wneuper/isa: src/Tools/isac/Knowledge/PolyEq.thy@8377b6c37640 (annotated)

neuper@37906	1	(* theory collecting all knowledge
neuper@37906	2	(predicates 'is_rootEq_in', 'is_sqrt_in', 'is_ratEq_in')
neuper@37906	3	for PolynomialEquations.
wneuper@59592	4	alternative dependencies see @{theory "Isac_Knowledge"}
neuper@37906	5	created by: rlang
neuper@37906	6	date: 02.07
neuper@37906	7	changed by: rlang
neuper@37906	8	last change by: rlang
neuper@37906	9	date: 03.06.03
neuper@37954	10	(c) by Richard Lang, 2003
neuper@37906	11	*)
neuper@37906	12
neuper@37954	13	theory PolyEq imports LinEq RootRatEq begin
neuper@37906	14
neuper@37906	15	(-------------------- rules -------------------------------------------------)
walther@60242	16	(* type real enforced by op " \<up> " *)
neuper@52148	17	axiomatization where
walther@60242	18	cancel_leading_coeff1: "Not (c =!= 0) ==> (a + bbdv + cbdv \<up> 2 = 0) =
walther@60242	19	(a/c + b/c*bdv + bdv \<up> 2 = 0)" and
walther@60242	20	cancel_leading_coeff2: "Not (c =!= 0) ==> (a - bbdv + cbdv \<up> 2 = 0) =
walther@60242	21	(a/c - b/c*bdv + bdv \<up> 2 = 0)" and
walther@60242	22	cancel_leading_coeff3: "Not (c =!= 0) ==> (a + bbdv - cbdv \<up> 2 = 0) =
walther@60242	23	(a/c + b/c*bdv - bdv \<up> 2 = 0)" and
neuper@37906	24
walther@60242	25	cancel_leading_coeff4: "Not (c =!= 0) ==> (a + bdv + c*bdv \<up> 2 = 0) =
walther@60242	26	(a/c + 1/c*bdv + bdv \<up> 2 = 0)" and
walther@60242	27	cancel_leading_coeff5: "Not (c =!= 0) ==> (a - bdv + c*bdv \<up> 2 = 0) =
walther@60242	28	(a/c - 1/c*bdv + bdv \<up> 2 = 0)" and
walther@60242	29	cancel_leading_coeff6: "Not (c =!= 0) ==> (a + bdv - c*bdv \<up> 2 = 0) =
walther@60242	30	(a/c + 1/c*bdv - bdv \<up> 2 = 0)" and
neuper@37906	31
walther@60242	32	cancel_leading_coeff7: "Not (c =!= 0) ==> ( bbdv + cbdv \<up> 2 = 0) =
walther@60242	33	( b/c*bdv + bdv \<up> 2 = 0)" and
walther@60242	34	cancel_leading_coeff8: "Not (c =!= 0) ==> ( bbdv - cbdv \<up> 2 = 0) =
walther@60242	35	( b/c*bdv - bdv \<up> 2 = 0)" and
neuper@37906	36
walther@60242	37	cancel_leading_coeff9: "Not (c =!= 0) ==> ( bdv + c*bdv \<up> 2 = 0) =
walther@60242	38	( 1/c*bdv + bdv \<up> 2 = 0)" and
walther@60242	39	cancel_leading_coeff10:"Not (c =!= 0) ==> ( bdv - c*bdv \<up> 2 = 0) =
walther@60242	40	( 1/c*bdv - bdv \<up> 2 = 0)" and
neuper@37906	41
walther@60242	42	cancel_leading_coeff11:"Not (c =!= 0) ==> (a + b*bdv \<up> 2 = 0) =
walther@60242	43	(a/b + bdv \<up> 2 = 0)" and
walther@60242	44	cancel_leading_coeff12:"Not (c =!= 0) ==> (a - b*bdv \<up> 2 = 0) =
walther@60242	45	(a/b - bdv \<up> 2 = 0)" and
walther@60242	46	cancel_leading_coeff13:"Not (c =!= 0) ==> ( b*bdv \<up> 2 = 0) =
walther@60242	47	( bdv \<up> 2 = 0/b)" and
neuper@37906	48
walther@60242	49	complete_square1: "(q + p*bdv + bdv \<up> 2 = 0) =
walther@60242	50	(q + (p/2 + bdv) \<up> 2 = (p/2) \<up> 2)" and
walther@60242	51	complete_square2: "( p*bdv + bdv \<up> 2 = 0) =
walther@60242	52	( (p/2 + bdv) \<up> 2 = (p/2) \<up> 2)" and
walther@60242	53	complete_square3: "( bdv + bdv \<up> 2 = 0) =
walther@60242	54	( (1/2 + bdv) \<up> 2 = (1/2) \<up> 2)" and
neuper@37906	55
walther@60242	56	complete_square4: "(q - p*bdv + bdv \<up> 2 = 0) =
walther@60242	57	(q + (p/2 - bdv) \<up> 2 = (p/2) \<up> 2)" and
walther@60242	58	complete_square5: "(q + p*bdv - bdv \<up> 2 = 0) =
walther@60242	59	(q + (p/2 - bdv) \<up> 2 = (p/2) \<up> 2)" and
neuper@37906	60
walther@60242	61	square_explicit1: "(a + b \<up> 2 = c) = ( b \<up> 2 = c - a)" and
walther@60242	62	square_explicit2: "(a - b \<up> 2 = c) = (-(b \<up> 2) = c - a)" and
neuper@37906	63
walther@60242	64	(bdv_explicit required type constrain to real in --- (-8 - 2x + x \<up> 2 = 0), by rewriting ---)
neuper@52148	65	bdv_explicit1: "(a + bdv = b) = (bdv = - a + (b::real))" and
neuper@52148	66	bdv_explicit2: "(a - bdv = b) = ((-1)*bdv = - a + (b::real))" and
neuper@52148	67	bdv_explicit3: "((-1)bdv = b) = (bdv = (-1)(b::real))" and
neuper@37906	68
neuper@52148	69	plus_leq: "(0 <= a + b) = ((-1)b <= a)"(Isa?*) and
neuper@52148	70	minus_leq: "(0 <= a - b) = ( b <= a)"(Isa?) and
neuper@37906	71
wneuper@59370	72	(-- normalise --)
neuper@37906	73	(WN0509 compare LinEq.all_left "[\|Not(b=!=0)\|] ==> (a=b) = (a+(-1)b=0)"*)
neuper@52148	74	all_left: "[\|Not(b=!=0)\|] ==> (a = b) = (a - b = 0)" and
walther@60242	75	makex1_x: "a\<up>1 = a" and
neuper@52148	76	real_assoc_1: "a+(b+c) = a+b+c" and
neuper@52148	77	real_assoc_2: "a(bc) = abc" and
neuper@37906	78
neuper@37906	79	(* ---- degree 0 ----*)
neuper@52148	80	d0_true: "(0=0) = True" and
neuper@52148	81	d0_false: "[\|Not(bdv occurs_in a);Not(a=0)\|] ==> (a=0) = False" and
neuper@37906	82	(* ---- degree 1 ----*)
neuper@37983	83	d1_isolate_add1:
neuper@52148	84	"[\|Not(bdv occurs_in a)\|] ==> (a + bbdv = 0) = (bbdv = (-1)*a)" and
neuper@37983	85	d1_isolate_add2:
neuper@52148	86	"[\|Not(bdv occurs_in a)\|] ==> (a + bdv = 0) = ( bdv = (-1)*a)" and
neuper@37983	87	d1_isolate_div:
neuper@52148	88	"[\|Not(b=0);Not(bdv occurs_in c)\|] ==> (b*bdv = c) = (bdv = c/b)" and
neuper@37906	89	(* ---- degree 2 ----*)
neuper@37983	90	d2_isolate_add1:
walther@60242	91	"[\|Not(bdv occurs_in a)\|] ==> (a + bbdv \<up> 2=0) = (bbdv \<up> 2= (-1)*a)" and
neuper@37983	92	d2_isolate_add2:
walther@60242	93	"[\|Not(bdv occurs_in a)\|] ==> (a + bdv \<up> 2=0) = ( bdv \<up> 2= (-1)*a)" and
neuper@37983	94	d2_isolate_div:
walther@60242	95	"[\|Not(b=0);Not(bdv occurs_in c)\|] ==> (b*bdv \<up> 2=c) = (bdv \<up> 2=c/b)" and
neuper@42394	96
walther@60242	97	d2_prescind1: "(abdv + bbdv \<up> 2 = 0) = (bdv(a +bbdv)=0)" and
walther@60242	98	d2_prescind2: "(abdv + bdv \<up> 2 = 0) = (bdv(a + bdv)=0)" and
walther@60242	99	d2_prescind3: "( bdv + bbdv \<up> 2 = 0) = (bdv(1+b*bdv)=0)" and
walther@60242	100	d2_prescind4: "( bdv + bdv \<up> 2 = 0) = (bdv*(1+ bdv)=0)" and
neuper@37906	101	(* eliminate degree 2 *)
neuper@37906	102	(* thm for neg arguments in sqroot have postfix _neg *)
neuper@37983	103	d2_sqrt_equation1: "[\|(0<=c);Not(bdv occurs_in c)\|] ==>
walther@60242	104	(bdv \<up> 2=c) = ((bdv=sqrt c) \| (bdv=(-1)*sqrt c ))" and
t@42197	105	d2_sqrt_equation1_neg:
walther@60242	106	"[\|(c<0);Not(bdv occurs_in c)\|] ==> (bdv \<up> 2=c) = False" and
walther@60242	107	d2_sqrt_equation2: "(bdv \<up> 2=0) = (bdv=0)" and
walther@60242	108	d2_sqrt_equation3: "(b*bdv \<up> 2=0) = (bdv=0)"
neuper@52148	109	axiomatization where (*AK..if replaced by "and" we get errors:
t@42203	110	exception PTREE "nth _ []" raised
t@42203	111	(line 783 of "/usr/local/isabisac/src/Tools/isac/Interpret/ctree.sml"):
t@42203	112	'fun nth _ [] = raise PTREE "nth _ []"'
t@42203	113	and
t@42203	114	exception Bind raised
t@42203	115	(line 1097 of "/usr/local/isabisac/test/Tools/isac/Frontend/interface.sml"):
t@42203	116	'val (Form f, tac, asms) = pt_extract (pt, p);' *)
walther@60242	117	(* WN120315 these 2 thms need "::real", because no " \<up> " constrains type as
neuper@42394	118	required in test --- rls d2_polyeq_bdv_only_simplify --- *)
neuper@52148	119	d2_reduce_equation1: "(bdv(a +bbdv)=0) = ((bdv=0)\|(a+b*bdv=(0::real)))" and
neuper@42394	120	d2_reduce_equation2: "(bdv*(a + bdv)=0) = ((bdv=0)\|(a+ bdv=(0::real)))"
neuper@52148	121
neuper@52148	122	axiomatization where (*..if replaced by "and" we get errors:
t@42203	123	exception PTREE "nth _ []" raised
t@42203	124	(line 783 of "/usr/local/isabisac/src/Tools/isac/Interpret/ctree.sml"):
t@42203	125	'fun nth _ [] = raise PTREE "nth _ []"'
t@42203	126	and
t@42203	127	exception Bind raised
t@42203	128	(line 1097 of "/usr/local/isabisac/test/Tools/isac/Frontend/interface.sml"):
t@42203	129	'val (Form f, tac, asms) = pt_extract (pt, p);' *)
walther@60273	130	d2_pqformula1: "[\|0<=p \<up> 2 - 4q\|] ==> (q+pbdv+ bdv \<up> 2=0) =
walther@60242	131	((bdv= (-1)(p/2) + sqrt(p \<up> 2 - 4q)/2)
walther@60242	132	\| (bdv= (-1)(p/2) - sqrt(p \<up> 2 - 4q)/2))" and
walther@60242	133	d2_pqformula1_neg: "[\|p \<up> 2 - 4q<0\|] ==> (q+pbdv+ bdv \<up> 2=0) = False" and
walther@60242	134	d2_pqformula2: "[\|0<=p \<up> 2 - 4q\|] ==> (q+pbdv+1*bdv \<up> 2=0) =
walther@60242	135	((bdv= (-1)(p/2) + sqrt(p \<up> 2 - 4q)/2)
walther@60242	136	\| (bdv= (-1)(p/2) - sqrt(p \<up> 2 - 4q)/2))" and
walther@60242	137	d2_pqformula2_neg: "[\|p \<up> 2 - 4q<0\|] ==> (q+pbdv+1*bdv \<up> 2=0) = False" and
walther@60242	138	d2_pqformula3: "[\|0<=1 - 4*q\|] ==> (q+ bdv+ bdv \<up> 2=0) =
neuper@37954	139	((bdv= (-1)(1/2) + sqrt(1 - 4q)/2)
neuper@52148	140	\| (bdv= (-1)(1/2) - sqrt(1 - 4q)/2))" and
walther@60242	141	d2_pqformula3_neg: "[\|1 - 4*q<0\|] ==> (q+ bdv+ bdv \<up> 2=0) = False" and
walther@60242	142	d2_pqformula4: "[\|0<=1 - 4q\|] ==> (q+ bdv+1bdv \<up> 2=0) =
neuper@37954	143	((bdv= (-1)(1/2) + sqrt(1 - 4q)/2)
neuper@52148	144	\| (bdv= (-1)(1/2) - sqrt(1 - 4q)/2))" and
walther@60242	145	d2_pqformula4_neg: "[\|1 - 4q<0\|] ==> (q+ bdv+1bdv \<up> 2=0) = False" and
walther@60242	146	d2_pqformula5: "[\|0<=p \<up> 2 - 0\|] ==> ( p*bdv+ bdv \<up> 2=0) =
walther@60242	147	((bdv= (-1)*(p/2) + sqrt(p \<up> 2 - 0)/2)
walther@60242	148	\| (bdv= (-1)*(p/2) - sqrt(p \<up> 2 - 0)/2))" and
t@42203	149	(* d2_pqformula5_neg not need p^2 never less zero in R *)
walther@60242	150	d2_pqformula6: "[\|0<=p \<up> 2 - 0\|] ==> ( pbdv+1bdv \<up> 2=0) =
walther@60242	151	((bdv= (-1)*(p/2) + sqrt(p \<up> 2 - 0)/2)
walther@60242	152	\| (bdv= (-1)*(p/2) - sqrt(p \<up> 2 - 0)/2))" and
neuper@37906	153	(* d2_pqformula6_neg not need p^2 never less zero in R *)
walther@60242	154	d2_pqformula7: "[\|0<=1 - 0\|] ==> ( bdv+ bdv \<up> 2=0) =
neuper@37954	155	((bdv= (-1)*(1/2) + sqrt(1 - 0)/2)
neuper@52148	156	\| (bdv= (-1)*(1/2) - sqrt(1 - 0)/2))" and
neuper@37906	157	(* d2_pqformula7_neg not need, because 1<0 ==> False*)
walther@60242	158	d2_pqformula8: "[\|0<=1 - 0\|] ==> ( bdv+1*bdv \<up> 2=0) =
neuper@37954	159	((bdv= (-1)*(1/2) + sqrt(1 - 0)/2)
neuper@52148	160	\| (bdv= (-1)*(1/2) - sqrt(1 - 0)/2))" and
neuper@37906	161	(* d2_pqformula8_neg not need, because 1<0 ==> False*)
neuper@37983	162	d2_pqformula9: "[\|Not(bdv occurs_in q); 0<= (-1)4q\|] ==>
walther@60242	163	(q+ 1bdv \<up> 2=0) = ((bdv= 0 + sqrt(0 - 4q)/2)
neuper@52148	164	\| (bdv= 0 - sqrt(0 - 4*q)/2))" and
neuper@37983	165	d2_pqformula9_neg:
walther@60242	166	"[\|Not(bdv occurs_in q); (-1)4q<0\|] ==> (q+ 1*bdv \<up> 2=0) = False" and
neuper@37983	167	d2_pqformula10:
walther@60242	168	"[\|Not(bdv occurs_in q); 0<= (-1)4q\|] ==> (q+ bdv \<up> 2=0) =
neuper@37906	169	((bdv= 0 + sqrt(0 - 4*q)/2)
neuper@52148	170	\| (bdv= 0 - sqrt(0 - 4*q)/2))" and
neuper@37983	171	d2_pqformula10_neg:
walther@60242	172	"[\|Not(bdv occurs_in q); (-1)4q<0\|] ==> (q+ bdv \<up> 2=0) = False" and
neuper@37983	173	d2_abcformula1:
walther@60242	174	"[\|0<=b \<up> 2 - 4ac\|] ==> (c + bbdv+abdv \<up> 2=0) =
walther@60242	175	((bdv=( -b + sqrt(b \<up> 2 - 4ac))/(2*a))
walther@60242	176	\| (bdv=( -b - sqrt(b \<up> 2 - 4ac))/(2*a)))" and
neuper@37983	177	d2_abcformula1_neg:
walther@60242	178	"[\|b \<up> 2 - 4ac<0\|] ==> (c + bbdv+abdv \<up> 2=0) = False" and
neuper@37983	179	d2_abcformula2:
walther@60242	180	"[\|0<=1 - 4ac\|] ==> (c+ bdv+a*bdv \<up> 2=0) =
neuper@37906	181	((bdv=( -1 + sqrt(1 - 4ac))/(2*a))
neuper@52148	182	\| (bdv=( -1 - sqrt(1 - 4ac))/(2*a)))" and
neuper@37983	183	d2_abcformula2_neg:
walther@60242	184	"[\|1 - 4ac<0\|] ==> (c+ bdv+a*bdv \<up> 2=0) = False" and
neuper@37983	185	d2_abcformula3:
walther@60242	186	"[\|0<=b \<up> 2 - 41c\|] ==> (c + b*bdv+ bdv \<up> 2=0) =
walther@60242	187	((bdv=( -b + sqrt(b \<up> 2 - 41c))/(2*1))
walther@60242	188	\| (bdv=( -b - sqrt(b \<up> 2 - 41c))/(2*1)))" and
neuper@37983	189	d2_abcformula3_neg:
walther@60242	190	"[\|b \<up> 2 - 41c<0\|] ==> (c + b*bdv+ bdv \<up> 2=0) = False" and
neuper@37983	191	d2_abcformula4:
walther@60242	192	"[\|0<=1 - 41c\|] ==> (c + bdv+ bdv \<up> 2=0) =
neuper@37906	193	((bdv=( -1 + sqrt(1 - 41c))/(2*1))
neuper@52148	194	\| (bdv=( -1 - sqrt(1 - 41c))/(2*1)))" and
neuper@37983	195	d2_abcformula4_neg:
walther@60242	196	"[\|1 - 41c<0\|] ==> (c + bdv+ bdv \<up> 2=0) = False" and
neuper@37983	197	d2_abcformula5:
walther@60242	198	"[\|Not(bdv occurs_in c); 0<=0 - 4ac\|] ==> (c + a*bdv \<up> 2=0) =
neuper@37906	199	((bdv=( 0 + sqrt(0 - 4ac))/(2*a))
neuper@52148	200	\| (bdv=( 0 - sqrt(0 - 4ac))/(2*a)))" and
neuper@37983	201	d2_abcformula5_neg:
walther@60242	202	"[\|Not(bdv occurs_in c); 0 - 4ac<0\|] ==> (c + a*bdv \<up> 2=0) = False" and
neuper@37983	203	d2_abcformula6:
walther@60242	204	"[\|Not(bdv occurs_in c); 0<=0 - 41c\|] ==> (c+ bdv \<up> 2=0) =
neuper@37906	205	((bdv=( 0 + sqrt(0 - 41c))/(2*1))
neuper@52148	206	\| (bdv=( 0 - sqrt(0 - 41c))/(2*1)))" and
neuper@37983	207	d2_abcformula6_neg:
walther@60242	208	"[\|Not(bdv occurs_in c); 0 - 41c<0\|] ==> (c+ bdv \<up> 2=0) = False" and
neuper@37983	209	d2_abcformula7:
walther@60242	210	"[\|0<=b \<up> 2 - 0\|] ==> ( bbdv+abdv \<up> 2=0) =
walther@60242	211	((bdv=( -b + sqrt(b \<up> 2 - 0))/(2*a))
walther@60242	212	\| (bdv=( -b - sqrt(b \<up> 2 - 0))/(2*a)))" and
neuper@37906	213	(* d2_abcformula7_neg not need b^2 never less zero in R *)
neuper@37983	214	d2_abcformula8:
walther@60242	215	"[\|0<=b \<up> 2 - 0\|] ==> ( b*bdv+ bdv \<up> 2=0) =
walther@60242	216	((bdv=( -b + sqrt(b \<up> 2 - 0))/(2*1))
walther@60242	217	\| (bdv=( -b - sqrt(b \<up> 2 - 0))/(2*1)))" and
neuper@37906	218	(* d2_abcformula8_neg not need b^2 never less zero in R *)
neuper@37983	219	d2_abcformula9:
walther@60242	220	"[\|0<=1 - 0\|] ==> ( bdv+a*bdv \<up> 2=0) =
neuper@37906	221	((bdv=( -1 + sqrt(1 - 0))/(2*a))
neuper@52148	222	\| (bdv=( -1 - sqrt(1 - 0))/(2*a)))" and
neuper@37906	223	(* d2_abcformula9_neg not need, because 1<0 ==> False*)
neuper@37983	224	d2_abcformula10:
walther@60242	225	"[\|0<=1 - 0\|] ==> ( bdv+ bdv \<up> 2=0) =
neuper@37906	226	((bdv=( -1 + sqrt(1 - 0))/(2*1))
neuper@52148	227	\| (bdv=( -1 - sqrt(1 - 0))/(2*1)))" and
neuper@37906	228	(* d2_abcformula10_neg not need, because 1<0 ==> False*)
neuper@37906	229
t@42203	230
neuper@37906	231	(* ---- degree 3 ----*)
neuper@37983	232	d3_reduce_equation1:
walther@60242	233	"(abdv + bbdv \<up> 2 + cbdv \<up> 3=0) = (bdv=0 \| (a + bbdv + c*bdv \<up> 2=0))" and
neuper@37983	234	d3_reduce_equation2:
walther@60242	235	"( bdv + bbdv \<up> 2 + cbdv \<up> 3=0) = (bdv=0 \| (1 + bbdv + cbdv \<up> 2=0))" and
neuper@37983	236	d3_reduce_equation3:
walther@60242	237	"(abdv + bdv \<up> 2 + cbdv \<up> 3=0) = (bdv=0 \| (a + bdv + c*bdv \<up> 2=0))" and
neuper@37983	238	d3_reduce_equation4:
walther@60242	239	"( bdv + bdv \<up> 2 + cbdv \<up> 3=0) = (bdv=0 \| (1 + bdv + cbdv \<up> 2=0))" and
neuper@37983	240	d3_reduce_equation5:
walther@60242	241	"(abdv + bbdv \<up> 2 + bdv \<up> 3=0) = (bdv=0 \| (a + b*bdv + bdv \<up> 2=0))" and
neuper@37983	242	d3_reduce_equation6:
walther@60242	243	"( bdv + bbdv \<up> 2 + bdv \<up> 3=0) = (bdv=0 \| (1 + bbdv + bdv \<up> 2=0))" and
neuper@37983	244	d3_reduce_equation7:
walther@60242	245	"(a*bdv + bdv \<up> 2 + bdv \<up> 3=0) = (bdv=0 \| (1 + bdv + bdv \<up> 2=0))" and
neuper@37983	246	d3_reduce_equation8:
walther@60242	247	"( bdv + bdv \<up> 2 + bdv \<up> 3=0) = (bdv=0 \| (1 + bdv + bdv \<up> 2=0))" and
neuper@37983	248	d3_reduce_equation9:
walther@60242	249	"(abdv + cbdv \<up> 3=0) = (bdv=0 \| (a + c*bdv \<up> 2=0))" and
neuper@37983	250	d3_reduce_equation10:
walther@60242	251	"( bdv + cbdv \<up> 3=0) = (bdv=0 \| (1 + cbdv \<up> 2=0))" and
neuper@37983	252	d3_reduce_equation11:
walther@60242	253	"(a*bdv + bdv \<up> 3=0) = (bdv=0 \| (a + bdv \<up> 2=0))" and
neuper@37983	254	d3_reduce_equation12:
walther@60242	255	"( bdv + bdv \<up> 3=0) = (bdv=0 \| (1 + bdv \<up> 2=0))" and
neuper@37983	256	d3_reduce_equation13:
walther@60242	257	"( bbdv \<up> 2 + cbdv \<up> 3=0) = (bdv=0 \| ( bbdv + cbdv \<up> 2=0))" and
neuper@37983	258	d3_reduce_equation14:
walther@60242	259	"( bdv \<up> 2 + cbdv \<up> 3=0) = (bdv=0 \| ( bdv + cbdv \<up> 2=0))" and
neuper@37983	260	d3_reduce_equation15:
walther@60242	261	"( bbdv \<up> 2 + bdv \<up> 3=0) = (bdv=0 \| ( bbdv + bdv \<up> 2=0))" and
neuper@37983	262	d3_reduce_equation16:
walther@60242	263	"( bdv \<up> 2 + bdv \<up> 3=0) = (bdv=0 \| ( bdv + bdv \<up> 2=0))" and
neuper@37983	264	d3_isolate_add1:
walther@60242	265	"[\|Not(bdv occurs_in a)\|] ==> (a + bbdv \<up> 3=0) = (bbdv \<up> 3= (-1)*a)" and
neuper@37983	266	d3_isolate_add2:
walther@60242	267	"[\|Not(bdv occurs_in a)\|] ==> (a + bdv \<up> 3=0) = ( bdv \<up> 3= (-1)*a)" and
neuper@37983	268	d3_isolate_div:
walther@60242	269	"[\|Not(b=0);Not(bdv occurs_in a)\|] ==> (b*bdv \<up> 3=c) = (bdv \<up> 3=c/b)" and
neuper@37983	270	d3_root_equation2:
walther@60242	271	"(bdv \<up> 3=0) = (bdv=0)" and
neuper@37983	272	d3_root_equation1:
walther@60242	273	"(bdv \<up> 3=c) = (bdv = nroot 3 c)" and
neuper@37906	274
neuper@37906	275	(* ---- degree 4 ----*)
neuper@37906	276	(* RL03.FIXME es wir nicht getestet ob u>0 *)
neuper@37989	277	d4_sub_u1:
walther@60242	278	"(c+bbdv \<up> 2+abdv \<up> 4=0) =
walther@60242	279	((au \<up> 2+bu+c=0) & (bdv \<up> 2=u))" and
neuper@37906	280
neuper@37906	281	(* ---- 7.3.02 von Termorder ---- *)
neuper@37906	282
neuper@52148	283	bdv_collect_1: "l * bdv + m * bdv = (l + m) * bdv" and
neuper@52148	284	bdv_collect_2: "bdv + m * bdv = (1 + m) * bdv" and
neuper@52148	285	bdv_collect_3: "l * bdv + bdv = (l + 1) * bdv" and
neuper@37906	286
neuper@37906	287	(* bdv_collect_assoc0_1 "l * bdv + m * bdv + k = (l + m) * bdv + k"
neuper@37906	288	bdv_collect_assoc0_2 "bdv + m * bdv + k = (1 + m) * bdv + k"
neuper@37906	289	bdv_collect_assoc0_3 "l * bdv + bdv + k = (l + 1) * bdv + k"
neuper@37906	290	*)
neuper@52148	291	bdv_collect_assoc1_1: "l * bdv + (m * bdv + k) = (l + m) * bdv + k" and
neuper@52148	292	bdv_collect_assoc1_2: "bdv + (m * bdv + k) = (1 + m) * bdv + k" and
neuper@52148	293	bdv_collect_assoc1_3: "l * bdv + (bdv + k) = (l + 1) * bdv + k" and
neuper@38030	294
neuper@52148	295	bdv_collect_assoc2_1: "k + l * bdv + m * bdv = k + (l + m) * bdv" and
neuper@52148	296	bdv_collect_assoc2_2: "k + bdv + m * bdv = k + (1 + m) * bdv" and
neuper@52148	297	bdv_collect_assoc2_3: "k + l * bdv + bdv = k + (l + 1) * bdv" and
neuper@37906	298
neuper@37906	299
walther@60242	300	bdv_n_collect_1: "l * bdv \<up> n + m * bdv \<up> n = (l + m) * bdv \<up> n" and
walther@60242	301	bdv_n_collect_2: " bdv \<up> n + m * bdv \<up> n = (1 + m) * bdv \<up> n" and
walther@60242	302	bdv_n_collect_3: "l * bdv \<up> n + bdv \<up> n = (l + 1) * bdv \<up> n" (order!) and
neuper@37906	303
walther@60358	304	bdv_n_collect_assoc1_1: "l * bdv \<up> n + (m * bdv \<up> n + k) = (l + m) * bdv \<up> n + k" and
walther@60242	305	bdv_n_collect_assoc1_2: "bdv \<up> n + (m * bdv \<up> n + k) = (1 + m) * bdv \<up> n + k" and
walther@60242	306	bdv_n_collect_assoc1_3: "l * bdv \<up> n + (bdv \<up> n + k) = (l + 1) * bdv \<up> n + k" and
neuper@37906	307
walther@60242	308	bdv_n_collect_assoc2_1: "k + l * bdv \<up> n + m * bdv \<up> n = k +(l + m) * bdv \<up> n" and
walther@60242	309	bdv_n_collect_assoc2_2: "k + bdv \<up> n + m * bdv \<up> n = k + (1 + m) * bdv \<up> n" and
walther@60242	310	bdv_n_collect_assoc2_3: "k + l * bdv \<up> n + bdv \<up> n = k + (l + 1) * bdv \<up> n" and
neuper@37906	311
neuper@37906	312	(WN.14.3.03)
neuper@52148	313	real_minus_div: "- (a / b) = (-1 * a) / b" and
neuper@38030	314
neuper@52148	315	separate_bdv: "(a * bdv) / b = (a / b) * (bdv::real)" and
walther@60242	316	separate_bdv_n: "(a * bdv \<up> n) / b = (a / b) * bdv \<up> n" and
neuper@52148	317	separate_1_bdv: "bdv / b = (1 / b) * (bdv::real)" and
walther@60242	318	separate_1_bdv_n: "bdv \<up> n / b = (1 / b) * bdv \<up> n"
neuper@37906	319
wneuper@59472	320	ML \<open>
neuper@37972	321	val thy = @{theory};
neuper@37972	322
neuper@37954	323	val PolyEq_prls = (3.10.02:just the following order due to subterm evaluation)
walther@60358	324	Rule_Set.append_rules "PolyEq_prls" Rule_Set.empty [
walther@60358	325	\<^rule_eval>\<open>ident\<close> (Prog_Expr.eval_ident "#ident_"),
walther@60358	326	\<^rule_eval>\<open>matches\<close> (Prog_Expr.eval_matches "#matches_"),
walther@60358	327	\<^rule_eval>\<open>lhs\<close> (Prog_Expr.eval_lhs ""),
walther@60358	328	\<^rule_eval>\<open>rhs\<close> (Prog_Expr.eval_rhs ""),
walther@60358	329	\<^rule_eval>\<open>is_expanded_in\<close> (eval_is_expanded_in ""),
walther@60358	330	\<^rule_eval>\<open>is_poly_in\<close> (eval_is_poly_in ""),
walther@60358	331	\<^rule_eval>\<open>has_degree_in\<close> (eval_has_degree_in ""),
walther@60358	332	\<^rule_eval>\<open>is_polyrat_in\<close> (eval_is_polyrat_in ""),
walther@60358	333	\<^rule_eval>\<open>HOL.eq\<close> (Prog_Expr.eval_equal "#equal_"),
walther@60358	334	\<^rule_eval>\<open>is_rootTerm_in\<close> (eval_is_rootTerm_in ""),
walther@60358	335	\<^rule_eval>\<open>is_ratequation_in\<close> (eval_is_ratequation_in ""),
walther@60358	336	\<^rule_thm>\<open>not_true\<close>,
walther@60358	337	\<^rule_thm>\<open>not_false\<close>,
walther@60358	338	\<^rule_thm>\<open>and_true\<close>,
walther@60358	339	\<^rule_thm>\<open>and_false\<close>,
walther@60358	340	\<^rule_thm>\<open>or_true\<close>,
walther@60358	341	\<^rule_thm>\<open>or_false\<close>];
neuper@37954	342
neuper@37954	343	val PolyEq_erls =
walther@60358	344	Rule_Set.merge "PolyEq_erls" LinEq_erls
walther@60358	345	(Rule_Set.append_rules "ops_preds" calculate_Rational [
walther@60358	346	\<^rule_eval>\<open>HOL.eq\<close> (Prog_Expr.eval_equal "#equal_"),
wenzelm@60297	347	\<^rule_thm>\<open>plus_leq\<close>,
wenzelm@60297	348	\<^rule_thm>\<open>minus_leq\<close>,
wenzelm@60297	349	\<^rule_thm>\<open>rat_leq1\<close>,
wenzelm@60297	350	\<^rule_thm>\<open>rat_leq2\<close>,
walther@60358	351	\<^rule_thm>\<open>rat_leq3\<close>]);
neuper@37954	352
neuper@37954	353	val PolyEq_crls =
walther@59852	354	Rule_Set.merge "PolyEq_crls" LinEq_crls
walther@60358	355	(Rule_Set.append_rules "ops_preds" calculate_Rational [
walther@60358	356	\<^rule_eval>\<open>HOL.eq\<close> (Prog_Expr.eval_equal "#equal_"),
wenzelm@60297	357	\<^rule_thm>\<open>plus_leq\<close>,
wenzelm@60297	358	\<^rule_thm>\<open>minus_leq\<close>,
wenzelm@60297	359	\<^rule_thm>\<open>rat_leq1\<close>,
wenzelm@60297	360	\<^rule_thm>\<open>rat_leq2\<close>,
wenzelm@60297	361	\<^rule_thm>\<open>rat_leq3\<close>
neuper@37954	362	]);
neuper@37954	363
s1210629013@55444	364	val cancel_leading_coeff = prep_rls'(
walther@59851	365	Rule_Def.Repeat {id = "cancel_leading_coeff", preconds = [],
walther@60358	366	rew_ord = ("e_rew_ord",Rewrite_Ord.e_rew_ord),
walther@60358	367	erls = PolyEq_erls, srls = Rule_Set.Empty, calc = [], errpatts = [],
walther@60358	368	rules = [
walther@60358	369	\<^rule_thm>\<open>cancel_leading_coeff1\<close>,
walther@60358	370	\<^rule_thm>\<open>cancel_leading_coeff2\<close>,
walther@60358	371	\<^rule_thm>\<open>cancel_leading_coeff3\<close>,
walther@60358	372	\<^rule_thm>\<open>cancel_leading_coeff4\<close>,
walther@60358	373	\<^rule_thm>\<open>cancel_leading_coeff5\<close>,
walther@60358	374	\<^rule_thm>\<open>cancel_leading_coeff6\<close>,
walther@60358	375	\<^rule_thm>\<open>cancel_leading_coeff7\<close>,
walther@60358	376	\<^rule_thm>\<open>cancel_leading_coeff8\<close>,
walther@60358	377	\<^rule_thm>\<open>cancel_leading_coeff9\<close>,
walther@60358	378	\<^rule_thm>\<open>cancel_leading_coeff10\<close>,
walther@60358	379	\<^rule_thm>\<open>cancel_leading_coeff11\<close>,
walther@60358	380	\<^rule_thm>\<open>cancel_leading_coeff12\<close>,
walther@60358	381	\<^rule_thm>\<open>cancel_leading_coeff13\<close> ],
walther@60358	382	scr = Rule.Empty_Prog});
s1210629013@55444	383
walther@59618	384	val prep_rls' = Auto_Prog.prep_rls @{theory};
wneuper@59472	385	\<close>
wneuper@59472	386	ML\<open>
s1210629013@55444	387	val complete_square = prep_rls'(
walther@59851	388	Rule_Def.Repeat {id = "complete_square", preconds = [],
walther@60358	389	rew_ord = ("e_rew_ord",Rewrite_Ord.e_rew_ord),
walther@60358	390	erls = PolyEq_erls, srls = Rule_Set.Empty, calc = [], errpatts = [],
walther@60358	391	rules = [
walther@60358	392	\<^rule_thm>\<open>complete_square1\<close>,
walther@60358	393	\<^rule_thm>\<open>complete_square2\<close>,
walther@60358	394	\<^rule_thm>\<open>complete_square3\<close>,
walther@60358	395	\<^rule_thm>\<open>complete_square4\<close>,
walther@60358	396	\<^rule_thm>\<open>complete_square5\<close>],
walther@60358	397	scr = Rule.Empty_Prog});
neuper@37954	398
s1210629013@55444	399	val polyeq_simplify = prep_rls'(
walther@59851	400	Rule_Def.Repeat {id = "polyeq_simplify", preconds = [],
walther@60358	401	rew_ord = ("termlessI",termlessI),
walther@60358	402	erls = PolyEq_erls,
walther@60358	403	srls = Rule_Set.Empty,
walther@60358	404	calc = [], errpatts = [],
walther@60358	405	rules = [
walther@60358	406	\<^rule_thm>\<open>real_assoc_1\<close>,
walther@60358	407	\<^rule_thm>\<open>real_assoc_2\<close>,
walther@60358	408	\<^rule_thm>\<open>real_diff_minus\<close>,
walther@60358	409	\<^rule_thm>\<open>real_unari_minus\<close>,
walther@60358	410	\<^rule_thm>\<open>realpow_multI\<close>,
walther@60358	411	\<^rule_eval>\<open>plus\<close> (**)(eval_binop "#add_"),
walther@60358	412	\<^rule_eval>\<open>minus\<close> (**)(eval_binop "#sub_"),
walther@60358	413	\<^rule_eval>\<open>times\<close> (**)(eval_binop "#mult_"),
walther@60358	414	\<^rule_eval>\<open>divide\<close> (Prog_Expr.eval_cancel "#divide_e"),
walther@60358	415	\<^rule_eval>\<open>sqrt\<close> (eval_sqrt "#sqrt_"),
walther@60358	416	\<^rule_eval>\<open>powr\<close> (**)(eval_binop "#power_"),
walther@60358	417	Rule.Rls_ reduce_012],
walther@60358	418	scr = Rule.Empty_Prog});
wneuper@59472	419	\<close>
wenzelm@60289	420	rule_set_knowledge
wenzelm@60286	421	cancel_leading_coeff = cancel_leading_coeff and
wenzelm@60286	422	complete_square = complete_square and
wenzelm@60286	423	PolyEq_erls = PolyEq_erls and
wenzelm@60286	424	polyeq_simplify = polyeq_simplify
wneuper@59472	425	ML\<open>
neuper@37954	426
walther@60358	427	(* the subsequent rule-sets are caused by the lack of rewriting at the time of implementation *)
neuper@37954	428	(* -- d0 -- *)
neuper@37954	429	(isolate the bound variable in an d0 equation; 'bdv' is a meta-constant)
s1210629013@55444	430	val d0_polyeq_simplify = prep_rls'(
walther@59851	431	Rule_Def.Repeat {id = "d0_polyeq_simplify", preconds = [],
walther@60358	432	rew_ord = ("e_rew_ord",Rewrite_Ord.e_rew_ord),
walther@60358	433	erls = PolyEq_erls,
walther@60358	434	srls = Rule_Set.Empty,
walther@60358	435	calc = [], errpatts = [],
walther@60358	436	rules = [
walther@60358	437	\<^rule_thm>\<open>d0_true\<close>,
walther@60358	438	\<^rule_thm>\<open>d0_false\<close>],
walther@60358	439	scr = Rule.Empty_Prog});
neuper@37954	440
neuper@37954	441	(* -- d1 -- *)
neuper@37954	442	(isolate the bound variable in an d1 equation; 'bdv' is a meta-constant)
s1210629013@55444	443	val d1_polyeq_simplify = prep_rls'(
walther@59851	444	Rule_Def.Repeat {id = "d1_polyeq_simplify", preconds = [],
walther@60358	445	rew_ord = ("e_rew_ord",Rewrite_Ord.e_rew_ord),
walther@60358	446	erls = PolyEq_erls,
walther@60358	447	srls = Rule_Set.Empty,
walther@60358	448	calc = [], errpatts = [],
walther@60358	449	rules = [
walther@60358	450	\<^rule_thm>\<open>d1_isolate_add1\<close>, (* a+bx=0 -> bx=-a *)
walther@60358	451	\<^rule_thm>\<open>d1_isolate_add2\<close>, (* a+ x=0 -> x=-a *)
walther@60358	452	\<^rule_thm>\<open>d1_isolate_div\<close> (* bx=c -> x=c/b *)],
walther@60358	453	scr = Rule.Empty_Prog});
walther@60358	454	\<close>
neuper@37954	455
wneuper@59472	456	subsection \<open>degree 2\<close>
wneuper@59472	457	ML\<open>
neuper@42394	458	(* isolate the bound variable in an d2 equation with bdv only;
neuper@42394	459	"bdv" is a meta-constant substituted for the "x" below by isac's rewriter. *)
s1210629013@55444	460	val d2_polyeq_bdv_only_simplify = prep_rls'(
walther@59857	461	Rule_Def.Repeat {id = "d2_polyeq_bdv_only_simplify", preconds = [], rew_ord = ("e_rew_ord",Rewrite_Ord.e_rew_ord),
walther@59851	462	erls = PolyEq_erls, srls = Rule_Set.Empty, calc = [], errpatts = [],
walther@60358	463	rules = [
walther@60358	464	\<^rule_thm>\<open>d2_prescind1\<close>, (* ax+bx^2=0 -> x(a+bx)=0 *)
wenzelm@60297	465	\<^rule_thm>\<open>d2_prescind2\<close>, (* ax+ x^2=0 -> x(a+ x)=0 *)
wenzelm@60297	466	\<^rule_thm>\<open>d2_prescind3\<close>, (* x+bx^2=0 -> x(1+bx)=0 *)
wenzelm@60297	467	\<^rule_thm>\<open>d2_prescind4\<close>, (* x+ x^2=0 -> x(1+ x)=0 *)
wenzelm@60297	468	\<^rule_thm>\<open>d2_sqrt_equation1\<close>, (* x^2=c -> x=+-sqrt(c) *)
wenzelm@60297	469	\<^rule_thm>\<open>d2_sqrt_equation1_neg\<close>, (* [0<c] x^2=c -> []*)
wenzelm@60297	470	\<^rule_thm>\<open>d2_sqrt_equation2\<close>, (* x^2=0 -> x=0 *)
wenzelm@60297	471	\<^rule_thm>\<open>d2_reduce_equation1\<close>,(* x(a+bx)=0 -> x=0 \|a+bx=0*)
wenzelm@60297	472	\<^rule_thm>\<open>d2_reduce_equation2\<close>,(* x(a+ x)=0 -> x=0 \|a+ x=0*)
walther@60358	473	\<^rule_thm>\<open>d2_isolate_div\<close>], (* bx^2=c -> x^2=c/b *)
walther@60358	474	scr = Rule.Empty_Prog});
walther@60358	475
walther@60358	476	(* isolate the bound variable in an d2 equation with sqrt only;
neuper@37954	477	'bdv' is a meta-constant*)
s1210629013@55444	478	val d2_polyeq_sq_only_simplify = prep_rls'(
walther@59851	479	Rule_Def.Repeat {id = "d2_polyeq_sq_only_simplify", preconds = [],
walther@60358	480	rew_ord = ("e_rew_ord",Rewrite_Ord.e_rew_ord),
walther@60358	481	erls = PolyEq_erls, srls = Rule_Set.Empty, calc = [], errpatts = [],
walther@60358	482	rules = [
walther@60358	483	\<^rule_thm>\<open>d2_isolate_add1\<close>,(* a+ bx^2=0 -> bx^2=(-1)a*)
walther@60358	484	\<^rule_thm>\<open>d2_isolate_add2\<close>, (* a+ x^2=0 -> x^2=(-1)a*)
walther@60358	485	\<^rule_thm>\<open>d2_sqrt_equation2\<close>, (* x^2=0 -> x=0 *)
walther@60358	486	\<^rule_thm>\<open>d2_sqrt_equation1\<close>, (* x^2=c -> x=+-sqrt(c)*)
walther@60358	487	\<^rule_thm>\<open>d2_sqrt_equation1_neg\<close>,(* [c<0] x^2=c -> x=[] *)
walther@60358	488	\<^rule_thm>\<open>d2_isolate_div\<close>], (* bx^2=c -> x^2=c/b*)
walther@60358	489	scr = Rule.Empty_Prog});
wneuper@59472	490	\<close>
wneuper@59472	491	ML\<open>
neuper@37954	492	(* isolate the bound variable in an d2 equation with pqFormula;
neuper@37954	493	'bdv' is a meta-constant*)
s1210629013@55444	494	val d2_polyeq_pqFormula_simplify = prep_rls'(
walther@59851	495	Rule_Def.Repeat {id = "d2_polyeq_pqFormula_simplify", preconds = [],
walther@60358	496	rew_ord = ("e_rew_ord",Rewrite_Ord.e_rew_ord), erls = PolyEq_erls,
walther@60358	497	srls = Rule_Set.Empty, calc = [], errpatts = [],
walther@60358	498	rules = [
walther@60358	499	\<^rule_thm>\<open>d2_pqformula1\<close>, (* q+px+ x^2=0 *)
walther@60358	500	\<^rule_thm>\<open>d2_pqformula1_neg\<close>, (* q+px+ x^2=0 *)
walther@60358	501	\<^rule_thm>\<open>d2_pqformula2\<close>, (* q+px+1x^2=0 *)
walther@60358	502	\<^rule_thm>\<open>d2_pqformula2_neg\<close>, (* q+px+1x^2=0 *)
walther@60358	503	\<^rule_thm>\<open>d2_pqformula3\<close>, (* q+ x+ x^2=0 *)
walther@60358	504	\<^rule_thm>\<open>d2_pqformula3_neg\<close>, (* q+ x+ x^2=0 *)
walther@60358	505	\<^rule_thm>\<open>d2_pqformula4\<close>, (* q+ x+1x^2=0 *)
walther@60358	506	\<^rule_thm>\<open>d2_pqformula4_neg\<close>, (* q+ x+1x^2=0 *)
walther@60358	507	\<^rule_thm>\<open>d2_pqformula5\<close>, (* qx+ x^2=0 *)
walther@60358	508	\<^rule_thm>\<open>d2_pqformula6\<close>, (* qx+1x^2=0 *)
walther@60358	509	\<^rule_thm>\<open>d2_pqformula7\<close>, (* x+ x^2=0 *)
walther@60358	510	\<^rule_thm>\<open>d2_pqformula8\<close>, (* x+1x^2=0 *)
walther@60358	511	\<^rule_thm>\<open>d2_pqformula9\<close>, (* q +1x^2=0 *)
walther@60358	512	\<^rule_thm>\<open>d2_pqformula9_neg\<close>, (* q +1x^2=0 *)
walther@60358	513	\<^rule_thm>\<open>d2_pqformula10\<close>, (* q + x^2=0 *)
walther@60358	514	\<^rule_thm>\<open>d2_pqformula10_neg\<close>, (* q + x^2=0 *)
walther@60358	515	\<^rule_thm>\<open>d2_sqrt_equation2\<close>, (* x^2=0 *)
walther@60358	516	\<^rule_thm>\<open>d2_sqrt_equation3\<close>], (* 1x^2=0 *)
walther@60358	517	scr = Rule.Empty_Prog});
walther@60358	518
walther@60358	519	(* isolate the bound variable in an d2 equation with abcFormula;
neuper@37954	520	'bdv' is a meta-constant*)
s1210629013@55444	521	val d2_polyeq_abcFormula_simplify = prep_rls'(
walther@59851	522	Rule_Def.Repeat {id = "d2_polyeq_abcFormula_simplify", preconds = [],
walther@60358	523	rew_ord = ("e_rew_ord",Rewrite_Ord.e_rew_ord), erls = PolyEq_erls,
walther@60358	524	srls = Rule_Set.Empty, calc = [], errpatts = [],
walther@60358	525	rules = [
walther@60358	526	\<^rule_thm>\<open>d2_abcformula1\<close>, (c+bx+cx^2=0 )
walther@60358	527	\<^rule_thm>\<open>d2_abcformula1_neg\<close>, (c+bx+cx^2=0 )
walther@60358	528	\<^rule_thm>\<open>d2_abcformula2\<close>, (c+ x+cx^2=0 )
walther@60358	529	\<^rule_thm>\<open>d2_abcformula2_neg\<close>, (c+ x+cx^2=0 )
walther@60358	530	\<^rule_thm>\<open>d2_abcformula3\<close>, (c+bx+ x^2=0 )
walther@60358	531	\<^rule_thm>\<open>d2_abcformula3_neg\<close>, (c+bx+ x^2=0 )
walther@60358	532	\<^rule_thm>\<open>d2_abcformula4\<close>, (c+ x+ x^2=0 )
walther@60358	533	\<^rule_thm>\<open>d2_abcformula4_neg\<close>, (c+ x+ x^2=0 )
walther@60358	534	\<^rule_thm>\<open>d2_abcformula5\<close>, (c+ cx^2=0 )
walther@60358	535	\<^rule_thm>\<open>d2_abcformula5_neg\<close>, (c+ cx^2=0 )
walther@60358	536	\<^rule_thm>\<open>d2_abcformula6\<close>, (c+ x^2=0 )
walther@60358	537	\<^rule_thm>\<open>d2_abcformula6_neg\<close>, (c+ x^2=0 )
walther@60358	538	\<^rule_thm>\<open>d2_abcformula7\<close>, (* bx+ax^2=0 *)
walther@60358	539	\<^rule_thm>\<open>d2_abcformula8\<close>, (* bx+ x^2=0 *)
walther@60358	540	\<^rule_thm>\<open>d2_abcformula9\<close>, (* x+ax^2=0 *)
walther@60358	541	\<^rule_thm>\<open>d2_abcformula10\<close>, (* x+ x^2=0 *)
walther@60358	542	\<^rule_thm>\<open>d2_sqrt_equation2\<close>, (* x^2=0 *)
walther@60358	543	\<^rule_thm>\<open>d2_sqrt_equation3\<close>], (* bx^2=0 *)
walther@60358	544	scr = Rule.Empty_Prog});
neuper@37954	545
neuper@37954	546	(* isolate the bound variable in an d2 equation;
neuper@37954	547	'bdv' is a meta-constant*)
s1210629013@55444	548	val d2_polyeq_simplify = prep_rls'(
walther@59851	549	Rule_Def.Repeat {id = "d2_polyeq_simplify", preconds = [],
walther@60358	550	rew_ord = ("e_rew_ord",Rewrite_Ord.e_rew_ord), erls = PolyEq_erls,
walther@60358	551	srls = Rule_Set.Empty, calc = [], errpatts = [],
walther@60358	552	rules = [
walther@60358	553	\<^rule_thm>\<open>d2_pqformula1\<close>, (* p+qx+ x^2=0 *)
walther@60358	554	\<^rule_thm>\<open>d2_pqformula1_neg\<close>, (* p+qx+ x^2=0 *)
walther@60358	555	\<^rule_thm>\<open>d2_pqformula2\<close>, (* p+qx+1x^2=0 *)
walther@60358	556	\<^rule_thm>\<open>d2_pqformula2_neg\<close>, (* p+qx+1x^2=0 *)
walther@60358	557	\<^rule_thm>\<open>d2_pqformula3\<close>, (* p+ x+ x^2=0 *)
walther@60358	558	\<^rule_thm>\<open>d2_pqformula3_neg\<close>, (* p+ x+ x^2=0 *)
walther@60358	559	\<^rule_thm>\<open>d2_pqformula4\<close>, (* p+ x+1x^2=0 *)
walther@60358	560	\<^rule_thm>\<open>d2_pqformula4_neg\<close>, (* p+ x+1x^2=0 *)
walther@60358	561	\<^rule_thm>\<open>d2_abcformula1\<close>, (* c+bx+cx^2=0 *)
walther@60358	562	\<^rule_thm>\<open>d2_abcformula1_neg\<close>, (* c+bx+cx^2=0 *)
walther@60358	563	\<^rule_thm>\<open>d2_abcformula2\<close>, (* c+ x+cx^2=0 *)
walther@60358	564	\<^rule_thm>\<open>d2_abcformula2_neg\<close>, (* c+ x+cx^2=0 *)
walther@60358	565	\<^rule_thm>\<open>d2_prescind1\<close>, (* ax+bx^2=0 -> x(a+bx)=0 *)
walther@60358	566	\<^rule_thm>\<open>d2_prescind2\<close>, (* ax+ x^2=0 -> x(a+ x)=0 *)
walther@60358	567	\<^rule_thm>\<open>d2_prescind3\<close>, (* x+bx^2=0 -> x(1+bx)=0 *)
walther@60358	568	\<^rule_thm>\<open>d2_prescind4\<close>, (* x+ x^2=0 -> x(1+ x)=0 *)
walther@60358	569	\<^rule_thm>\<open>d2_isolate_add1\<close>, (* a+ bx^2=0 -> bx^2=(-1)a*)
walther@60358	570	\<^rule_thm>\<open>d2_isolate_add2\<close>, (* a+ x^2=0 -> x^2=(-1)a*)
walther@60358	571	\<^rule_thm>\<open>d2_sqrt_equation1\<close>, (* x^2=c -> x=+-sqrt(c)*)
walther@60358	572	\<^rule_thm>\<open>d2_sqrt_equation1_neg\<close>, (* [c<0] x^2=c -> x=[]*)
walther@60358	573	\<^rule_thm>\<open>d2_sqrt_equation2\<close>, (* x^2=0 -> x=0 *)
walther@60358	574	\<^rule_thm>\<open>d2_reduce_equation1\<close>, (* x(a+bx)=0 -> x=0 \| a+bx=0*)
walther@60358	575	\<^rule_thm>\<open>d2_reduce_equation2\<close>, (* x(a+ x)=0 -> x=0 \| a+ x=0*)
walther@60358	576	\<^rule_thm>\<open>d2_isolate_div\<close>], (* bx^2=c -> x^2=c/b*)
walther@60358	577	scr = Rule.Empty_Prog});
neuper@37954	578
neuper@37954	579	(* -- d3 -- *)
neuper@37954	580	(* isolate the bound variable in an d3 equation; 'bdv' is a meta-constant *)
s1210629013@55444	581	val d3_polyeq_simplify = prep_rls'(
walther@59851	582	Rule_Def.Repeat {id = "d3_polyeq_simplify", preconds = [],
walther@60358	583	rew_ord = ("e_rew_ord",Rewrite_Ord.e_rew_ord), erls = PolyEq_erls,
walther@60358	584	srls = Rule_Set.Empty, calc = [], errpatts = [],
walther@60358	585	rules = [
walther@60358	586	\<^rule_thm>\<open>d3_reduce_equation1\<close>, (abdv + bbdv \<up> 2 + cbdv \<up> 3=0) = (bdv=0 \| (a + bbdv + cbdv \<up> 2=0)*)
walther@60358	587	\<^rule_thm>\<open>d3_reduce_equation2\<close>, (* bdv + bbdv \<up> 2 + cbdv \<up> 3=0) = (bdv=0 \| (1 + bbdv + cbdv \<up> 2=0)*)
walther@60358	588	\<^rule_thm>\<open>d3_reduce_equation3\<close>, (abdv + bdv \<up> 2 + cbdv \<up> 3=0) = (bdv=0 \| (a + bdv + cbdv \<up> 2=0)*)
walther@60358	589	\<^rule_thm>\<open>d3_reduce_equation4\<close>, (* bdv + bdv \<up> 2 + cbdv \<up> 3=0) = (bdv=0 \| (1 + bdv + cbdv \<up> 2=0)*)
walther@60358	590	\<^rule_thm>\<open>d3_reduce_equation5\<close>, (abdv + bbdv \<up> 2 + bdv \<up> 3=0) = (bdv=0 \| (a + bbdv + bdv \<up> 2=0)*)
walther@60358	591	\<^rule_thm>\<open>d3_reduce_equation6\<close>, (* bdv + bbdv \<up> 2 + bdv \<up> 3=0) = (bdv=0 \| (1 + bbdv + bdv \<up> 2=0)*)
walther@60358	592	\<^rule_thm>\<open>d3_reduce_equation7\<close>, (abdv + bdv \<up> 2 + bdv \<up> 3=0) = (bdv=0 \| (1 + bdv + bdv \<up> 2=0)*)
walther@60358	593	\<^rule_thm>\<open>d3_reduce_equation8\<close>, (* bdv + bdv \<up> 2 + bdv \<up> 3=0) = (bdv=0 \| (1 + bdv + bdv \<up> 2=0)*)
walther@60358	594	\<^rule_thm>\<open>d3_reduce_equation9\<close>, (abdv + cbdv \<up> 3=0) = (bdv=0 \| (a + cbdv \<up> 2=0)*)
walther@60358	595	\<^rule_thm>\<open>d3_reduce_equation10\<close>, (* bdv + cbdv \<up> 3=0) = (bdv=0 \| (1 + cbdv \<up> 2=0)*)
walther@60358	596	\<^rule_thm>\<open>d3_reduce_equation11\<close>, (abdv + bdv \<up> 3=0) = (bdv=0 \| (a + bdv \<up> 2=0)*)
walther@60358	597	\<^rule_thm>\<open>d3_reduce_equation12\<close>, (* bdv + bdv \<up> 3=0) = (bdv=0 \| (1 + bdv \<up> 2=0)*)
walther@60358	598	\<^rule_thm>\<open>d3_reduce_equation13\<close>, (* bbdv \<up> 2 + cbdv \<up> 3=0) = (bdv=0 \| ( bbdv + cbdv \<up> 2=0)*)
walther@60358	599	\<^rule_thm>\<open>d3_reduce_equation14\<close>, (* bdv \<up> 2 + cbdv \<up> 3=0) = (bdv=0 \| ( bdv + cbdv \<up> 2=0)*)
walther@60358	600	\<^rule_thm>\<open>d3_reduce_equation15\<close>, (* bbdv \<up> 2 + bdv \<up> 3=0) = (bdv=0 \| ( bbdv + bdv \<up> 2=0)*)
walther@60358	601	\<^rule_thm>\<open>d3_reduce_equation16\<close>, (* bdv \<up> 2 + bdv \<up> 3=0) = (bdv=0 \| ( bdv + bdv \<up> 2=0)*)
walther@60358	602	\<^rule_thm>\<open>d3_isolate_add1\<close>, ([\|Not(bdv occurs_in a)\|] ==> (a + bbdv \<up> 3=0) = (bdv=0 \| (bbdv \<up> 3=a))
walther@60358	603	\<^rule_thm>\<open>d3_isolate_add2\<close>, ([\|Not(bdv occurs_in a)\|] ==> (a + bdv \<up> 3=0) = (bdv=0 \| ( bdv \<up> 3=a))
walther@60358	604	\<^rule_thm>\<open>d3_isolate_div\<close>, ([\|Not(b=0)\|] ==> (bbdv \<up> 3=c) = (bdv \<up> 3=c/b*)
walther@60358	605	\<^rule_thm>\<open>d3_root_equation2\<close>, ((bdv \<up> 3=0) = (bdv=0) )
walther@60358	606	\<^rule_thm>\<open>d3_root_equation1\<close>], (bdv \<up> 3=c) = (bdv = nroot 3 c)
walther@60358	607	scr = Rule.Empty_Prog});
neuper@37954	608
neuper@37954	609	(* -- d4 -- *)
neuper@37954	610	(isolate the bound variable in an d4 equation; 'bdv' is a meta-constant)
s1210629013@55444	611	val d4_polyeq_simplify = prep_rls'(
walther@59851	612	Rule_Def.Repeat {id = "d4_polyeq_simplify", preconds = [],
walther@60358	613	rew_ord = ("e_rew_ord",Rewrite_Ord.e_rew_ord), erls = PolyEq_erls,
walther@60358	614	srls = Rule_Set.Empty, calc = [], errpatts = [],
walther@60358	615	rules = [
walther@60358	616	\<^rule_thm>\<open>d4_sub_u1\<close> (* ax^4+bx^2+c=0 -> x=+-sqrt(ax^2+bx^+c) *)],
walther@60358	617	scr = Rule.Empty_Prog});
wneuper@59472	618	\<close>
wenzelm@60289	619	rule_set_knowledge
wenzelm@60286	620	d0_polyeq_simplify = d0_polyeq_simplify and
wenzelm@60286	621	d1_polyeq_simplify = d1_polyeq_simplify and
wenzelm@60286	622	d2_polyeq_simplify = d2_polyeq_simplify and
wenzelm@60286	623	d2_polyeq_bdv_only_simplify = d2_polyeq_bdv_only_simplify and
wenzelm@60286	624	d2_polyeq_sq_only_simplify = d2_polyeq_sq_only_simplify and
neuper@52125	625
wenzelm@60286	626	d2_polyeq_pqFormula_simplify = d2_polyeq_pqFormula_simplify and
wenzelm@60286	627	d2_polyeq_abcFormula_simplify = d2_polyeq_abcFormula_simplify and
wenzelm@60286	628	d3_polyeq_simplify = d3_polyeq_simplify and
wenzelm@60286	629	d4_polyeq_simplify = d4_polyeq_simplify
walther@60258	630
wenzelm@60306	631	problem pbl_equ_univ_poly : "polynomial/univariate/equation" =
wenzelm@60306	632	\<open>PolyEq_prls\<close>
wenzelm@60306	633	CAS: "solve (e_e::bool, v_v)"
wenzelm@60306	634	Given: "equality e_e" "solveFor v_v"
wenzelm@60306	635	Where:
wenzelm@60306	636	"~((e_e::bool) is_ratequation_in (v_v::real))"
wenzelm@60306	637	"~((lhs e_e) is_rootTerm_in (v_v::real))"
wenzelm@60306	638	"~((rhs e_e) is_rootTerm_in (v_v::real))"
wenzelm@60306	639	Find: "solutions v_v'i'"
wenzelm@60306	640
wenzelm@60306	641	(--- d0 ---)
wenzelm@60306	642	problem pbl_equ_univ_poly_deg0 : "degree_0/polynomial/univariate/equation" =
wenzelm@60306	643	\<open>PolyEq_prls\<close>
wenzelm@60306	644	Method: "PolyEq/solve_d0_polyeq_equation"
wenzelm@60306	645	CAS: "solve (e_e::bool, v_v)"
wenzelm@60306	646	Given: "equality e_e" "solveFor v_v"
wenzelm@60306	647	Where:
wenzelm@60306	648	"matches (?a = 0) e_e"
wenzelm@60306	649	"(lhs e_e) is_poly_in v_v"
wenzelm@60306	650	"((lhs e_e) has_degree_in v_v ) = 0"
wenzelm@60306	651	Find: "solutions v_v'i'"
wenzelm@60306	652
wenzelm@60306	653	(--- d1 ---)
wenzelm@60306	654	problem pbl_equ_univ_poly_deg1 : "degree_1/polynomial/univariate/equation" =
wenzelm@60306	655	\<open>PolyEq_prls\<close>
wenzelm@60306	656	Method: "PolyEq/solve_d1_polyeq_equation"
wenzelm@60306	657	CAS: "solve (e_e::bool, v_v)"
wenzelm@60306	658	Given: "equality e_e" "solveFor v_v"
wenzelm@60306	659	Where:
wenzelm@60306	660	"matches (?a = 0) e_e"
wenzelm@60306	661	"(lhs e_e) is_poly_in v_v"
wenzelm@60306	662	"((lhs e_e) has_degree_in v_v ) = 1"
wenzelm@60306	663	Find: "solutions v_v'i'"
wenzelm@60306	664
wenzelm@60306	665	(--- d2 ---)
wenzelm@60306	666	problem pbl_equ_univ_poly_deg2 : "degree_2/polynomial/univariate/equation" =
wenzelm@60306	667	\<open>PolyEq_prls\<close>
wenzelm@60306	668	Method: "PolyEq/solve_d2_polyeq_equation"
wenzelm@60306	669	CAS: "solve (e_e::bool, v_v)"
wenzelm@60306	670	Given: "equality e_e" "solveFor v_v"
wenzelm@60306	671	Where:
wenzelm@60306	672	"matches (?a = 0) e_e"
wenzelm@60306	673	"(lhs e_e) is_poly_in v_v "
wenzelm@60306	674	"((lhs e_e) has_degree_in v_v ) = 2"
wenzelm@60306	675	Find: "solutions v_v'i'"
wenzelm@60306	676
wenzelm@60306	677	problem pbl_equ_univ_poly_deg2_sqonly : "sq_only/degree_2/polynomial/univariate/equation" =
wenzelm@60306	678	\<open>PolyEq_prls\<close>
wenzelm@60306	679	Method: "PolyEq/solve_d2_polyeq_sqonly_equation"
wenzelm@60306	680	CAS: "solve (e_e::bool, v_v)"
wenzelm@60306	681	Given: "equality e_e" "solveFor v_v"
wenzelm@60306	682	Where:
wenzelm@60306	683	"matches ( ?a + ?v_ \<up> 2 = 0) e_e \|
wenzelm@60306	684	matches ( ?a + ?b*?v_ \<up> 2 = 0) e_e \|
wenzelm@60306	685	matches ( ?v_ \<up> 2 = 0) e_e \|
wenzelm@60306	686	matches ( ?b*?v_ \<up> 2 = 0) e_e"
wenzelm@60306	687	"Not (matches (?a + ?v_ + ?v_ \<up> 2 = 0) e_e) &
wenzelm@60306	688	Not (matches (?a + ?b*?v_ + ?v_ \<up> 2 = 0) e_e) &
wenzelm@60306	689	Not (matches (?a + ?v_ + ?c*?v_ \<up> 2 = 0) e_e) &
wenzelm@60306	690	Not (matches (?a + ?b?v_ + ?c?v_ \<up> 2 = 0) e_e) &
wenzelm@60306	691	Not (matches ( ?v_ + ?v_ \<up> 2 = 0) e_e) &
wenzelm@60306	692	Not (matches ( ?b*?v_ + ?v_ \<up> 2 = 0) e_e) &
wenzelm@60306	693	Not (matches ( ?v_ + ?c*?v_ \<up> 2 = 0) e_e) &
wenzelm@60306	694	Not (matches ( ?b?v_ + ?c?v_ \<up> 2 = 0) e_e)"
wenzelm@60306	695	Find: "solutions v_v'i'"
wenzelm@60306	696
wenzelm@60306	697	problem pbl_equ_univ_poly_deg2_bdvonly : "bdv_only/degree_2/polynomial/univariate/equation" =
wenzelm@60306	698	\<open>PolyEq_prls\<close>
wenzelm@60306	699	Method: "PolyEq/solve_d2_polyeq_bdvonly_equation"
wenzelm@60306	700	CAS: "solve (e_e::bool, v_v)"
wenzelm@60306	701	Given: "equality e_e" "solveFor v_v"
wenzelm@60306	702	Where:
wenzelm@60306	703	"matches (?a*?v_ + ?v_ \<up> 2 = 0) e_e \|
wenzelm@60306	704	matches ( ?v_ + ?v_ \<up> 2 = 0) e_e \|
wenzelm@60306	705	matches ( ?v_ + ?b*?v_ \<up> 2 = 0) e_e \|
wenzelm@60306	706	matches (?a?v_ + ?b?v_ \<up> 2 = 0) e_e \|
wenzelm@60306	707	matches ( ?v_ \<up> 2 = 0) e_e \|
wenzelm@60306	708	matches ( ?b*?v_ \<up> 2 = 0) e_e "
wenzelm@60306	709	Find: "solutions v_v'i'"
wenzelm@60306	710
wenzelm@60306	711	problem pbl_equ_univ_poly_deg2_pq : "pqFormula/degree_2/polynomial/univariate/equation" =
wenzelm@60306	712	\<open>PolyEq_prls\<close>
wenzelm@60306	713	Method: "PolyEq/solve_d2_polyeq_pq_equation"
wenzelm@60306	714	CAS: "solve (e_e::bool, v_v)"
wenzelm@60306	715	Given: "equality e_e" "solveFor v_v"
wenzelm@60306	716	Where:
wenzelm@60306	717	"matches (?a + 1*?v_ \<up> 2 = 0) e_e \|
wenzelm@60306	718	matches (?a + ?v_ \<up> 2 = 0) e_e"
wenzelm@60306	719	Find: "solutions v_v'i'"
wenzelm@60306	720
wenzelm@60306	721	problem pbl_equ_univ_poly_deg2_abc : "abcFormula/degree_2/polynomial/univariate/equation" =
wenzelm@60306	722	\<open>PolyEq_prls\<close>
wenzelm@60306	723	Method: "PolyEq/solve_d2_polyeq_abc_equation"
wenzelm@60306	724	CAS: "solve (e_e::bool, v_v)"
wenzelm@60306	725	Given: "equality e_e" "solveFor v_v"
wenzelm@60306	726	Where:
wenzelm@60306	727	"matches (?a + ?v_ \<up> 2 = 0) e_e \|
wenzelm@60306	728	matches (?a + ?b*?v_ \<up> 2 = 0) e_e"
wenzelm@60306	729	Find: "solutions v_v'i'"
wenzelm@60306	730
wenzelm@60306	731	(--- d3 ---)
wenzelm@60306	732	problem pbl_equ_univ_poly_deg3 : "degree_3/polynomial/univariate/equation" =
wenzelm@60306	733	\<open>PolyEq_prls\<close>
wenzelm@60306	734	Method: "PolyEq/solve_d3_polyeq_equation"
wenzelm@60306	735	CAS: "solve (e_e::bool, v_v)"
wenzelm@60306	736	Given: "equality e_e" "solveFor v_v"
wenzelm@60306	737	Where:
wenzelm@60306	738	"matches (?a = 0) e_e"
wenzelm@60306	739	"(lhs e_e) is_poly_in v_v"
wenzelm@60306	740	"((lhs e_e) has_degree_in v_v) = 3"
wenzelm@60306	741	Find: "solutions v_v'i'"
wenzelm@60306	742
wenzelm@60306	743	(--- d4 ---)
wenzelm@60306	744	problem pbl_equ_univ_poly_deg4 : "degree_4/polynomial/univariate/equation" =
wenzelm@60306	745	\<open>PolyEq_prls\<close>
wenzelm@60306	746	(Method: "PolyEq/solve_d4_polyeq_equation")
wenzelm@60306	747	CAS: "solve (e_e::bool, v_v)"
wenzelm@60306	748	Given: "equality e_e" "solveFor v_v"
wenzelm@60306	749	Where:
wenzelm@60306	750	"matches (?a = 0) e_e"
wenzelm@60306	751	"(lhs e_e) is_poly_in v_v"
wenzelm@60306	752	"((lhs e_e) has_degree_in v_v) = 4"
wenzelm@60306	753	Find: "solutions v_v'i'"
wenzelm@60306	754
wenzelm@60306	755	(--- normalise ---)
wenzelm@60306	756	problem pbl_equ_univ_poly_norm : "normalise/polynomial/univariate/equation" =
wenzelm@60306	757	\<open>PolyEq_prls\<close>
wenzelm@60306	758	Method: "PolyEq/normalise_poly"
wenzelm@60306	759	CAS: "solve (e_e::bool, v_v)"
wenzelm@60306	760	Given: "equality e_e" "solveFor v_v"
wenzelm@60306	761	Where:
wenzelm@60306	762	"(Not((matches (?a = 0 ) e_e ))) \|
wenzelm@60306	763	(Not(((lhs e_e) is_poly_in v_v)))"
wenzelm@60306	764	Find: "solutions v_v'i'"
wenzelm@60306	765
wenzelm@60306	766	(-------------------------expanded-----------------------)
wenzelm@60306	767	problem "pbl_equ_univ_expand" : "expanded/univariate/equation" =
wenzelm@60306	768	\<open>PolyEq_prls\<close>
wenzelm@60306	769	CAS: "solve (e_e::bool, v_v)"
wenzelm@60306	770	Given: "equality e_e" "solveFor v_v"
wenzelm@60306	771	Where:
wenzelm@60306	772	"matches (?a = 0) e_e"
wenzelm@60306	773	"(lhs e_e) is_expanded_in v_v "
wenzelm@60306	774	Find: "solutions v_v'i'"
wenzelm@60306	775
wenzelm@60306	776	(--- d2 ---)
wenzelm@60306	777	problem pbl_equ_univ_expand_deg2 : "degree_2/expanded/univariate/equation" =
wenzelm@60306	778	\<open>PolyEq_prls\<close>
wenzelm@60306	779	Method: "PolyEq/complete_square"
wenzelm@60306	780	CAS: "solve (e_e::bool, v_v)"
wenzelm@60306	781	Given: "equality e_e" "solveFor v_v"
wenzelm@60306	782	Where: "((lhs e_e) has_degree_in v_v) = 2"
wenzelm@60306	783	Find: "solutions v_v'i'"
neuper@37954	784
wneuper@59472	785	text \<open>"-------------------------methods-----------------------"\<close>
wenzelm@60303	786
wenzelm@60303	787	method met_polyeq : "PolyEq" =
wenzelm@60303	788	\<open>{rew_ord'="tless_true",rls'=Atools_erls,calc = [], srls = Rule_Set.empty, prls=Rule_Set.empty,
wenzelm@60303	789	crls=PolyEq_crls, errpats = [], nrls = norm_Rational}\<close>
wneuper@59545	790
wneuper@59504	791	partial_function (tailrec) normalize_poly_eq :: "bool \<Rightarrow> real \<Rightarrow> bool"
wneuper@59504	792	where
walther@59635	793	"normalize_poly_eq e_e v_v = (
walther@59635	794	let
walther@59635	795	e_e = (
walther@59637	796	(Try (Rewrite ''all_left'')) #>
walther@59637	797	(Try (Repeat (Rewrite ''makex1_x''))) #>
walther@59637	798	(Try (Repeat (Rewrite_Set ''expand_binoms''))) #>
walther@59637	799	(Try (Repeat (Rewrite_Set_Inst [(''bdv'', v_v)] ''make_ratpoly_in''))) #>
walther@59635	800	(Try (Repeat (Rewrite_Set ''polyeq_simplify''))) ) e_e
walther@59635	801	in
walther@59635	802	SubProblem (''PolyEq'', [''polynomial'', ''univariate'', ''equation''], [''no_met''])
wneuper@59504	803	[BOOL e_e, REAL v_v])"
wenzelm@60303	804
wenzelm@60303	805	method met_polyeq_norm : "PolyEq/normalise_poly" =
wenzelm@60303	806	\<open>{rew_ord'="termlessI", rls'=PolyEq_erls, srls=Rule_Set.empty, prls=PolyEq_prls, calc=[],
wenzelm@60303	807	crls=PolyEq_crls, errpats = [], nrls = norm_Rational}\<close>
wenzelm@60303	808	Program: normalize_poly_eq.simps
wenzelm@60303	809	Given: "equality e_e" "solveFor v_v"
wenzelm@60303	810	Where: "(Not((matches (?a = 0 ) e_e ))) \| (Not(((lhs e_e) is_poly_in v_v)))"
wenzelm@60303	811	Find: "solutions v_v'i'"
wneuper@59545	812
wneuper@59504	813	partial_function (tailrec) solve_poly_equ :: "bool \<Rightarrow> real \<Rightarrow> bool list"
wneuper@59504	814	where
walther@59635	815	"solve_poly_equ e_e v_v = (
walther@59635	816	let
walther@59635	817	e_e = (Try (Rewrite_Set_Inst [(''bdv'', v_v)] ''d0_polyeq_simplify'')) e_e
walther@59635	818	in
walther@59635	819	Or_to_List e_e)"
wenzelm@60303	820
wenzelm@60303	821	method met_polyeq_d0 : "PolyEq/solve_d0_polyeq_equation" =
wenzelm@60303	822	\<open>{rew_ord'="termlessI", rls'=PolyEq_erls, srls=Rule_Set.empty, prls=PolyEq_prls,
wenzelm@60309	823	calc=[("sqrt", (\<^const_name>\<open>sqrt\<close>, eval_sqrt "#sqrt_"))], crls=PolyEq_crls, errpats = [],
wenzelm@60303	824	nrls = norm_Rational}\<close>
wenzelm@60303	825	Program: solve_poly_equ.simps
wenzelm@60303	826	Given: "equality e_e" "solveFor v_v"
wenzelm@60303	827	Where: "(lhs e_e) is_poly_in v_v " "((lhs e_e) has_degree_in v_v) = 0"
wenzelm@60303	828	Find: "solutions v_v'i'"
wneuper@59545	829
wneuper@59504	830	partial_function (tailrec) solve_poly_eq1 :: "bool \<Rightarrow> real \<Rightarrow> bool list"
walther@59635	831	where
walther@59635	832	"solve_poly_eq1 e_e v_v = (
walther@59635	833	let
walther@59635	834	e_e = (
walther@59637	835	(Try (Rewrite_Set_Inst [(''bdv'', v_v)] ''d1_polyeq_simplify'')) #>
walther@59637	836	(Try (Rewrite_Set ''polyeq_simplify'')) #>
walther@59635	837	(Try (Rewrite_Set ''norm_Rational_parenthesized'')) ) e_e;
walther@59635	838	L_L = Or_to_List e_e
walther@59635	839	in
walther@59635	840	Check_elementwise L_L {(v_v::real). Assumptions})"
wenzelm@60303	841
wenzelm@60303	842	method met_polyeq_d1 : "PolyEq/solve_d1_polyeq_equation" =
wenzelm@60303	843	\<open>{rew_ord'="termlessI", rls'=PolyEq_erls, srls=Rule_Set.empty, prls=PolyEq_prls,
wenzelm@60309	844	calc=[("sqrt", (\<^const_name>\<open>sqrt\<close>, eval_sqrt "#sqrt_"))], crls=PolyEq_crls, errpats = [],
wenzelm@60303	845	nrls = norm_Rational}\<close>
wenzelm@60303	846	Program: solve_poly_eq1.simps
wenzelm@60303	847	Given: "equality e_e" "solveFor v_v"
wenzelm@60303	848	Where: "(lhs e_e) is_poly_in v_v" "((lhs e_e) has_degree_in v_v) = 1"
wenzelm@60303	849	Find: "solutions v_v'i'"
wneuper@59545	850
wneuper@59504	851	partial_function (tailrec) solve_poly_equ2 :: "bool \<Rightarrow> real \<Rightarrow> bool list"
wneuper@59504	852	where
walther@59635	853	"solve_poly_equ2 e_e v_v = (
walther@59635	854	let
walther@59635	855	e_e = (
walther@59637	856	(Try (Rewrite_Set_Inst [(''bdv'', v_v)] ''d2_polyeq_simplify'')) #>
walther@59637	857	(Try (Rewrite_Set ''polyeq_simplify'')) #>
walther@59637	858	(Try (Rewrite_Set_Inst [(''bdv'', v_v)] ''d1_polyeq_simplify'')) #>
walther@59637	859	(Try (Rewrite_Set ''polyeq_simplify'')) #>
walther@59635	860	(Try (Rewrite_Set ''norm_Rational_parenthesized'')) ) e_e;
walther@59635	861	L_L = Or_to_List e_e
walther@59635	862	in
walther@59635	863	Check_elementwise L_L {(v_v::real). Assumptions})"
wenzelm@60303	864
wenzelm@60303	865	method met_polyeq_d22 : "PolyEq/solve_d2_polyeq_equation" =
wenzelm@60303	866	\<open>{rew_ord'="termlessI", rls'=PolyEq_erls, srls=Rule_Set.empty, prls=PolyEq_prls,
wenzelm@60309	867	calc=[("sqrt", (\<^const_name>\<open>sqrt\<close>, eval_sqrt "#sqrt_"))], crls=PolyEq_crls, errpats = [],
wenzelm@60303	868	nrls = norm_Rational}\<close>
wenzelm@60303	869	Program: solve_poly_equ2.simps
wenzelm@60303	870	Given: "equality e_e" "solveFor v_v"
wenzelm@60303	871	Where: "(lhs e_e) is_poly_in v_v " "((lhs e_e) has_degree_in v_v) = 2"
wenzelm@60303	872	Find: "solutions v_v'i'"
wneuper@59545	873
wneuper@59504	874	partial_function (tailrec) solve_poly_equ0 :: "bool \<Rightarrow> real \<Rightarrow> bool list"
walther@59635	875	where
walther@59635	876	"solve_poly_equ0 e_e v_v = (
walther@59635	877	let
walther@59635	878	e_e = (
walther@59637	879	(Try (Rewrite_Set_Inst [(''bdv'', v_v)] ''d2_polyeq_bdv_only_simplify'')) #>
walther@59637	880	(Try (Rewrite_Set ''polyeq_simplify'')) #>
walther@59637	881	(Try (Rewrite_Set_Inst [(''bdv'',v_v::real)] ''d1_polyeq_simplify'')) #>
walther@59637	882	(Try (Rewrite_Set ''polyeq_simplify'')) #>
walther@59635	883	(Try (Rewrite_Set ''norm_Rational_parenthesized'')) ) e_e;
wneuper@59504	884	L_L = Or_to_List e_e
walther@59635	885	in
walther@59635	886	Check_elementwise L_L {(v_v::real). Assumptions})"
wenzelm@60303	887
wenzelm@60303	888	method met_polyeq_d2_bdvonly : "PolyEq/solve_d2_polyeq_bdvonly_equation" =
wenzelm@60303	889	\<open>{rew_ord'="termlessI", rls'=PolyEq_erls, srls=Rule_Set.empty, prls=PolyEq_prls,
wenzelm@60309	890	calc=[("sqrt", (\<^const_name>\<open>sqrt\<close>, eval_sqrt "#sqrt_"))], crls=PolyEq_crls, errpats = [],
wenzelm@60303	891	nrls = norm_Rational}\<close>
wenzelm@60303	892	Program: solve_poly_equ0.simps
wenzelm@60303	893	Given: "equality e_e" "solveFor v_v"
wenzelm@60303	894	Where: "(lhs e_e) is_poly_in v_v " "((lhs e_e) has_degree_in v_v) = 2"
wenzelm@60303	895	Find: "solutions v_v'i'"
wneuper@59545	896
wneuper@59504	897	partial_function (tailrec) solve_poly_equ_sqrt :: "bool \<Rightarrow> real \<Rightarrow> bool list"
wneuper@59504	898	where
walther@59635	899	"solve_poly_equ_sqrt e_e v_v = (
walther@59635	900	let
walther@59635	901	e_e = (
walther@59637	902	(Try (Rewrite_Set_Inst [(''bdv'', v_v)] ''d2_polyeq_sq_only_simplify'')) #>
walther@59637	903	(Try (Rewrite_Set ''polyeq_simplify'')) #>
walther@59635	904	(Try (Rewrite_Set ''norm_Rational_parenthesized'')) ) e_e;
wneuper@59504	905	L_L = Or_to_List e_e
walther@59635	906	in
walther@59635	907	Check_elementwise L_L {(v_v::real). Assumptions})"
wenzelm@60303	908
wenzelm@60303	909	method met_polyeq_d2_sqonly : "PolyEq/solve_d2_polyeq_sqonly_equation" =
wenzelm@60303	910	\<open>{rew_ord'="termlessI", rls'=PolyEq_erls, srls=Rule_Set.empty, prls=PolyEq_prls,
wenzelm@60309	911	calc=[("sqrt", (\<^const_name>\<open>sqrt\<close>, eval_sqrt "#sqrt_"))], crls=PolyEq_crls, errpats = [],
wenzelm@60303	912	nrls = norm_Rational}\<close>
wenzelm@60303	913	Program: solve_poly_equ_sqrt.simps
wenzelm@60303	914	Given: "equality e_e" "solveFor v_v"
wenzelm@60303	915	Where: "(lhs e_e) is_poly_in v_v " "((lhs e_e) has_degree_in v_v) = 2"
wenzelm@60303	916	Find: "solutions v_v'i'"
wneuper@59545	917
wneuper@59504	918	partial_function (tailrec) solve_poly_equ_pq :: "bool \<Rightarrow> real \<Rightarrow> bool list"
walther@59635	919	where
walther@59635	920	"solve_poly_equ_pq e_e v_v = (
walther@59635	921	let
walther@59635	922	e_e = (
walther@59637	923	(Try (Rewrite_Set_Inst [(''bdv'', v_v)] ''d2_polyeq_pqFormula_simplify'')) #>
walther@59637	924	(Try (Rewrite_Set ''polyeq_simplify'')) #>
walther@59635	925	(Try (Rewrite_Set ''norm_Rational_parenthesized'')) ) e_e;
walther@59635	926	L_L = Or_to_List e_e
walther@59635	927	in
walther@59635	928	Check_elementwise L_L {(v_v::real). Assumptions})"
wenzelm@60303	929
wenzelm@60303	930	method met_polyeq_d2_pq : "PolyEq/solve_d2_polyeq_pq_equation" =
wenzelm@60303	931	\<open>{rew_ord'="termlessI", rls'=PolyEq_erls, srls=Rule_Set.empty, prls=PolyEq_prls,
wenzelm@60309	932	calc=[("sqrt", (\<^const_name>\<open>sqrt\<close>, eval_sqrt "#sqrt_"))], crls=PolyEq_crls, errpats = [],
wenzelm@60303	933	nrls = norm_Rational}\<close>
wenzelm@60303	934	Program: solve_poly_equ_pq.simps
wenzelm@60303	935	Given: "equality e_e" "solveFor v_v"
wenzelm@60303	936	Where: "(lhs e_e) is_poly_in v_v " "((lhs e_e) has_degree_in v_v) = 2"
wenzelm@60303	937	Find: "solutions v_v'i'"
wneuper@59545	938
wneuper@59504	939	partial_function (tailrec) solve_poly_equ_abc :: "bool \<Rightarrow> real \<Rightarrow> bool list"
wneuper@59504	940	where
walther@59635	941	"solve_poly_equ_abc e_e v_v = (
walther@59635	942	let
walther@59635	943	e_e = (
walther@59637	944	(Try (Rewrite_Set_Inst [(''bdv'', v_v)] ''d2_polyeq_abcFormula_simplify'')) #>
walther@59637	945	(Try (Rewrite_Set ''polyeq_simplify'')) #>
walther@59635	946	(Try (Rewrite_Set ''norm_Rational_parenthesized'')) ) e_e;
walther@59635	947	L_L = Or_to_List e_e
wneuper@59504	948	in Check_elementwise L_L {(v_v::real). Assumptions})"
wenzelm@60303	949
wenzelm@60303	950	method met_polyeq_d2_abc : "PolyEq/solve_d2_polyeq_abc_equation" =
wenzelm@60303	951	\<open>{rew_ord'="termlessI", rls'=PolyEq_erls,srls=Rule_Set.empty, prls=PolyEq_prls,
wenzelm@60309	952	calc=[("sqrt", (\<^const_name>\<open>sqrt\<close>, eval_sqrt "#sqrt_"))], crls=PolyEq_crls, errpats = [],
wenzelm@60303	953	nrls = norm_Rational}\<close>
wenzelm@60303	954	Program: solve_poly_equ_abc.simps
wenzelm@60303	955	Given: "equality e_e" "solveFor v_v"
wenzelm@60303	956	Where: "(lhs e_e) is_poly_in v_v " "((lhs e_e) has_degree_in v_v) = 2"
wenzelm@60303	957	Find: "solutions v_v'i'"
wneuper@59545	958
wneuper@59504	959	partial_function (tailrec) solve_poly_equ3 :: "bool \<Rightarrow> real \<Rightarrow> bool list"
walther@59635	960	where
walther@59635	961	"solve_poly_equ3 e_e v_v = (
walther@59635	962	let
walther@59635	963	e_e = (
walther@59637	964	(Try (Rewrite_Set_Inst [(''bdv'', v_v)] ''d3_polyeq_simplify'')) #>
walther@59637	965	(Try (Rewrite_Set ''polyeq_simplify'')) #>
walther@59637	966	(Try (Rewrite_Set_Inst [(''bdv'', v_v)] ''d2_polyeq_simplify'')) #>
walther@59637	967	(Try (Rewrite_Set ''polyeq_simplify'')) #>
walther@59637	968	(Try (Rewrite_Set_Inst [(''bdv'',v_v)] ''d1_polyeq_simplify'')) #>
walther@59637	969	(Try (Rewrite_Set ''polyeq_simplify'')) #>
walther@59635	970	(Try (Rewrite_Set ''norm_Rational_parenthesized''))) e_e;
walther@59635	971	L_L = Or_to_List e_e
walther@59635	972	in
walther@59635	973	Check_elementwise L_L {(v_v::real). Assumptions})"
wenzelm@60303	974
wenzelm@60303	975	method met_polyeq_d3 : "PolyEq/solve_d3_polyeq_equation" =
wenzelm@60303	976	\<open>{rew_ord'="termlessI", rls'=PolyEq_erls, srls=Rule_Set.empty, prls=PolyEq_prls,
wenzelm@60309	977	calc=[("sqrt", (\<^const_name>\<open>sqrt\<close>, eval_sqrt "#sqrt_"))], crls=PolyEq_crls, errpats = [],
wenzelm@60303	978	nrls = norm_Rational}\<close>
wenzelm@60303	979	Program: solve_poly_equ3.simps
wenzelm@60303	980	Given: "equality e_e" "solveFor v_v"
wenzelm@60303	981	Where: "(lhs e_e) is_poly_in v_v " "((lhs e_e) has_degree_in v_v) = 3"
wenzelm@60303	982	Find: "solutions v_v'i'"
wenzelm@60303	983
wenzelm@60303	984	(.solves all expanded (ie. normalised) terms of degree 2.)
s1210629013@55373	985	(*Oct.02 restriction: 'eval_true 0 =< discriminant' ony for integer values
s1210629013@55373	986	by 'PolyEq_erls'; restricted until Float.thy is implemented*)
wneuper@59504	987	partial_function (tailrec) solve_by_completing_square :: "bool \<Rightarrow> real \<Rightarrow> bool list"
wneuper@59504	988	where
walther@59635	989	"solve_by_completing_square e_e v_v = (
walther@59635	990	let e_e = (
walther@59637	991	(Try (Rewrite_Set_Inst [(''bdv'', v_v)] ''cancel_leading_coeff'')) #>
walther@59637	992	(Try (Rewrite_Set_Inst [(''bdv'', v_v)] ''complete_square'')) #>
walther@59637	993	(Try (Rewrite ''square_explicit1'')) #>
walther@59637	994	(Try (Rewrite ''square_explicit2'')) #>
walther@59637	995	(Rewrite ''root_plus_minus'') #>
walther@59637	996	(Try (Repeat (Rewrite_Inst [(''bdv'', v_v)] ''bdv_explicit1''))) #>
walther@59637	997	(Try (Repeat (Rewrite_Inst [(''bdv'', v_v)] ''bdv_explicit2''))) #>
walther@59637	998	(Try (Repeat (Rewrite_Inst [(''bdv'', v_v)] ''bdv_explicit3''))) #>
walther@59637	999	(Try (Rewrite_Set ''calculate_RootRat'')) #>
walther@59635	1000	(Try (Repeat (Calculate ''SQRT'')))) e_e
walther@59635	1001	in
walther@59635	1002	Or_to_List e_e)"
wenzelm@60303	1003
wenzelm@60303	1004	method met_polyeq_complsq : "PolyEq/complete_square" =
wenzelm@60303	1005	\<open>{rew_ord'="termlessI",rls'=PolyEq_erls,srls=Rule_Set.empty,prls=PolyEq_prls,
wenzelm@60309	1006	calc=[("sqrt", (\<^const_name>\<open>sqrt\<close>, eval_sqrt "#sqrt_"))], crls=PolyEq_crls, errpats = [],
wenzelm@60303	1007	nrls = norm_Rational}\<close>
wenzelm@60303	1008	Program: solve_by_completing_square.simps
wenzelm@60303	1009	Given: "equality e_e" "solveFor v_v"
wenzelm@60303	1010	Where: "matches (?a = 0) e_e" "((lhs e_e) has_degree_in v_v) = 2"
wenzelm@60303	1011	Find: "solutions v_v'i'"
s1210629013@55373	1012
wneuper@59472	1013	ML\<open>
neuper@37954	1014
walther@60342	1015	(* termorder hacked by MG, adapted later by WN *)
walther@60342	1016	(*)local (. for make_polynomial_in .*)
neuper@37954	1017
neuper@37954	1018	open Term; (* for type order = EQUAL \| LESS \| GREATER *)
neuper@37954	1019
neuper@37954	1020	fun pr_ord EQUAL = "EQUAL"
neuper@37954	1021	\| pr_ord LESS = "LESS"
neuper@37954	1022	\| pr_ord GREATER = "GREATER";
neuper@37954	1023
walther@60263	1024	fun dest_hd' _ (Const (a, T)) = (((a, 0), T), 0)
walther@60278	1025	\| dest_hd' x (t as Free (a, T)) =
neuper@37954	1026	if x = t then ((("\|\|\|\|\|\|\|\|\|\|\|\|\|", 0), T), 0) (WN)
neuper@37954	1027	else (((a, 0), T), 1)
walther@60263	1028	\| dest_hd' _ (Var v) = (v, 2)
walther@60263	1029	\| dest_hd' _ (Bound i) = ((("", i), dummyT), 3)
walther@60263	1030	\| dest_hd' _ (Abs (_, T, _)) = ((("", 0), T), 4)
walther@60263	1031	\| dest_hd' _ _ = raise ERROR "dest_hd': uncovered case in fun.def.";
neuper@37954	1032
walther@60342	1033	fun size_of_term' i pr x (t as Const (\<^const_name>\<open>powr\<close>, _) $
walther@60342	1034	Free (var, _) $ Free (pot, _)) =
walther@60342	1035	(if pr then tracing (idt "#" i ^ "size_of_term' powr: " ^ UnparseC.term t) else ();
walther@60342	1036	case x of (WN)
walther@60317	1037	(Free (xstr, _)) =>
walther@60342	1038	if xstr = var
walther@60342	1039	then (if pr then tracing (idt "#" i ^ "xstr = var --> " ^ string_of_int (1000 * (the (TermC.int_opt_of_string pot)))) else ();
walther@60342	1040	1000 * (the (TermC.int_opt_of_string pot)))
walther@60342	1041	else (if pr then tracing (idt "#" i ^ "x <> Free --> " ^ "3") else (); 3)
walther@60317	1042	\| _ => raise ERROR ("size_of_term' called with subst = " ^ UnparseC.term x))
walther@60342	1043	\| size_of_term' i pr x (t as Abs (_, _, body)) =
walther@60342	1044	(if pr then tracing (idt "#" i ^ "size_of_term' Abs: " ^ UnparseC.term t) else ();
walther@60342	1045	1 + size_of_term' (i + 1) pr x body)
walther@60342	1046	\| size_of_term' i pr x (f $ t) =
walther@60342	1047	let
walther@60342	1048	val _ = if pr then tracing (idt "#" i ^ "size_of_term' $$$: " ^ UnparseC.term f ^ " $$$ " ^ UnparseC.term t) else ();
walther@60342	1049	val s1 = size_of_term' (i + 1) pr x f
walther@60342	1050	val s2 = size_of_term' (i + 1) pr x t
walther@60342	1051	val _ = if pr then tracing (idt "#" i ^ "size_of_term' $$$-->: " ^ string_of_int s1 ^ " + " ^ string_of_int s2 ^ " = " ^ string_of_int(s1 + s2)) else ();
walther@60342	1052	in (s1 + s2) end
walther@60342	1053	\| size_of_term' i pr x t =
walther@60342	1054	(if pr then tracing (idt "#" i ^ "size_of_term' bot: " ^ UnparseC.term t) else ();
walther@60342	1055	case t of
walther@60342	1056	Free (subst, _) =>
walther@60342	1057	(case x of
walther@60342	1058	Free (xstr, _) =>
walther@60342	1059	if xstr = subst
walther@60342	1060	then (if pr then tracing (idt "#" i ^ "xstr = var --> " ^ "1000") else (); 1000)
walther@60342	1061	else (if pr then tracing (idt "#" i ^ "x <> Free --> " ^ "1") else (); 1)
walther@60342	1062	\| _ => raise ERROR ("size_of_term' called with subst = " ^ UnparseC.term x))
walther@60342	1063	\| _ => (if pr then tracing (idt "#" i ^ "bot --> " ^ "1") else (); 1));
neuper@37954	1064
walther@60342	1065	fun term_ord' i pr x thy (Abs (_, T, t), Abs(_, U, u)) = (* ~ term.ML *)
walther@60342	1066	let
walther@60342	1067	val _ = if pr then tracing (idt "#" i ^ "term_ord' Abs") else ();
walther@60342	1068	val ord =
walther@60342	1069	case term_ord' (i + 1) pr x thy (t, u) of EQUAL => Term_Ord.typ_ord (T, U) \| ord => ord
walther@60342	1070	val _ = if pr then tracing (idt "#" i ^ "term_ord' Abs --> " ^ pr_ord ord) else ()
walther@60342	1071	in ord end
walther@60342	1072	\| term_ord' i pr x _ (t, u) =
walther@60342	1073	let
walther@60342	1074	val _ = if pr then tracing (idt "#" i ^ "term_ord' bot (" ^ UnparseC.term t ^ ", " ^ UnparseC.term u ^ ")") else ();
walther@60342	1075	val ord =
walther@60342	1076	case int_ord (size_of_term' (i + 1) pr x t, size_of_term' (i + 1) pr x u) of
walther@60342	1077	EQUAL =>
walther@60342	1078	let val (f, ts) = strip_comb t and (g, us) = strip_comb u
walther@60342	1079	in
walther@60342	1080	(case hd_ord (i + 1) pr x (f, g) of
walther@60342	1081	EQUAL => (terms_ord x (i + 1) pr) (ts, us)
walther@60342	1082	\| ord => ord)
walther@60342	1083	end
walther@60342	1084	\| ord => ord
walther@60342	1085	val _ = if pr then tracing (idt "#" i ^ "term_ord' bot --> " ^ pr_ord ord) else ()
walther@60342	1086	in ord end
walther@60342	1087	and hd_ord i pr x (f, g) = (* ~ term.ML *)
walther@60342	1088	let
walther@60342	1089	val _ = if pr then tracing (idt "#" i ^ "hd_ord (" ^ UnparseC.term f ^ ", " ^ UnparseC.term g ^ ")") else ();
walther@60342	1090	val ord = prod_ord
walther@60342	1091	(prod_ord Term_Ord.indexname_ord Term_Ord.typ_ord) int_ord
walther@60342	1092	(dest_hd' x f, dest_hd' x g)
walther@60342	1093	val _ = if pr then tracing (idt "#" i ^ "hd_ord --> " ^ pr_ord ord) else ();
walther@60342	1094	in ord end
walther@60342	1095	and terms_ord x i pr (ts, us) =
walther@60342	1096	let
walther@60342	1097	val _ = if pr then tracing (idt "#" i ^ "terms_ord (" ^ UnparseC.terms ts ^ ", " ^ UnparseC.terms us ^ ")") else ();
walther@60342	1098	val ord = list_ord (term_ord' (i + 1) pr x (ThyC.get_theory "Isac_Knowledge"))(ts, us);
walther@60342	1099	val _ = if pr then tracing (idt "#" i ^ "terms_ord --> " ^ pr_ord ord) else ();
walther@60342	1100	in ord end
neuper@52070	1101
walther@60342	1102	(*)in(local*)
neuper@37954	1103
walther@60324	1104	fun ord_make_polynomial_in (pr:bool) thy subst (ts, us) =
walther@60342	1105	(( )tracing ("* subs variable is: " ^ Env.subst2str subst); ( **)
neuper@37954	1106	case subst of
walther@60342	1107	(_, x) :: _ =>
walther@60342	1108	term_ord' 1 pr x thy (TermC.numerals_to_Free ts, TermC.numerals_to_Free us) = LESS
walther@60263	1109	\| _ => raise ERROR ("ord_make_polynomial_in called with subst = " ^ Env.subst2str subst))
walther@60263	1110
neuper@37989	1111	end;(local)
neuper@37954	1112
wneuper@59472	1113	\<close>
wneuper@59472	1114	ML\<open>
s1210629013@55444	1115	val order_add_mult_in = prep_rls'(
walther@59851	1116	Rule_Def.Repeat{id = "order_add_mult_in", preconds = [],
walther@60358	1117	rew_ord = ("ord_make_polynomial_in", ord_make_polynomial_in false @{theory "Poly"}),
walther@60358	1118	erls = Rule_Set.empty,srls = Rule_Set.Empty,
walther@60358	1119	calc = [], errpatts = [],
walther@60358	1120	rules = [
walther@60358	1121	\<^rule_thm>\<open>mult.commute\<close>, (* z * w = w * z *)
walther@60358	1122	\<^rule_thm>\<open>real_mult_left_commute\<close>, (z1.0 (z2.0 * z3.0) = z2.0 * (z1.0 * z3.0)*)
walther@60358	1123	\<^rule_thm>\<open>mult.assoc\<close>, (z1.0 z2.0 * z3.0 = z1.0 * (z2.0 * z3.0)*)
walther@60358	1124	\<^rule_thm>\<open>add.commute\<close>, (z + w = w + z)
walther@60358	1125	\<^rule_thm>\<open>add.left_commute\<close>, (x + (y + z) = y + (x + z))
walther@60358	1126	\<^rule_thm>\<open>add.assoc\<close>], (z1.0 + z2.0 + z3.0 = z1.0 + (z2.0 + z3.0))
walther@60358	1127	scr = Rule.Empty_Prog});
neuper@37954	1128
wneuper@59472	1129	\<close>
wneuper@59472	1130	ML\<open>
s1210629013@55444	1131	val collect_bdv = prep_rls'(
walther@59851	1132	Rule_Def.Repeat{id = "collect_bdv", preconds = [],
walther@60358	1133	rew_ord = ("dummy_ord", Rewrite_Ord.dummy_ord),
walther@60358	1134	erls = Rule_Set.empty,srls = Rule_Set.Empty,
walther@60358	1135	calc = [], errpatts = [],
walther@60358	1136	rules = [\<^rule_thm>\<open>bdv_collect_1\<close>,
walther@60358	1137	\<^rule_thm>\<open>bdv_collect_2\<close>,
walther@60358	1138	\<^rule_thm>\<open>bdv_collect_3\<close>,
walther@60358	1139
walther@60358	1140	\<^rule_thm>\<open>bdv_collect_assoc1_1\<close>,
walther@60358	1141	\<^rule_thm>\<open>bdv_collect_assoc1_2\<close>,
walther@60358	1142	\<^rule_thm>\<open>bdv_collect_assoc1_3\<close>,
walther@60358	1143
walther@60358	1144	\<^rule_thm>\<open>bdv_collect_assoc2_1\<close>,
walther@60358	1145	\<^rule_thm>\<open>bdv_collect_assoc2_2\<close>,
walther@60358	1146	\<^rule_thm>\<open>bdv_collect_assoc2_3\<close>,
walther@60358	1147
walther@60358	1148
walther@60358	1149	\<^rule_thm>\<open>bdv_n_collect_1\<close>,
walther@60358	1150	\<^rule_thm>\<open>bdv_n_collect_2\<close>,
walther@60358	1151	\<^rule_thm>\<open>bdv_n_collect_3\<close>,
walther@60358	1152
walther@60358	1153	\<^rule_thm>\<open>bdv_n_collect_assoc1_1\<close>,
walther@60358	1154	\<^rule_thm>\<open>bdv_n_collect_assoc1_2\<close>,
walther@60358	1155	\<^rule_thm>\<open>bdv_n_collect_assoc1_3\<close>,
walther@60358	1156
walther@60358	1157	\<^rule_thm>\<open>bdv_n_collect_assoc2_1\<close>,
walther@60358	1158	\<^rule_thm>\<open>bdv_n_collect_assoc2_2\<close>,
walther@60358	1159	\<^rule_thm>\<open>bdv_n_collect_assoc2_3\<close>],
walther@60358	1160	scr = Rule.Empty_Prog});
neuper@37954	1161
wneuper@59472	1162	\<close>
wneuper@59472	1163	ML\<open>
neuper@37954	1164	(*.transforms an arbitrary term without roots to a polynomial [4]
neuper@37954	1165	according to knowledge/Poly.sml.*)
s1210629013@55444	1166	val make_polynomial_in = prep_rls'(
walther@60358	1167	Rule_Set.Sequence {
walther@60358	1168	id = "make_polynomial_in", preconds = [], rew_ord = ("dummy_ord", Rewrite_Ord.dummy_ord),
walther@60358	1169	erls = Atools_erls, srls = Rule_Set.Empty, calc = [], errpatts = [],
walther@60358	1170	rules = [
walther@60358	1171	Rule.Rls_ expand_poly,
walther@60358	1172	Rule.Rls_ order_add_mult_in,
walther@60358	1173	Rule.Rls_ simplify_power,
walther@60358	1174	Rule.Rls_ collect_numerals,
walther@60358	1175	Rule.Rls_ reduce_012,
walther@60358	1176	\<^rule_thm>\<open>realpow_oneI\<close>,
walther@60358	1177	Rule.Rls_ discard_parentheses,
walther@60358	1178	Rule.Rls_ collect_bdv],
walther@60358	1179	scr = Rule.Empty_Prog});
neuper@37954	1180
wneuper@59472	1181	\<close>
wneuper@59472	1182	ML\<open>
walther@60358	1183	val separate_bdvs = Rule_Set.append_rules "separate_bdvs" collect_bdv [
walther@60358	1184	\<^rule_thm>\<open>separate_bdv\<close>, ("?a ?bdv / ?b = ?a / ?b * ?bdv"*)
walther@60358	1185	\<^rule_thm>\<open>separate_bdv_n\<close>,
walther@60358	1186	\<^rule_thm>\<open>separate_1_bdv\<close>, ("?bdv / ?b = (1 / ?b) ?bdv"*)
walther@60358	1187	\<^rule_thm>\<open>separate_1_bdv_n\<close>, ("?bdv \<up> ?n / ?b = 1 / ?b ?bdv \<up> ?n"*)
walther@60358	1188	\<^rule_thm>\<open>add_divide_distrib\<close> (*"(?x + ?y) / ?z = ?x / ?z + ?y / ?z"
walther@60358	1189	WN051031 DOES NOT BELONG TO HERE*)];
wneuper@59472	1190	\<close>
wneuper@59472	1191	ML\<open>
s1210629013@55444	1192	val make_ratpoly_in = prep_rls'(
walther@60358	1193	Rule_Set.Sequence {
walther@60358	1194	id = "make_ratpoly_in", preconds = []:term list, rew_ord = ("dummy_ord", Rewrite_Ord.dummy_ord),
walther@60358	1195	erls = Atools_erls, srls = Rule_Set.Empty, calc = [], errpatts = [],
walther@60358	1196	rules = [
walther@60358	1197	Rule.Rls_ norm_Rational,
walther@60358	1198	Rule.Rls_ order_add_mult_in,
walther@60358	1199	Rule.Rls_ discard_parentheses,
walther@60358	1200	Rule.Rls_ separate_bdvs,
walther@60358	1201	(* Rule.Rls_ rearrange_assoc, WN060916 why does cancel_p not work?*)
walther@60358	1202	Rule.Rls_ cancel_p
walther@60358	1203	(\<^rule_eval>\<open>divide\<close> (eval_cancel "#divide_e") too weak!)],
walther@60358	1204	scr = Rule.Empty_Prog});
wneuper@59472	1205	\<close>
wenzelm@60289	1206	rule_set_knowledge
wenzelm@60286	1207	order_add_mult_in = order_add_mult_in and
wenzelm@60286	1208	collect_bdv = collect_bdv and
wenzelm@60286	1209	make_polynomial_in = make_polynomial_in and
wenzelm@60286	1210	make_ratpoly_in = make_ratpoly_in and
wenzelm@60286	1211	separate_bdvs = separate_bdvs
wenzelm@60286	1212	ML \<open>
walther@60278	1213	\<close> ML \<open>
walther@60278	1214	\<close> ML \<open>
walther@60278	1215	\<close>
neuper@37906	1216	end
neuper@37906	1217
neuper@37906	1218
neuper@37906	1219
neuper@37906	1220
neuper@37906	1221
neuper@37906	1222

author	wneuper <walther.neuper@jku.at>
	Tue, 10 Aug 2021 09:43:07 +0200
changeset 60358	8377b6c37640
parent 60342	e96abd81a321
child 60360	49680d595342
permissions	-rw-r--r--