_pow2",TermC.num_str @{thm real_plus_binom_pow2}),
neuper@37950	776	("(a + b)^^^2 = a^^^2 + 2ab + b^^^2")
wneuper@59416	777	Rule.Thm ("real_minus_binom_pow2_p",TermC.num_str @{thm real_minus_binom_pow2_p}),
neuper@37950	778	("(a - b)^^^2 = a^^^2 + -2ab + b^^^2")
wneuper@59416	779	Rule.Thm ("real_plus_minus_binom1_p",
wneuper@59389	780	TermC.num_str @{thm real_plus_minus_binom1_p}),
neuper@37950	781	("(a + b)(a - b) = a^^^2 + -1b^^^2")
wneuper@59416	782	Rule.Thm ("real_plus_minus_binom2_p",
wneuper@59389	783	TermC.num_str @{thm real_plus_minus_binom2_p}),
neuper@37950	784	("(a - b)(a + b) = a^^^2 + -1b^^^2")
neuper@37950	785
wneuper@59416	786	Rule.Thm ("minus_minus",TermC.num_str @{thm minus_minus}),
neuper@37950	787	("- (- ?z) = ?z")
wneuper@59416	788	Rule.Thm ("real_diff_minus",TermC.num_str @{thm real_diff_minus}),
neuper@37950	789	("a - b = a + -1 b"*)
wneuper@59416	790	Rule.Thm ("sym_real_mult_minus1",
wneuper@59389	791	TermC.num_str (@{thm real_mult_minus1} RS @{thm sym}))
neuper@37950	792	(- ?z = "-1 ?z"*)
neuper@37950	793
wneuper@59416	794	(*Rule.Thm ("real_minus_add_distrib",
wneuper@59389	795	TermC.num_str @{thm real_minus_add_distrib}),*)
neuper@37950	796	("- (?x + ?y) = - ?x + - ?y")
wneuper@59416	797	(Rule.Thm ("real_diff_plus",TermC.num_str @{thm real_diff_plus}))
neuper@37950	798	("a - b = a + -b")
wneuper@59416	799	], scr = Rule.EmptyScr};
neuper@37950	800
neuper@37950	801	val simplify_power =
wneuper@59416	802	Rule.Rls{id = "simplify_power", preconds = [],
wneuper@59416	803	rew_ord = ("dummy_ord", Rule.dummy_ord),
wneuper@59416	804	erls = Rule.e_rls, srls = Rule.Erls,
neuper@42451	805	calc = [], errpatts = [],
wneuper@59416	806	rules = [Rule.Thm ("realpow_multI", TermC.num_str @{thm realpow_multI}),
neuper@37950	807	("(r s) ^^^ n = r ^^^ n * s ^^^ n"*)
neuper@37950	808
wneuper@59416	809	Rule.Thm ("sym_realpow_twoI",
wneuper@59389	810	TermC.num_str( @{thm realpow_twoI} RS @{thm sym})),
neuper@37950	811	("r1 r1 = r1 ^^^ 2"*)
wneuper@59416	812	Rule.Thm ("realpow_plus_1",TermC.num_str @{thm realpow_plus_1}),
neuper@37950	813	("r r ^^^ n = r ^^^ (n + 1)"*)
wneuper@59416	814	Rule.Thm ("realpow_pow",TermC.num_str @{thm realpow_pow}),
neuper@37950	815	("(a ^^^ b) ^^^ c = a ^^^ (b c)"*)
wneuper@59416	816	Rule.Thm ("sym_realpow_addI",
wneuper@59389	817	TermC.num_str (@{thm realpow_addI} RS @{thm sym})),
neuper@37950	818	("r ^^^ n r ^^^ m = r ^^^ (n + m)"*)
wneuper@59416	819	Rule.Thm ("realpow_oneI",TermC.num_str @{thm realpow_oneI}),
neuper@37950	820	("r ^^^ 1 = r")
wneuper@59416	821	Rule.Thm ("realpow_eq_oneI",TermC.num_str @{thm realpow_eq_oneI})
neuper@37950	822	("1 ^^^ n = 1")
wneuper@59416	823	], scr = Rule.EmptyScr};
neuper@37950	824	(*MG.0401: termorders for multivariate polys dropped due to principal problems:
neuper@37950	825	(total-degree-)ordering of monoms NOT possible with size_of_term GIVEN*)
neuper@37950	826	val order_add_mult =
wneuper@59416	827	Rule.Rls{id = "order_add_mult", preconds = [],
neuper@37972	828	rew_ord = ("ord_make_polynomial",ord_make_polynomial false thy),
wneuper@59416	829	erls = Rule.e_rls,srls = Rule.Erls,
neuper@42451	830	calc = [], errpatts = [],
wneuper@59416	831	rules = [Rule.Thm ("mult_commute",TermC.num_str @{thm mult.commute}),
neuper@37950	832	(* z * w = w * z *)
wneuper@59416	833	Rule.Thm ("real_mult_left_commute",TermC.num_str @{thm real_mult_left_commute}),
neuper@37950	834	(z1.0 (z2.0 * z3.0) = z2.0 * (z1.0 * z3.0)*)
wneuper@59416	835	Rule.Thm ("mult_assoc",TermC.num_str @{thm mult.assoc}),
neuper@37950	836	(z1.0 z2.0 * z3.0 = z1.0 * (z2.0 * z3.0)*)
wneuper@59416	837	Rule.Thm ("add_commute",TermC.num_str @{thm add.commute}),
neuper@37950	838	(z + w = w + z)
wneuper@59416	839	Rule.Thm ("add_left_commute",TermC.num_str @{thm add.left_commute}),
neuper@37950	840	(x + (y + z) = y + (x + z))
wneuper@59416	841	Rule.Thm ("add_assoc",TermC.num_str @{thm add.assoc})
neuper@37950	842	(z1.0 + z2.0 + z3.0 = z1.0 + (z2.0 + z3.0))
wneuper@59416	843	], scr = Rule.EmptyScr};
neuper@37950	844	(*MG.0401: termorders for multivariate polys dropped due to principal problems:
neuper@37950	845	(total-degree-)ordering of monoms NOT possible with size_of_term GIVEN*)
neuper@37950	846	val order_mult =
wneuper@59416	847	Rule.Rls{id = "order_mult", preconds = [],
neuper@37972	848	rew_ord = ("ord_make_polynomial",ord_make_polynomial false thy),
wneuper@59416	849	erls = Rule.e_rls,srls = Rule.Erls,
neuper@42451	850	calc = [], errpatts = [],
wneuper@59416	851	rules = [Rule.Thm ("mult_commute",TermC.num_str @{thm mult.commute}),
neuper@37950	852	(* z * w = w * z *)
wneuper@59416	853	Rule.Thm ("real_mult_left_commute",TermC.num_str @{thm real_mult_left_commute}),
neuper@37950	854	(z1.0 (z2.0 * z3.0) = z2.0 * (z1.0 * z3.0)*)
wneuper@59416	855	Rule.Thm ("mult_assoc",TermC.num_str @{thm mult.assoc})
neuper@37950	856	(z1.0 z2.0 * z3.0 = z1.0 * (z2.0 * z3.0)*)
wneuper@59416	857	], scr = Rule.EmptyScr};
neuper@42451	858	*}
neuper@42451	859
neuper@42451	860	ML {*
neuper@37950	861	val collect_numerals =
wneuper@59416	862	Rule.Rls{id = "collect_numerals", preconds = [],
wneuper@59416	863	rew_ord = ("dummy_ord", Rule.dummy_ord),
wneuper@59416	864	erls = Atools_erls(erls3.4.03),srls = Rule.Erls,
neuper@38014	865	calc = [("PLUS" , ("Groups.plus_class.plus", eval_binop "#add_")),
neuper@38034	866	("TIMES" , ("Groups.times_class.times", eval_binop "#mult_")),
neuper@37950	867	("POWER", ("Atools.pow", eval_binop "#power_"))
neuper@42451	868	], errpatts = [],
wneuper@59416	869	rules = [Rule.Thm ("real_num_collect",TermC.num_str @{thm real_num_collect}),
neuper@37950	870	("[\| l is_const; m is_const \|]==>l n + m * n = (l + m) * n"*)
wneuper@59416	871	Rule.Thm ("real_num_collect_assoc",TermC.num_str @{thm real_num_collect_assoc}),
neuper@37950	872	(*"[\| l is_const; m is_const \|] ==>
neuper@37950	873	l * n + (m * n + k) = (l + m) * n + k"*)
wneuper@59416	874	Rule.Thm ("real_one_collect",TermC.num_str @{thm real_one_collect}),
neuper@37950	875	("m is_const ==> n + m n = (1 + m) * n"*)
wneuper@59416	876	Rule.Thm ("real_one_collect_assoc",TermC.num_str @{thm real_one_collect_assoc}),
neuper@37950	877	("m is_const ==> k + (n + m n) = k + (1 + m) * n"*)
wneuper@59416	878	Rule.Calc ("Groups.plus_class.plus", eval_binop "#add_"),
wneuper@59416	879	Rule.Calc ("Groups.times_class.times", eval_binop "#mult_"),
wneuper@59416	880	Rule.Calc ("Atools.pow", eval_binop "#power_")
wneuper@59416	881	], scr = Rule.EmptyScr};
neuper@37950	882	val reduce_012 =
wneuper@59416	883	Rule.Rls{id = "reduce_012", preconds = [],
wneuper@59416	884	rew_ord = ("dummy_ord", Rule.dummy_ord),
wneuper@59416	885	erls = Rule.e_rls,srls = Rule.Erls,
neuper@42451	886	calc = [], errpatts = [],
wneuper@59416	887	rules = [Rule.Thm ("mult_1_left",TermC.num_str @{thm mult_1_left}),
neuper@37950	888	("1 z = z"*)
wneuper@59416	889	(Rule.Thm ("real_mult_minus1",TermC.num_str @{thm real_mult_minus1}),14.3.03)
neuper@37950	890	("-1 z = - z"*)
wneuper@59416	891	Rule.Thm ("minus_mult_left",
wneuper@59389	892	TermC.num_str (@{thm minus_mult_left} RS @{thm sym})),
neuper@37950	893	(- (?x ?y) = "- ?x * ?y"*)
wneuper@59416	894	(*Rule.Thm ("real_minus_mult_cancel",
wneuper@59389	895	TermC.num_str @{thm real_minus_mult_cancel}),
neuper@37950	896	("- ?x - ?y = ?x * ?y")---)
wneuper@59416	897	Rule.Thm ("mult_zero_left",TermC.num_str @{thm mult_zero_left}),
neuper@37950	898	("0 z = 0"*)
wneuper@59416	899	Rule.Thm ("add_0_left",TermC.num_str @{thm add_0_left}),
neuper@37950	900	("0 + z = z")
wneuper@59416	901	Rule.Thm ("right_minus",TermC.num_str @{thm right_minus}),
neuper@37950	902	("?z + - ?z = 0")
wneuper@59416	903	Rule.Thm ("sym_real_mult_2",
wneuper@59389	904	TermC.num_str (@{thm real_mult_2} RS @{thm sym})),
neuper@37950	905	("z1 + z1 = 2 z1"*)
wneuper@59416	906	Rule.Thm ("real_mult_2_assoc",TermC.num_str @{thm real_mult_2_assoc})
neuper@37950	907	("z1 + (z1 + k) = 2 z1 + k"*)
wneuper@59416	908	], scr = Rule.EmptyScr};
neuper@52139	909
neuper@37950	910	val discard_parentheses =
wneuper@59416	911	Rule.append_rls "discard_parentheses" Rule.e_rls
wneuper@59416	912	[Rule.Thm ("sym_mult_assoc",
wneuper@59389	913	TermC.num_str (@{thm mult.assoc} RS @{thm sym})),
wneuper@59416	914	Rule.Thm ("sym_add_assoc",
wneuper@59389	915	TermC.num_str (@{thm add.assoc} RS @{thm sym}))];
neuper@37950	916
wneuper@59429	917	(* probably perfectly replaced by auto-generated version *)
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'(
wneuper@59416	957	Rule.Seq{id = "make_polynomial", preconds = []:term list,
wneuper@59416	958	rew_ord = ("dummy_ord", Rule.dummy_ord),
wneuper@59416	959	erls = Atools_erls, srls = Rule.Erls,
neuper@42451	960	calc = [], errpatts = [],
wneuper@59416	961	rules = [Rule.Rls_ expand_poly,
wneuper@59416	962	Rule.Rls_ order_add_mult,
wneuper@59416	963	Rule.Rls_ simplify_power, (realpow_eq_oneI, eg. x^1 --> x )
wneuper@59416	964	Rule.Rls_ collect_numerals, (eg. x^(2+ -1) --> x^1 )
wneuper@59416	965	Rule.Rls_ reduce_012,
wneuper@59416	966	Rule.Thm ("realpow_oneI",TermC.num_str @{thm realpow_oneI}),(in --^)
wneuper@59416	967	Rule.Rls_ discard_parentheses
neuper@37950	968	],
wneuper@59416	969	scr = Rule.EmptyScr
wneuper@59406	970	}); *)
neuper@37950	971
wneuper@59429	972	(* replacement by auto-generated version seemed to cause ERROR in algein.sml *)
neuper@37950	973	val scr_expand_binoms =
neuper@37974	974	"Script Expand_binoms t_t =" ^
neuper@37950	975	"(Repeat " ^
neuper@37950	976	"((Try (Repeat (Rewrite real_plus_binom_pow2 False))) @@ " ^
neuper@37950	977	" (Try (Repeat (Rewrite real_plus_binom_times False))) @@ " ^
neuper@37950	978	" (Try (Repeat (Rewrite real_minus_binom_pow2 False))) @@ " ^
neuper@37950	979	" (Try (Repeat (Rewrite real_minus_binom_times False))) @@ " ^
neuper@37950	980	" (Try (Repeat (Rewrite real_plus_minus_binom1 False))) @@ " ^
neuper@37950	981	" (Try (Repeat (Rewrite real_plus_minus_binom2 False))) @@ " ^
neuper@37950	982
neuper@37971	983	" (Try (Repeat (Rewrite mult_1_left False))) @@ " ^
neuper@37971	984	" (Try (Repeat (Rewrite mult_zero_left False))) @@ " ^
neuper@37971	985	" (Try (Repeat (Rewrite add_0_left False))) @@ " ^
neuper@37950	986
neuper@37975	987	" (Try (Repeat (Calculate PLUS ))) @@ " ^
neuper@37975	988	" (Try (Repeat (Calculate TIMES ))) @@ " ^
neuper@37975	989	" (Try (Repeat (Calculate POWER))) @@ " ^
neuper@37950	990
neuper@37950	991	" (Try (Repeat (Rewrite sym_realpow_twoI False))) @@ " ^
neuper@37950	992	" (Try (Repeat (Rewrite realpow_plus_1 False))) @@ " ^
neuper@37950	993	" (Try (Repeat (Rewrite sym_real_mult_2 False))) @@ " ^
neuper@37950	994	" (Try (Repeat (Rewrite real_mult_2_assoc False))) @@ " ^
neuper@37950	995
neuper@37950	996	" (Try (Repeat (Rewrite real_num_collect False))) @@ " ^
neuper@37950	997	" (Try (Repeat (Rewrite real_num_collect_assoc False))) @@ " ^
neuper@37950	998
neuper@37950	999	" (Try (Repeat (Rewrite real_one_collect False))) @@ " ^
neuper@37950	1000	" (Try (Repeat (Rewrite real_one_collect_assoc False))) @@ " ^
neuper@37950	1001
neuper@37975	1002	" (Try (Repeat (Calculate PLUS ))) @@ " ^
neuper@37975	1003	" (Try (Repeat (Calculate TIMES ))) @@ " ^
neuper@37975	1004	" (Try (Repeat (Calculate POWER)))) " ^
neuper@37974	1005	" t_t)";
neuper@37974	1006
neuper@37950	1007	val expand_binoms =
wneuper@59416	1008	Rule.Rls{id = "expand_binoms", preconds = [], rew_ord = ("termlessI",termlessI),
wneuper@59416	1009	erls = Atools_erls, srls = Rule.Erls,
neuper@38014	1010	calc = [("PLUS" , ("Groups.plus_class.plus", eval_binop "#add_")),
neuper@38034	1011	("TIMES" , ("Groups.times_class.times", eval_binop "#mult_")),
neuper@37950	1012	("POWER", ("Atools.pow", eval_binop "#power_"))
neuper@42451	1013	], errpatts = [],
wneuper@59416	1014	rules = [Rule.Thm ("real_plus_binom_pow2",
wneuper@59389	1015	TermC.num_str @{thm real_plus_binom_pow2}),
neuper@37950	1016	("(a + b) ^^^ 2 = a ^^^ 2 + 2 a * b + b ^^^ 2"*)
wneuper@59416	1017	Rule.Thm ("real_plus_binom_times",
wneuper@59389	1018	TermC.num_str @{thm real_plus_binom_times}),
neuper@37950	1019	("(a + b)(a + b) = ...*)
wneuper@59416	1020	Rule.Thm ("real_minus_binom_pow2",
wneuper@59389	1021	TermC.num_str @{thm real_minus_binom_pow2}),
neuper@37950	1022	("(a - b) ^^^ 2 = a ^^^ 2 - 2 a * b + b ^^^ 2"*)
wneuper@59416	1023	Rule.Thm ("real_minus_binom_times",
wneuper@59389	1024	TermC.num_str @{thm real_minus_binom_times}),
neuper@37950	1025	("(a - b)(a - b) = ...*)
wneuper@59416	1026	Rule.Thm ("real_plus_minus_binom1",
wneuper@59389	1027	TermC.num_str @{thm real_plus_minus_binom1}),
neuper@37950	1028	("(a + b) (a - b) = a ^^^ 2 - b ^^^ 2"*)
wneuper@59416	1029	Rule.Thm ("real_plus_minus_binom2",
wneuper@59389	1030	TermC.num_str @{thm real_plus_minus_binom2}),
neuper@37950	1031	("(a - b) (a + b) = a ^^^ 2 - b ^^^ 2"*)
neuper@37950	1032	(RL 020915)
wneuper@59416	1033	Rule.Thm ("real_pp_binom_times",TermC.num_str @{thm real_pp_binom_times}),
neuper@37950	1034	((a + b)(c + d) = ac + ad + bc + bd*)
wneuper@59416	1035	Rule.Thm ("real_pm_binom_times",TermC.num_str @{thm real_pm_binom_times}),
neuper@37950	1036	((a + b)(c - d) = ac - ad + bc - bd*)
wneuper@59416	1037	Rule.Thm ("real_mp_binom_times",TermC.num_str @{thm real_mp_binom_times}),
neuper@37950	1038	((a - b)(c + d) = ac + ad - bc - bd*)
wneuper@59416	1039	Rule.Thm ("real_mm_binom_times",TermC.num_str @{thm real_mm_binom_times}),
neuper@37950	1040	((a - b)(c - d) = ac - ad - bc + bd*)
wneuper@59416	1041	Rule.Thm ("realpow_multI",TermC.num_str @{thm realpow_multI}),
neuper@37950	1042	((ab)^^^n = a^^^n * b^^^n*)
wneuper@59416	1043	Rule.Thm ("real_plus_binom_pow3",TermC.num_str @{thm real_plus_binom_pow3}),
neuper@37950	1044	(* (a + b)^^^3 = a^^^3 + 3a^^^2b + 3ab^^^2 + b^^^3 *)
wneuper@59416	1045	Rule.Thm ("real_minus_binom_pow3",
wneuper@59389	1046	TermC.num_str @{thm real_minus_binom_pow3}),
neuper@37950	1047	(* (a - b)^^^3 = a^^^3 - 3a^^^2b + 3ab^^^2 - b^^^3 *)
neuper@37950	1048
neuper@37950	1049
wneuper@59416	1050	(*Rule.Thm ("distrib_right" ,TermC.num_str @{thm distrib_right}),
neuper@37950	1051	("(z1.0 + z2.0) w = z1.0 * w + z2.0 * w"*)
wneuper@59416	1052	Rule.Thm ("distrib_left",TermC.num_str @{thm distrib_left}),
neuper@37950	1053	("w (z1.0 + z2.0) = w * z1.0 + w * z2.0"*)
wneuper@59416	1054	Rule.Thm ("left_diff_distrib" ,TermC.num_str @{thm left_diff_distrib}),
neuper@37950	1055	("(z1.0 - z2.0) w = z1.0 * w - z2.0 * w"*)
wneuper@59416	1056	Rule.Thm ("right_diff_distrib",TermC.num_str @{thm right_diff_distrib}),
neuper@37950	1057	("w (z1.0 - z2.0) = w * z1.0 - w * z2.0"*)
neuper@37974	1058	*)
wneuper@59416	1059	Rule.Thm ("mult_1_left",TermC.num_str @{thm mult_1_left}),
neuper@37974	1060	("1 z = z"*)
wneuper@59416	1061	Rule.Thm ("mult_zero_left",TermC.num_str @{thm mult_zero_left}),
neuper@37974	1062	("0 z = 0"*)
wneuper@59416	1063	Rule.Thm ("add_0_left",TermC.num_str @{thm add_0_left}),("0 + z = z")
neuper@37950	1064
wneuper@59416	1065	Rule.Calc ("Groups.plus_class.plus", eval_binop "#add_"),
wneuper@59416	1066	Rule.Calc ("Groups.times_class.times", eval_binop "#mult_"),
wneuper@59416	1067	Rule.Calc ("Atools.pow", eval_binop "#power_"),
wneuper@59416	1068	(*Rule.Thm ("mult_commute",TermC.num_str @{thm mult_commute}),
neuper@37974	1069	(AC-rewriting)
wneuper@59416	1070	Rule.Thm ("real_mult_left_commute",
wneuper@59389	1071	TermC.num_str @{thm real_mult_left_commute}),
wneuper@59416	1072	Rule.Thm ("mult_assoc",TermC.num_str @{thm mult.assoc}),
wneuper@59416	1073	Rule.Thm ("add_commute",TermC.num_str @{thm add.commute}),
wneuper@59416	1074	Rule.Thm ("add_left_commute",TermC.num_str @{thm add.left_commute}),
wneuper@59416	1075	Rule.Thm ("add_assoc",TermC.num_str @{thm add.assoc}),
neuper@37974	1076	*)
wneuper@59416	1077	Rule.Thm ("sym_realpow_twoI",
wneuper@59389	1078	TermC.num_str (@{thm realpow_twoI} RS @{thm sym})),
neuper@37950	1079	("r1 r1 = r1 ^^^ 2"*)
wneuper@59416	1080	Rule.Thm ("realpow_plus_1",TermC.num_str @{thm realpow_plus_1}),
neuper@37950	1081	("r r ^^^ n = r ^^^ (n + 1)"*)
wneuper@59416	1082	(*Rule.Thm ("sym_real_mult_2",
wneuper@59389	1083	TermC.num_str (@{thm real_mult_2} RS @{thm sym})),
neuper@37950	1084	("z1 + z1 = 2 z1"))
wneuper@59416	1085	Rule.Thm ("real_mult_2_assoc",TermC.num_str @{thm real_mult_2_assoc}),
neuper@37950	1086	("z1 + (z1 + k) = 2 z1 + k"*)
neuper@37950	1087
wneuper@59416	1088	Rule.Thm ("real_num_collect",TermC.num_str @{thm real_num_collect}),
neuper@37974	1089	("[\| l is_const; m is_const \|] ==>l n + m * n = (l + m) * n"*)
wneuper@59416	1090	Rule.Thm ("real_num_collect_assoc",
wneuper@59389	1091	TermC.num_str @{thm real_num_collect_assoc}),
neuper@37974	1092	(*"[\| l is_const; m is_const \|] ==>
neuper@37974	1093	l * n + (m * n + k) = (l + m) * n + k"*)
wneuper@59416	1094	Rule.Thm ("real_one_collect",TermC.num_str @{thm real_one_collect}),
neuper@37950	1095	("m is_const ==> n + m n = (1 + m) * n"*)
wneuper@59416	1096	Rule.Thm ("real_one_collect_assoc",
wneuper@59389	1097	TermC.num_str @{thm real_one_collect_assoc}),
neuper@37950	1098	("m is_const ==> k + (n + m n) = k + (1 + m) * n"*)
neuper@37950	1099
wneuper@59416	1100	Rule.Calc ("Groups.plus_class.plus", eval_binop "#add_"),
wneuper@59416	1101	Rule.Calc ("Groups.times_class.times", eval_binop "#mult_"),
wneuper@59416	1102	Rule.Calc ("Atools.pow", eval_binop "#power_")
neuper@37950	1103	],
wneuper@59416	1104	scr = Rule.Prog ((Thm.term_of o the o (TermC.parse thy)) scr_expand_binoms)
wneuper@59406	1105	};
neuper@37950	1106
neuper@37950	1107
neuper@37950	1108	(. MG.03: make_polynomial_ ... uses SML-fun for ordering .)
neuper@37950	1109
neuper@37950	1110	(FIXME.0401: make SML-order local to make_polynomial(_) )
neuper@37950	1111	(FIXME.0401: replace 'make_polynomial'(old) by 'make_polynomial_'(MG) )
neuper@37950	1112	(* Polynom --> List von Monomen *)
neuper@38014	1113	fun poly2list (Const ("Groups.plus_class.plus",_) $ t1 $ t2) =
neuper@37950	1114	(poly2list t1) @ (poly2list t2)
neuper@37950	1115	\| poly2list t = [t];
neuper@37950	1116
neuper@37950	1117	(* Monom --> Liste von Variablen *)
neuper@38034	1118	fun monom2list (Const ("Groups.times_class.times",_) $ t1 $ t2) =
neuper@37950	1119	(monom2list t1) @ (monom2list t2)
neuper@37950	1120	\| monom2list t = [t];
neuper@37950	1121
neuper@37950	1122	(* liefert Variablenname (String) einer Variablen und Basis bei Potenz *)
neuper@37950	1123	fun get_basStr (Const ("Atools.pow",_) $ Free (str, _) $ _) = str
neuper@37950	1124	\| get_basStr (Free (str, _)) = str
neuper@37950	1125	\| get_basStr t = "\|\|\|"; (* gross gewichtet; für Brüch ect. *)
neuper@37950	1126	(*\| get_basStr t =
wneuper@59416	1127	error("get_basStr: called with t= "^(Rule.term2str t));*)
neuper@37950	1128
neuper@37950	1129	(* liefert Hochzahl (String) einer Variablen bzw Gewichtstring (zum Sortieren) *)
neuper@37950	1130	fun get_potStr (Const ("Atools.pow",_) $ Free _ $ Free (str, _)) = str
neuper@37950	1131	\| get_potStr (Const ("Atools.pow",_) $ Free _ $ _ ) = "\|\|\|" (* gross gewichtet *)
neuper@37950	1132	\| get_potStr (Free (str, _)) = "---" (* keine Hochzahl --> kleinst gewichtet *)
neuper@37950	1133	\| get_potStr t = "\|\|\|\|\|\|"; (* gross gewichtet; für Brüch ect. *)
neuper@37950	1134	(*\| get_potStr t =
wneuper@59416	1135	error("get_potStr: called with t= "^(Rule.term2str t));*)
neuper@37950	1136
neuper@37950	1137	(* Umgekehrte string_ord *)
neuper@37950	1138	val string_ord_rev = rev_order o string_ord;
neuper@37950	1139
neuper@37950	1140	(* Ordnung zum lexikographischen Vergleich zweier Variablen (oder Potenzen)
neuper@37950	1141	innerhalb eines Monomes:
neuper@37950	1142	- zuerst lexikographisch nach Variablenname
neuper@37950	1143	- wenn gleich: nach steigender Potenz *)
neuper@37950	1144	fun var_ord (a,b: term) = prod_ord string_ord string_ord
neuper@37950	1145	((get_basStr a, get_potStr a), (get_basStr b, get_potStr b));
neuper@37950	1146
neuper@37950	1147	(* Ordnung zum lexikographischen Vergleich zweier Variablen (oder Potenzen);
neuper@37950	1148	verwendet zum Sortieren von Monomen mittels Gesamtgradordnung:
neuper@37950	1149	- zuerst lexikographisch nach Variablenname
neuper@37950	1150	- wenn gleich: nach sinkender Potenz*)
neuper@37950	1151	fun var_ord_revPow (a,b: term) = prod_ord string_ord string_ord_rev
neuper@37950	1152	((get_basStr a, get_potStr a), (get_basStr b, get_potStr b));
neuper@37950	1153
neuper@37950	1154
neuper@37950	1155	(* Ordnet ein Liste von Variablen (und Potenzen) lexikographisch *)
neuper@37950	1156	val sort_varList = sort var_ord;
neuper@37950	1157
neuper@37950	1158	(* Entfernet aeussersten Operator (Wurzel) aus einem Term und schreibt
neuper@37950	1159	Argumente in eine Liste *)
neuper@37950	1160	fun args u : term list =
neuper@37950	1161	let fun stripc (f$t, ts) = stripc (f, t::ts)
neuper@37950	1162	\| stripc (t as Free _, ts) = (t::ts)
neuper@37950	1163	\| stripc (_, ts) = ts
neuper@37950	1164	in stripc (u, []) end;
neuper@37950	1165
neuper@37950	1166	(* liefert True, falls der Term (Liste von Termen) nur Zahlen
neuper@37950	1167	(keine Variablen) enthaelt *)
neuper@37950	1168	fun filter_num [] = true
wneuper@59389	1169	\| filter_num [Free x] = if (TermC.is_num (Free x)) then true
neuper@37950	1170	else false
neuper@37950	1171	\| filter_num ((Free _)::_) = false
neuper@37950	1172	\| filter_num ts =
wneuper@59389	1173	(filter_num o (filter_out TermC.is_num) o flat o (map args)) ts;
neuper@37950	1174
neuper@37950	1175	(* liefert True, falls der Term nur Zahlen (keine Variablen) enthaelt
neuper@37950	1176	dh. er ist ein numerischer Wert und entspricht einem Koeffizienten *)
neuper@37950	1177	fun is_nums t = filter_num [t];
neuper@37950	1178
neuper@37950	1179	(* Berechnet den Gesamtgrad eines Monoms *)
neuper@37950	1180	local
neuper@37950	1181	fun counter (n, []) = n
neuper@37950	1182	\| counter (n, x :: xs) =
neuper@37950	1183	if (is_nums x) then
neuper@37950	1184	counter (n, xs)
neuper@37950	1185	else
neuper@37950	1186	(case x of
neuper@37950	1187	(Const ("Atools.pow", _) $ Free (str_b, _) $ Free (str_h, T)) =>
neuper@37950	1188	if (is_nums (Free (str_h, T))) then
wneuper@59390	1189	counter (n + (the (TermC.int_of_str_opt str_h)), xs)
neuper@37950	1190	else counter (n + 1000, xs) (FIXME.MG?!)
neuper@37950	1191	\| (Const ("Atools.pow", _) $ Free (str_b, _) $ _ ) =>
neuper@37950	1192	counter (n + 1000, xs) (FIXME.MG?!)
neuper@37950	1193	\| (Free (str, _)) => counter (n + 1, xs)
wneuper@59416	1194	(\| _ => error("monom_degree: called with factor: "^(Rule.term2str x))))
neuper@37950	1195	\| _ => counter (n + 10000, xs)) (FIXME.MG?! ... Brüche ect.)
neuper@37950	1196	in
neuper@37950	1197	fun monom_degree l = counter (0, l)
neuper@37980	1198	end;(local)
neuper@37950	1199
neuper@37950	1200	(* wie Ordnung dict_ord (lexicographische Ordnung zweier Listen, mit Vergleich
neuper@37950	1201	der Listen-Elemente mit elem_ord) - Elemente die Bedingung cond erfuellen,
neuper@37950	1202	werden jedoch dabei ignoriert (uebersprungen) *)
neuper@37950	1203	fun dict_cond_ord _ _ ([], []) = EQUAL
neuper@37950	1204	\| dict_cond_ord _ _ ([], _ :: _) = LESS
neuper@37950	1205	\| dict_cond_ord _ _ (_ :: _, []) = GREATER
neuper@37950	1206	\| dict_cond_ord elem_ord cond (x :: xs, y :: ys) =
neuper@37950	1207	(case (cond x, cond y) of
neuper@37950	1208	(false, false) => (case elem_ord (x, y) of
neuper@37950	1209	EQUAL => dict_cond_ord elem_ord cond (xs, ys)
neuper@37950	1210	\| ord => ord)
neuper@37950	1211	\| (false, true) => dict_cond_ord elem_ord cond (x :: xs, ys)
neuper@37950	1212	\| (true, false) => dict_cond_ord elem_ord cond (xs, y :: ys)
neuper@37950	1213	\| (true, true) => dict_cond_ord elem_ord cond (xs, ys) );
neuper@37950	1214
neuper@37950	1215	(* Gesamtgradordnung zum Vergleich von Monomen (Liste von Variablen/Potenzen):
neuper@37950	1216	zuerst nach Gesamtgrad, bei gleichem Gesamtgrad lexikographisch ordnen -
neuper@37950	1217	dabei werden Koeffizienten ignoriert (23a^^^24b gilt wie a^^^2b) )
neuper@37950	1218	fun degree_ord (xs, ys) =
neuper@37950	1219	prod_ord int_ord (dict_cond_ord var_ord_revPow is_nums)
neuper@37950	1220	((monom_degree xs, xs), (monom_degree ys, ys));
neuper@37950	1221
neuper@37950	1222	fun hd_str str = substring (str, 0, 1);
neuper@37950	1223	fun tl_str str = substring (str, 1, (size str) - 1);
neuper@37950	1224
neuper@37950	1225	(* liefert nummerischen Koeffizienten eines Monoms oder NONE *)
neuper@38031	1226	fun get_koeff_of_mon [] = error("get_koeff_of_mon: called with l = []")
neuper@37950	1227	\| get_koeff_of_mon (l as x::xs) = if is_nums x then SOME x
neuper@37950	1228	else NONE;
neuper@37950	1229
neuper@37950	1230	(* wandelt Koeffizient in (zum sortieren geeigneten) String um *)
neuper@37950	1231	fun koeff2ordStr (SOME x) = (case x of
neuper@37950	1232	(Free (str, T)) =>
neuper@37950	1233	if (hd_str str) = "-" then (tl_str str)^"0" (* 3 < -3 *)
neuper@37950	1234	else str
neuper@37950	1235	\| _ => "aaa") (* "num.Ausdruck" --> gross *)
neuper@37950	1236	\| koeff2ordStr NONE = "---"; (* "kein Koeff" --> kleinste *)
neuper@37950	1237
neuper@37950	1238	(* Order zum Vergleich von Koeffizienten (strings):
neuper@37950	1239	"kein Koeff" < "0" < "1" < "-1" < "2" < "-2" < ... < "num.Ausdruck" *)
neuper@37950	1240	fun compare_koeff_ord (xs, ys) =
neuper@37950	1241	string_ord ((koeff2ordStr o get_koeff_of_mon) xs,
neuper@37950	1242	(koeff2ordStr o get_koeff_of_mon) ys);
neuper@37950	1243
neuper@37950	1244	(* Gesamtgradordnung degree_ord + Ordnen nach Koeffizienten falls EQUAL *)
neuper@37950	1245	fun koeff_degree_ord (xs, ys) =
neuper@37950	1246	prod_ord degree_ord compare_koeff_ord ((xs, xs), (ys, ys));
neuper@37950	1247
neuper@37950	1248	(* Ordnet ein Liste von Monomen (Monom = Liste von Variablen) mittels
neuper@37950	1249	Gesamtgradordnung *)
neuper@37950	1250	val sort_monList = sort koeff_degree_ord;
neuper@37950	1251
neuper@37950	1252	(* Alternativ zu degree_ord koennte auch die viel einfachere und
neuper@37950	1253	kuerzere Ordnung simple_ord verwendet werden - ist aber nicht
neuper@37950	1254	fuer unsere Zwecke geeignet!
neuper@37950	1255
neuper@37950	1256	fun simple_ord (al,bl: term list) = dict_ord string_ord
neuper@37950	1257	(map get_basStr al, map get_basStr bl);
neuper@37950	1258
neuper@37950	1259	val sort_monList = sort simple_ord; *)
neuper@37950	1260
neuper@37950	1261	(* aus 2 Variablen wird eine Summe bzw ein Produkt erzeugt
neuper@37950	1262	(mit gewuenschtem Typen T) *)
neuper@38014	1263	fun plus T = Const ("Groups.plus_class.plus", [T,T] ---> T);
neuper@38034	1264	fun mult T = Const ("Groups.times_class.times", [T,T] ---> T);
neuper@37950	1265	fun binop op_ t1 t2 = op_ $ t1 $ t2;
neuper@37950	1266	fun create_prod T (a,b) = binop (mult T) a b;
neuper@37950	1267	fun create_sum T (a,b) = binop (plus T) a b;
neuper@37950	1268
neuper@37950	1269	(* löscht letztes Element einer Liste *)
neuper@37950	1270	fun drop_last l = take ((length l)-1,l);
neuper@37950	1271
neuper@37950	1272	(* Liste von Variablen --> Monom *)
neuper@37950	1273	fun create_monom T vl = foldr (create_prod T) (drop_last vl, last_elem vl);
neuper@37950	1274	(* Bemerkung:
neuper@37950	1275	foldr bewirkt rechtslastige Klammerung des Monoms - ist notwendig, damit zwei
neuper@37950	1276	gleiche Monome zusammengefasst werden können (collect_numerals)!
neuper@37950	1277	zB: 2(x(yz)) + 3(x(yz)) --> (2+3)(x(yz)))
neuper@37950	1278
neuper@37950	1279	(* Liste von Monomen --> Polynom *)
neuper@37950	1280	fun create_polynom T ml = foldl (create_sum T) (hd ml, tl ml);
neuper@37950	1281	(* Bemerkung:
neuper@37950	1282	foldl bewirkt linkslastige Klammerung des Polynoms (der Summanten) -
neuper@37950	1283	bessere Darstellung, da keine Klammern sichtbar!
neuper@37950	1284	(und discard_parentheses in make_polynomial hat weniger zu tun) *)
neuper@37950	1285
neuper@37950	1286	(* sorts the variables (faktors) of an expanded polynomial lexicographical *)
neuper@37950	1287	fun sort_variables t =
neuper@37950	1288	let
neuper@37950	1289	val ll = map monom2list (poly2list t);
neuper@37950	1290	val lls = map sort_varList ll;
neuper@37950	1291	val T = type_of t;
neuper@37950	1292	val ls = map (create_monom T) lls;
neuper@37950	1293	in create_polynom T ls end;
neuper@37950	1294
neuper@37950	1295	(* sorts the monoms of an expanded and variable-sorted polynomial
neuper@37950	1296	by total_degree *)
neuper@37950	1297	fun sort_monoms t =
neuper@37950	1298	let
neuper@37950	1299	val ll = map monom2list (poly2list t);
neuper@37950	1300	val lls = sort_monList ll;
neuper@37950	1301	val T = type_of t;
neuper@37950	1302	val ls = map (create_monom T) lls;
neuper@37950	1303	in create_polynom T ls end;
neuper@37950	1304
neuper@37950	1305	(* auch Klammerung muss übereinstimmen;
neuper@37950	1306	sort_variables klammert Produkte rechtslastig*)
neuper@37950	1307	fun is_multUnordered t = ((is_polyexp t) andalso not (t = sort_variables t));
neuper@37950	1308
neuper@42451	1309	*}
neuper@42451	1310	ML {*
neuper@37950	1311	fun eval_is_multUnordered (thmid:string) _
neuper@37950	1312	(t as (Const("Poly.is'_multUnordered", _) $ arg)) thy =
neuper@37950	1313	if is_multUnordered arg
wneuper@59416	1314	then SOME (TermC.mk_thmid thmid (Rule.term_to_string''' thy arg) "",
wneuper@59390	1315	HOLogic.Trueprop $ (TermC.mk_equality (t, @{term True})))
wneuper@59416	1316	else SOME (TermC.mk_thmid thmid (Rule.term_to_string''' thy arg) "",
wneuper@59390	1317	HOLogic.Trueprop $ (TermC.mk_equality (t, @{term False})))
neuper@37950	1318	\| eval_is_multUnordered _ _ _ _ = NONE;
neuper@37950	1319
wneuper@59416	1320	fun attach_form (_: Rule.rule list list) (_: term) (_: term) = (still missing)
wneuper@59416	1321	[]:(Rule.rule * (term * term list)) list;
wneuper@59416	1322	fun init_state (_: term) = Rule.e_rrlsstate;
wneuper@59416	1323	fun locate_rule (_: Rule.rule list list) (_: term) (_: Rule.rule) =
wneuper@59416	1324	([]:(Rule.rule * (term * term list)) list);
wneuper@59416	1325	fun next_rule (_: Rule.rule list list) (_: term) = (NONE: Rule.rule option);
wneuper@59406	1326	fun normal_form t = SOME (sort_variables t, []: term list);
neuper@37950	1327
neuper@37950	1328	val order_mult_ =
wneuper@59416	1329	Rule.Rrls {id = "order_mult_",
neuper@37950	1330	prepat =
neuper@38036	1331	(* ?p matched with the current term gives an environment,
neuper@38037	1332	which evaluates (the instantiated) "?p is_multUnordered" to true *)
wneuper@59389	1333	[([TermC.parse_patt thy "?p is_multUnordered"],
wneuper@59389	1334	TermC.parse_patt thy "?p :: real")],
wneuper@59416	1335	rew_ord = ("dummy_ord", Rule.dummy_ord),
wneuper@59416	1336	erls = Rule.append_rls "Rule.e_rls-is_multUnordered" Rule.e_rls
wneuper@59416	1337	[Rule.Calc ("Poly.is'_multUnordered",
neuper@37976	1338	eval_is_multUnordered "")],
neuper@38036	1339	calc = [("PLUS" , ("Groups.plus_class.plus", eval_binop "#add_")),
neuper@38036	1340	("TIMES" , ("Groups.times_class.times", eval_binop "#mult_")),
wneuper@59360	1341	("DIVIDE", ("Rings.divide_class.divide",
neuper@38036	1342	eval_cancel "#divide_e")),
neuper@37976	1343	("POWER" , ("Atools.pow", eval_binop "#power_"))],
wneuper@59406	1344	errpatts = [],
wneuper@59416	1345	scr = Rule.Rfuns {init_state = init_state,
neuper@37950	1346	normal_form = normal_form,
neuper@37950	1347	locate_rule = locate_rule,
neuper@37950	1348	next_rule = next_rule,
neuper@37950	1349	attach_form = attach_form}};
neuper@37950	1350	val order_mult_rls_ =
wneuper@59416	1351	Rule.Rls {id = "order_mult_rls_", preconds = [],
wneuper@59416	1352	rew_ord = ("dummy_ord", Rule.dummy_ord),
wneuper@59416	1353	erls = Rule.e_rls,srls = Rule.Erls,
neuper@42451	1354	calc = [], errpatts = [],
wneuper@59416	1355	rules = [Rule.Rls_ order_mult_
wneuper@59416	1356	], scr = Rule.EmptyScr};
neuper@42451	1357	*}
neuper@42451	1358	ML {*
neuper@37950	1359
neuper@37950	1360	fun is_addUnordered t = ((is_polyexp t) andalso not (t = sort_monoms t));
neuper@37950	1361
neuper@37950	1362	(WN.18.6.03 )
neuper@37950	1363	(("is_addUnordered", ("Poly.is'_addUnordered", eval_is_addUnordered "")))
neuper@37950	1364	fun eval_is_addUnordered (thmid:string) _
neuper@37950	1365	(t as (Const("Poly.is'_addUnordered", _) $ arg)) thy =
neuper@37950	1366	if is_addUnordered arg
wneuper@59416	1367	then SOME (TermC.mk_thmid thmid (Rule.term_to_string''' thy arg) "",
wneuper@59390	1368	HOLogic.Trueprop $ (TermC.mk_equality (t, @{term True})))
wneuper@59416	1369	else SOME (TermC.mk_thmid thmid (Rule.term_to_string''' thy arg) "",
wneuper@59390	1370	HOLogic.Trueprop $ (TermC.mk_equality (t, @{term False})))
neuper@37950	1371	\| eval_is_addUnordered _ _ _ _ = NONE;
neuper@37950	1372
wneuper@59416	1373	fun attach_form (_: Rule.rule list list) (_: term) (_: term) = (still missing)
wneuper@59416	1374	[]: (Rule.rule * (term * term list)) list;
wneuper@59416	1375	fun init_state (_: term) = Rule.e_rrlsstate;
wneuper@59416	1376	fun locate_rule (_: Rule.rule list list) (_: term) (_: Rule.rule) =
wneuper@59416	1377	([]: (Rule.rule * (term * term list)) list);
wneuper@59416	1378	fun next_rule (_: Rule.rule list list) (_: term) = (NONE: Rule.rule option);
wneuper@59406	1379	fun normal_form t = SOME (sort_monoms t,[]: term list);
neuper@37950	1380
wneuper@59406	1381	} ML {
neuper@37950	1382	val order_add_ =
wneuper@59416	1383	Rule.Rrls {id = "order_add_",
neuper@37950	1384	prepat = (*WN.18.6.03 Preconditions und Pattern,
wneuper@59416	1385	die beide passen muessen, damit das Rule.Rrls angewandt wird*)
wneuper@59389	1386	[([TermC.parse_patt @{theory} "?p is_addUnordered"],
wneuper@59389	1387	TermC.parse_patt @{theory} "?p :: real"
neuper@37950	1388	(*WN.18.6.03 also KEIN pattern, dieses erzeugt nur das Environment
neuper@37950	1389	fuer die Evaluation der Precondition "p is_addUnordered"*))],
wneuper@59416	1390	rew_ord = ("dummy_ord", Rule.dummy_ord),
wneuper@59416	1391	erls = Rule.append_rls "Rule.e_rls-is_addUnordered" Rule.e_rls(MG: poly_erls)
wneuper@59416	1392	[Rule.Calc ("Poly.is'_addUnordered",
neuper@38037	1393	eval_is_addUnordered "")],
neuper@38037	1394	calc = [("PLUS" ,("Groups.plus_class.plus", eval_binop "#add_")),
neuper@38037	1395	("TIMES" ,("Groups.times_class.times", eval_binop "#mult_")),
wneuper@59360	1396	("DIVIDE",("Rings.divide_class.divide",
neuper@38037	1397	eval_cancel "#divide_e")),
neuper@38037	1398	("POWER" ,("Atools.pow" ,eval_binop "#power_"))],
neuper@42451	1399	errpatts = [],
wneuper@59416	1400	scr = Rule.Rfuns {init_state = init_state,
neuper@37950	1401	normal_form = normal_form,
neuper@37950	1402	locate_rule = locate_rule,
neuper@37950	1403	next_rule = next_rule,
neuper@37950	1404	attach_form = attach_form}};
neuper@37950	1405
wneuper@59406	1406	val order_add_rls_ =
wneuper@59416	1407	Rule.Rls {id = "order_add_rls_", preconds = [],
wneuper@59416	1408	rew_ord = ("dummy_ord", Rule.dummy_ord),
wneuper@59416	1409	erls = Rule.e_rls,srls = Rule.Erls,
neuper@42451	1410	calc = [], errpatts = [],
wneuper@59416	1411	rules = [Rule.Rls_ order_add_
wneuper@59416	1412	], scr = Rule.EmptyScr};
neuper@42398	1413	*}
neuper@37950	1414
neuper@42398	1415	text {* rule-set make_polynomial also named norm_Poly:
neuper@42398	1416	Rewrite order has not been implemented properly; the order is better in
neuper@42398	1417	make_polynomial_in (coded in SML).
neuper@42398	1418	Notes on state of development:
neuper@42398	1419	\# surprise 2006: test --- norm_Poly NOT COMPLETE ---
neuper@42398	1420	\# migration Isabelle2002 --> 2011 weakened the rule set, see test
neuper@42398	1421	--- Matthias Goldgruber 2003 rewrite orders ---, error "ord_make_polynomial_in #16b"
neuper@42398	1422	*}
neuper@42398	1423	ML {*
neuper@37950	1424	(. see MG-DA.p.52ff .)
neuper@37950	1425	val make_polynomial(*MG.03, overwrites version from above,
neuper@37950	1426	previously 'make_polynomial_'*) =
wneuper@59416	1427	Rule.Seq {id = "make_polynomial", preconds = []:term list,
wneuper@59416	1428	rew_ord = ("dummy_ord", Rule.dummy_ord),
wneuper@59416	1429	erls = Atools_erls, srls = Rule.Erls,calc = [], errpatts = [],
wneuper@59416	1430	rules = [Rule.Rls_ discard_minus,
wneuper@59416	1431	Rule.Rls_ expand_poly_,
wneuper@59416	1432	Rule.Calc ("Groups.times_class.times", eval_binop "#mult_"),
wneuper@59416	1433	Rule.Rls_ order_mult_rls_,
wneuper@59416	1434	Rule.Rls_ simplify_power_,
wneuper@59416	1435	Rule.Rls_ calc_add_mult_pow_,
wneuper@59416	1436	Rule.Rls_ reduce_012_mult_,
wneuper@59416	1437	Rule.Rls_ order_add_rls_,
wneuper@59416	1438	Rule.Rls_ collect_numerals_,
wneuper@59416	1439	Rule.Rls_ reduce_012_,
wneuper@59416	1440	Rule.Rls_ discard_parentheses1
neuper@37950	1441	],
wneuper@59416	1442	scr = Rule.EmptyScr
wneuper@59406	1443	};
neuper@48763	1444	*}
neuper@48763	1445	ML {*
neuper@37950	1446	val norm_Poly(=make_polynomial) =
wneuper@59416	1447	Rule.Seq {id = "norm_Poly", preconds = []:term list,
wneuper@59416	1448	rew_ord = ("dummy_ord", Rule.dummy_ord),
wneuper@59416	1449	erls = Atools_erls, srls = Rule.Erls, calc = [], errpatts = [],
wneuper@59416	1450	rules = [Rule.Rls_ discard_minus,
wneuper@59416	1451	Rule.Rls_ expand_poly_,
wneuper@59416	1452	Rule.Calc ("Groups.times_class.times", eval_binop "#mult_"),
wneuper@59416	1453	Rule.Rls_ order_mult_rls_,
wneuper@59416	1454	Rule.Rls_ simplify_power_,
wneuper@59416	1455	Rule.Rls_ calc_add_mult_pow_,
wneuper@59416	1456	Rule.Rls_ reduce_012_mult_,
wneuper@59416	1457	Rule.Rls_ order_add_rls_,
wneuper@59416	1458	Rule.Rls_ collect_numerals_,
wneuper@59416	1459	Rule.Rls_ reduce_012_,
wneuper@59416	1460	Rule.Rls_ discard_parentheses1
neuper@37950	1461	],
wneuper@59416	1462	scr = Rule.EmptyScr
wneuper@59406	1463	};
neuper@48763	1464	*}
neuper@48763	1465	ML {*
wneuper@59416	1466	(* MG:03 Like make_polynomial_ but without Rule.Rls_ discard_parentheses1
neuper@37950	1467	and expand_poly_rat_ instead of expand_poly_, see MG-DA.p.56ff*)
neuper@37950	1468	(* MG necessary for termination of norm_Rational(_mg) in Rational.ML*)
neuper@37950	1469	val make_rat_poly_with_parentheses =
wneuper@59416	1470	Rule.Seq{id = "make_rat_poly_with_parentheses", preconds = []:term list,
wneuper@59416	1471	rew_ord = ("dummy_ord", Rule.dummy_ord),
wneuper@59416	1472	erls = Atools_erls, srls = Rule.Erls, calc = [], errpatts = [],
wneuper@59416	1473	rules = [Rule.Rls_ discard_minus,
wneuper@59416	1474	Rule.Rls_ expand_poly_rat_,(ignors rationals)
wneuper@59416	1475	Rule.Calc ("Groups.times_class.times", eval_binop "#mult_"),
wneuper@59416	1476	Rule.Rls_ order_mult_rls_,
wneuper@59416	1477	Rule.Rls_ simplify_power_,
wneuper@59416	1478	Rule.Rls_ calc_add_mult_pow_,
wneuper@59416	1479	Rule.Rls_ reduce_012_mult_,
wneuper@59416	1480	Rule.Rls_ order_add_rls_,
wneuper@59416	1481	Rule.Rls_ collect_numerals_,
wneuper@59416	1482	Rule.Rls_ reduce_012_
wneuper@59416	1483	(Rule.Rls_ discard_parentheses1 )
neuper@37950	1484	],
wneuper@59416	1485	scr = Rule.EmptyScr
wneuper@59406	1486	};
neuper@48763	1487	*}
neuper@48763	1488	ML {*
neuper@37950	1489	(*.a minimal ruleset for reverse rewriting of factions [2];
neuper@37950	1490	compare expand_binoms.*)
neuper@37950	1491	val rev_rew_p =
wneuper@59416	1492	Rule.Seq{id = "rev_rew_p", preconds = [], rew_ord = ("termlessI",termlessI),
wneuper@59416	1493	erls = Atools_erls, srls = Rule.Erls,
neuper@38014	1494	calc = [(*("PLUS" , ("Groups.plus_class.plus", eval_binop "#add_")),
neuper@38034	1495	("TIMES" , ("Groups.times_class.times", eval_binop "#mult_")),
neuper@37950	1496	("POWER", ("Atools.pow", eval_binop "#power_"))*)
neuper@42451	1497	], errpatts = [],
wneuper@59416	1498	rules = [Rule.Thm ("real_plus_binom_times" ,TermC.num_str @{thm real_plus_binom_times}),
neuper@37950	1499	("(a + b)(a + b) = a ^ 2 + 2 * a * b + b ^ 2*)
wneuper@59416	1500	Rule.Thm ("real_plus_binom_times1" ,TermC.num_str @{thm real_plus_binom_times1}),
neuper@37950	1501	("(a + 1b)(a + -1b) = a^^^2 + -1b^^^2")
wneuper@59416	1502	Rule.Thm ("real_plus_binom_times2" ,TermC.num_str @{thm real_plus_binom_times2}),
neuper@37950	1503	("(a + -1b)(a + 1b) = a^^^2 + -1b^^^2")
neuper@37950	1504
wneuper@59416	1505	Rule.Thm ("mult_1_left",TermC.num_str @{thm mult_1_left}),("1 z = z"*)
neuper@37950	1506
wneuper@59416	1507	Rule.Thm ("distrib_right" ,TermC.num_str @{thm distrib_right}),
neuper@37950	1508	("(z1.0 + z2.0) w = z1.0 * w + z2.0 * w"*)
wneuper@59416	1509	Rule.Thm ("distrib_left",TermC.num_str @{thm distrib_left}),
neuper@37950	1510	("w (z1.0 + z2.0) = w * z1.0 + w * z2.0"*)
neuper@37950	1511
wneuper@59416	1512	Rule.Thm ("mult_assoc", TermC.num_str @{thm mult.assoc}),
neuper@37950	1513	("?z1.1 ?z2.1 * ?z3. =1 ?z1.1 * (?z2.1 * ?z3.1)"*)
wneuper@59416	1514	Rule.Rls_ order_mult_rls_,
wneuper@59416	1515	(Rule.Rls_ order_add_rls_,)
neuper@37950	1516
wneuper@59416	1517	Rule.Calc ("Groups.plus_class.plus", eval_binop "#add_"),
wneuper@59416	1518	Rule.Calc ("Groups.times_class.times", eval_binop "#mult_"),
wneuper@59416	1519	Rule.Calc ("Atools.pow", eval_binop "#power_"),
neuper@37950	1520
wneuper@59416	1521	Rule.Thm ("sym_realpow_twoI",
wneuper@59389	1522	TermC.num_str (@{thm realpow_twoI} RS @{thm sym})),
neuper@37950	1523	("r1 r1 = r1 ^^^ 2"*)
wneuper@59416	1524	Rule.Thm ("sym_real_mult_2",
wneuper@59389	1525	TermC.num_str (@{thm real_mult_2} RS @{thm sym})),
neuper@37950	1526	("z1 + z1 = 2 z1"*)
wneuper@59416	1527	Rule.Thm ("real_mult_2_assoc",TermC.num_str @{thm real_mult_2_assoc}),
neuper@37950	1528	("z1 + (z1 + k) = 2 z1 + k"*)
neuper@37950	1529
wneuper@59416	1530	Rule.Thm ("real_num_collect",TermC.num_str @{thm real_num_collect}),
neuper@37950	1531	("[\| l is_const; m is_const \|]==>l n + m * n = (l + m) * n"*)
wneuper@59416	1532	Rule.Thm ("real_num_collect_assoc",TermC.num_str @{thm real_num_collect_assoc}),
neuper@37950	1533	(*"[\| l is_const; m is_const \|] ==>
neuper@37950	1534	l * n + (m * n + k) = (l + m) * n + k"*)
wneuper@59416	1535	Rule.Thm ("real_one_collect",TermC.num_str @{thm real_one_collect}),
neuper@37950	1536	("m is_const ==> n + m n = (1 + m) * n"*)
wneuper@59416	1537	Rule.Thm ("real_one_collect_assoc",TermC.num_str @{thm real_one_collect_assoc}),
neuper@37950	1538	("m is_const ==> k + (n + m n) = k + (1 + m) * n"*)
neuper@37950	1539
wneuper@59416	1540	Rule.Thm ("realpow_multI", TermC.num_str @{thm realpow_multI}),
neuper@37950	1541	("(r s) ^^^ n = r ^^^ n * s ^^^ n"*)
neuper@37950	1542
wneuper@59416	1543	Rule.Calc ("Groups.plus_class.plus", eval_binop "#add_"),
wneuper@59416	1544	Rule.Calc ("Groups.times_class.times", eval_binop "#mult_"),
wneuper@59416	1545	Rule.Calc ("Atools.pow", eval_binop "#power_"),
neuper@37950	1546
wneuper@59416	1547	Rule.Thm ("mult_1_left",TermC.num_str @{thm mult_1_left}),("1 z = z"*)
wneuper@59416	1548	Rule.Thm ("mult_zero_left",TermC.num_str @{thm mult_zero_left}),("0 z = 0"*)
wneuper@59416	1549	Rule.Thm ("add_0_left",TermC.num_str @{thm add_0_left})(0 + z = z)
neuper@37950	1550
wneuper@59416	1551	(Rule.Rls_ order_add_rls_)
neuper@37950	1552	],
neuper@37950	1553
wneuper@59416	1554	scr = Rule.EmptyScr};
neuper@48763	1555	*}
neuper@52125	1556
wneuper@59374	1557	ML {* val prep_rls' = LTool.prep_rls @{theory} *}
s1210629013@55444	1558
neuper@52125	1559	setup {* KEStore_Elems.add_rlss
s1210629013@55444	1560	[("norm_Poly", (Context.theory_name @{theory}, prep_rls' norm_Poly)),
s1210629013@55444	1561	("Poly_erls", (Context.theory_name @{theory}, prep_rls' Poly_erls)),(FIXXXME:del with rls.rls')
s1210629013@55444	1562	("expand", (Context.theory_name @{theory}, prep_rls' expand)),
s1210629013@55444	1563	("expand_poly", (Context.theory_name @{theory}, prep_rls' expand_poly)),
s1210629013@55444	1564	("simplify_power", (Context.theory_name @{theory}, prep_rls' simplify_power)),
neuper@52125	1565
s1210629013@55444	1566	("order_add_mult", (Context.theory_name @{theory}, prep_rls' order_add_mult)),
s1210629013@55444	1567	("collect_numerals", (Context.theory_name @{theory}, prep_rls' collect_numerals)),
s1210629013@55444	1568	("collect_numerals_", (Context.theory_name @{theory}, prep_rls' collect_numerals_)),
s1210629013@55444	1569	("reduce_012", (Context.theory_name @{theory}, prep_rls' reduce_012)),
s1210629013@55444	1570	("discard_parentheses", (Context.theory_name @{theory}, prep_rls' discard_parentheses)),
neuper@52125	1571
s1210629013@55444	1572	("make_polynomial", (Context.theory_name @{theory}, prep_rls' make_polynomial)),
s1210629013@55444	1573	("expand_binoms", (Context.theory_name @{theory}, prep_rls' expand_binoms)),
s1210629013@55444	1574	("rev_rew_p", (Context.theory_name @{theory}, prep_rls' rev_rew_p)),
s1210629013@55444	1575	("discard_minus", (Context.theory_name @{theory}, prep_rls' discard_minus)),
s1210629013@55444	1576	("expand_poly_", (Context.theory_name @{theory}, prep_rls' expand_poly_)),
neuper@52125	1577
s1210629013@55444	1578	("expand_poly_rat_", (Context.theory_name @{theory}, prep_rls' expand_poly_rat_)),
s1210629013@55444	1579	("simplify_power_", (Context.theory_name @{theory}, prep_rls' simplify_power_)),
s1210629013@55444	1580	("calc_add_mult_pow_", (Context.theory_name @{theory}, prep_rls' calc_add_mult_pow_)),
s1210629013@55444	1581	("reduce_012_mult_", (Context.theory_name @{theory}, prep_rls' reduce_012_mult_)),
s1210629013@55444	1582	("reduce_012_", (Context.theory_name @{theory}, prep_rls' reduce_012_)),
neuper@52125	1583
s1210629013@55444	1584	("discard_parentheses1", (Context.theory_name @{theory}, prep_rls' discard_parentheses1)),
s1210629013@55444	1585	("order_mult_rls_", (Context.theory_name @{theory}, prep_rls' order_mult_rls_)),
s1210629013@55444	1586	("order_add_rls_", (Context.theory_name @{theory}, prep_rls' order_add_rls_)),
neuper@52125	1587	("make_rat_poly_with_parentheses",
s1210629013@55444	1588	(Context.theory_name @{theory}, prep_rls' make_rat_poly_with_parentheses))] *}
s1210629013@52145	1589	setup {* KEStore_Elems.add_calcs
s1210629013@52145	1590	[("is_polyrat_in", ("Poly.is'_polyrat'_in",
s1210629013@52145	1591	eval_is_polyrat_in "#eval_is_polyrat_in")),
s1210629013@52145	1592	("is_expanded_in", ("Poly.is'_expanded'_in", eval_is_expanded_in "")),
s1210629013@52145	1593	("is_poly_in", ("Poly.is'_poly'_in", eval_is_poly_in "")),
s1210629013@52145	1594	("has_degree_in", ("Poly.has'_degree'_in", eval_has_degree_in "")),
s1210629013@52145	1595	("is_polyexp", ("Poly.is'_polyexp", eval_is_polyexp "")),
s1210629013@52145	1596	("is_multUnordered", ("Poly.is'_multUnordered", eval_is_multUnordered"")),
s1210629013@52145	1597	("is_addUnordered", ("Poly.is'_addUnordered", eval_is_addUnordered ""))] *}
s1210629013@52145	1598
neuper@37950	1599	( problems )
s1210629013@55359	1600	setup {* KEStore_Elems.add_pbts
wneuper@59406	1601	[(Specify.prep_pbt thy "pbl_simp_poly" [] Celem.e_pblID
s1210629013@55339	1602	(["polynomial","simplification"],
s1210629013@55339	1603	[("#Given" ,["Term t_t"]),
s1210629013@55339	1604	("#Where" ,["t_t is_polyexp"]),
s1210629013@55339	1605	("#Find" ,["normalform n_n"])],
wneuper@59416	1606	Rule.append_rls "e_rls" Rule.e_rls [(for preds in where_)
wneuper@59416	1607	Rule.Calc ("Poly.is'_polyexp", eval_is_polyexp "")],
s1210629013@55339	1608	SOME "Simplify t_t",
s1210629013@55339	1609	[["simplification","for_polynomials"]]))] *}
wneuper@59429	1610
neuper@37950	1611	( methods )
wneuper@59429	1612	(*-----
wneuper@59429	1613	consts
wneuper@59429	1614	norm_Poly :: ID
wneuper@59429	1615	partial_function (tailrec) simplify :: "real \<Rightarrow> real"
wneuper@59429	1616	where
wneuper@59429	1617	"simplify term = ((Rewrite_Set norm_Poly False) term)"
wneuper@59429	1618
wneuper@59429	1619	-----*)
s1210629013@55373	1620	setup {* KEStore_Elems.add_mets
wneuper@59406	1621	[Specify.prep_met thy "met_simp_poly" [] Celem.e_metID
s1210629013@55373	1622	(["simplification","for_polynomials"],
s1210629013@55373	1623	[("#Given" ,["Term t_t"]),
s1210629013@55373	1624	("#Where" ,["t_t is_polyexp"]),
s1210629013@55373	1625	("#Find" ,["normalform n_n"])],
wneuper@59416	1626	{rew_ord'="tless_true", rls' = Rule.e_rls, calc = [], srls = Rule.e_rls,
wneuper@59416	1627	prls = Rule.append_rls "simplification_for_polynomials_prls" Rule.e_rls
s1210629013@55373	1628	[(for preds in where_)
wneuper@59416	1629	Rule.Calc ("Poly.is'_polyexp",eval_is_polyexp"")],
wneuper@59416	1630	crls = Rule.e_rls, errpats = [], nrls = norm_Poly},
s1210629013@55373	1631	"Script SimplifyScript (t_t::real) = " ^
s1210629013@55373	1632	" ((Rewrite_Set norm_Poly False) t_t)")]
s1210629013@55373	1633	*}
neuper@37950	1634
wneuper@59429	1635	ML {*
wneuper@59429	1636	} ML {
wneuper@59429	1637	*}
neuper@37906	1638	end

author	Walther Neuper <wneuper@ist.tugraz.at>
	Wed, 11 Apr 2018 14:44:46 +0200
changeset 59429	c0fe04973189
parent 59416	229e5c9cf78b
child 59472	3e904f8ec16c
permissions	-rw-r--r--