wneuper/isa: src/Tools/isac/Knowledge/PolyEq.thy@73e7175a7d3f (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
neuper@38030	304	bdv_n_collect_assoc1_1:
walther@60242	305	"l * bdv \<up> n + (m * bdv \<up> n + k) = (l + m) * bdv \<up> n + k" and
walther@60242	306	bdv_n_collect_assoc1_2: "bdv \<up> n + (m * bdv \<up> n + k) = (1 + m) * bdv \<up> n + k" and
walther@60242	307	bdv_n_collect_assoc1_3: "l * bdv \<up> n + (bdv \<up> n + k) = (l + 1) * bdv \<up> n + k" and
neuper@37906	308
walther@60242	309	bdv_n_collect_assoc2_1: "k + l * bdv \<up> n + m * bdv \<up> n = k +(l + m) * bdv \<up> n" and
walther@60242	310	bdv_n_collect_assoc2_2: "k + bdv \<up> n + m * bdv \<up> n = k + (1 + m) * bdv \<up> n" and
walther@60242	311	bdv_n_collect_assoc2_3: "k + l * bdv \<up> n + bdv \<up> n = k + (l + 1) * bdv \<up> n" and
neuper@37906	312
neuper@37906	313	(WN.14.3.03)
neuper@52148	314	real_minus_div: "- (a / b) = (-1 * a) / b" and
neuper@38030	315
neuper@52148	316	separate_bdv: "(a * bdv) / b = (a / b) * (bdv::real)" and
walther@60242	317	separate_bdv_n: "(a * bdv \<up> n) / b = (a / b) * bdv \<up> n" and
neuper@52148	318	separate_1_bdv: "bdv / b = (1 / b) * (bdv::real)" and
walther@60242	319	separate_1_bdv_n: "bdv \<up> n / b = (1 / b) * bdv \<up> n"
neuper@37906	320
wneuper@59472	321	ML \<open>
neuper@37954	322	(-------------------------rulse-------------------------)
neuper@37954	323	val PolyEq_prls = (3.10.02:just the following order due to subterm evaluation)
walther@59852	324	Rule_Set.append_rules "PolyEq_prls" Rule_Set.empty
wenzelm@60294	325	[\<^rule_eval>\<open>Prog_Expr.ident\<close> (Prog_Expr.eval_ident "#ident_"),
wenzelm@60294	326	\<^rule_eval>\<open>Prog_Expr.matches\<close> (Prog_Expr.eval_matches ""),
wenzelm@60294	327	\<^rule_eval>\<open>Prog_Expr.lhs\<close> (Prog_Expr.eval_lhs ""),
wenzelm@60294	328	\<^rule_eval>\<open>Prog_Expr.rhs\<close> (Prog_Expr.eval_rhs ""),
wenzelm@60294	329	\<^rule_eval>\<open>is_expanded_in\<close> (eval_is_expanded_in ""),
wenzelm@60294	330	\<^rule_eval>\<open>is_poly_in\<close> (eval_is_poly_in ""),
wenzelm@60294	331	\<^rule_eval>\<open>has_degree_in\<close> (eval_has_degree_in ""),
wenzelm@60294	332	\<^rule_eval>\<open>is_polyrat_in\<close> (eval_is_polyrat_in ""),
wenzelm@60294	333	(\<^rule_eval>\<open>Prog_Expr.occurs_in\<close> (Prog_Expr.eval_occurs_in ""), )
wenzelm@60294	334	(\<^rule_eval>\<open>Prog_Expr.is_const\<close> (Prog_Expr.eval_const "#is_const_"),)
wenzelm@60294	335	\<^rule_eval>\<open>HOL.eq\<close> (Prog_Expr.eval_equal "#equal_"),
wenzelm@60294	336	\<^rule_eval>\<open>is_rootTerm_in\<close> (eval_is_rootTerm_in ""),
wenzelm@60294	337	\<^rule_eval>\<open>is_ratequation_in\<close> (eval_is_ratequation_in ""),
wenzelm@60297	338	\<^rule_thm>\<open>not_true\<close>,
wenzelm@60297	339	\<^rule_thm>\<open>not_false\<close>,
wenzelm@60297	340	\<^rule_thm>\<open>and_true\<close>,
wenzelm@60297	341	\<^rule_thm>\<open>and_false\<close>,
wenzelm@60297	342	\<^rule_thm>\<open>or_true\<close>,
wenzelm@60297	343	\<^rule_thm>\<open>or_false\<close>
neuper@37954	344	];
neuper@37954	345
neuper@37954	346	val PolyEq_erls =
walther@59852	347	Rule_Set.merge "PolyEq_erls" LinEq_erls
walther@59852	348	(Rule_Set.append_rules "ops_preds" calculate_Rational
wenzelm@60294	349	[\<^rule_eval>\<open>HOL.eq\<close> (Prog_Expr.eval_equal "#equal_"),
wenzelm@60297	350	\<^rule_thm>\<open>plus_leq\<close>,
wenzelm@60297	351	\<^rule_thm>\<open>minus_leq\<close>,
wenzelm@60297	352	\<^rule_thm>\<open>rat_leq1\<close>,
wenzelm@60297	353	\<^rule_thm>\<open>rat_leq2\<close>,
wenzelm@60297	354	\<^rule_thm>\<open>rat_leq3\<close>
neuper@37954	355	]);
neuper@37954	356
neuper@37954	357	val PolyEq_crls =
walther@59852	358	Rule_Set.merge "PolyEq_crls" LinEq_crls
walther@59852	359	(Rule_Set.append_rules "ops_preds" calculate_Rational
wenzelm@60294	360	[\<^rule_eval>\<open>HOL.eq\<close> (Prog_Expr.eval_equal "#equal_"),
wenzelm@60297	361	\<^rule_thm>\<open>plus_leq\<close>,
wenzelm@60297	362	\<^rule_thm>\<open>minus_leq\<close>,
wenzelm@60297	363	\<^rule_thm>\<open>rat_leq1\<close>,
wenzelm@60297	364	\<^rule_thm>\<open>rat_leq2\<close>,
wenzelm@60297	365	\<^rule_thm>\<open>rat_leq3\<close>
neuper@37954	366	]);
neuper@37954	367
s1210629013@55444	368	val cancel_leading_coeff = prep_rls'(
walther@59851	369	Rule_Def.Repeat {id = "cancel_leading_coeff", preconds = [],
walther@59857	370	rew_ord = ("e_rew_ord",Rewrite_Ord.e_rew_ord),
walther@59851	371	erls = PolyEq_erls, srls = Rule_Set.Empty, calc = [], errpatts = [],
neuper@37989	372	rules =
wenzelm@60297	373	[\<^rule_thm>\<open>cancel_leading_coeff1\<close>,
wenzelm@60297	374	\<^rule_thm>\<open>cancel_leading_coeff2\<close>,
wenzelm@60297	375	\<^rule_thm>\<open>cancel_leading_coeff3\<close>,
wenzelm@60297	376	\<^rule_thm>\<open>cancel_leading_coeff4\<close>,
wenzelm@60297	377	\<^rule_thm>\<open>cancel_leading_coeff5\<close>,
wenzelm@60297	378	\<^rule_thm>\<open>cancel_leading_coeff6\<close>,
wenzelm@60297	379	\<^rule_thm>\<open>cancel_leading_coeff7\<close>,
wenzelm@60297	380	\<^rule_thm>\<open>cancel_leading_coeff8\<close>,
wenzelm@60297	381	\<^rule_thm>\<open>cancel_leading_coeff9\<close>,
wenzelm@60297	382	\<^rule_thm>\<open>cancel_leading_coeff10\<close>,
wenzelm@60297	383	\<^rule_thm>\<open>cancel_leading_coeff11\<close>,
wenzelm@60297	384	\<^rule_thm>\<open>cancel_leading_coeff12\<close>,
wenzelm@60297	385	\<^rule_thm>\<open>cancel_leading_coeff13\<close>
walther@59878	386	],scr = Rule.Empty_Prog});
s1210629013@55444	387
walther@59618	388	val prep_rls' = Auto_Prog.prep_rls @{theory};
wneuper@59472	389	\<close>
wneuper@59472	390	ML\<open>
s1210629013@55444	391	val complete_square = prep_rls'(
walther@59851	392	Rule_Def.Repeat {id = "complete_square", preconds = [],
walther@59857	393	rew_ord = ("e_rew_ord",Rewrite_Ord.e_rew_ord),
walther@59851	394	erls = PolyEq_erls, srls = Rule_Set.Empty, calc = [], errpatts = [],
wenzelm@60297	395	rules = [\<^rule_thm>\<open>complete_square1\<close>,
wenzelm@60297	396	\<^rule_thm>\<open>complete_square2\<close>,
wenzelm@60297	397	\<^rule_thm>\<open>complete_square3\<close>,
wenzelm@60297	398	\<^rule_thm>\<open>complete_square4\<close>,
wenzelm@60297	399	\<^rule_thm>\<open>complete_square5\<close>
neuper@37954	400	],
walther@59878	401	scr = Rule.Empty_Prog
wneuper@59406	402	});
neuper@37954	403
s1210629013@55444	404	val polyeq_simplify = prep_rls'(
walther@59851	405	Rule_Def.Repeat {id = "polyeq_simplify", preconds = [],
neuper@37954	406	rew_ord = ("termlessI",termlessI),
neuper@37954	407	erls = PolyEq_erls,
walther@59851	408	srls = Rule_Set.Empty,
neuper@42451	409	calc = [], errpatts = [],
wenzelm@60297	410	rules = [\<^rule_thm>\<open>real_assoc_1\<close>,
wenzelm@60297	411	\<^rule_thm>\<open>real_assoc_2\<close>,
wenzelm@60297	412	\<^rule_thm>\<open>real_diff_minus\<close>,
wenzelm@60297	413	\<^rule_thm>\<open>real_unari_minus\<close>,
wenzelm@60297	414	\<^rule_thm>\<open>realpow_multI\<close>,
wenzelm@60294	415	\<^rule_eval>\<open>plus\<close> (**)(eval_binop "#add_"),
wenzelm@60294	416	\<^rule_eval>\<open>minus\<close> (**)(eval_binop "#sub_"),
wenzelm@60294	417	\<^rule_eval>\<open>times\<close> (**)(eval_binop "#mult_"),
wenzelm@60294	418	\<^rule_eval>\<open>divide\<close> (Prog_Expr.eval_cancel "#divide_e"),
wenzelm@60294	419	\<^rule_eval>\<open>sqrt\<close> (eval_sqrt "#sqrt_"),
wenzelm@60294	420	\<^rule_eval>\<open>powr\<close> (**)(eval_binop "#power_"),
wneuper@59416	421	Rule.Rls_ reduce_012
neuper@37954	422	],
walther@59878	423	scr = Rule.Empty_Prog
wneuper@59406	424	});
wneuper@59472	425	\<close>
wenzelm@60289	426	rule_set_knowledge
wenzelm@60286	427	cancel_leading_coeff = cancel_leading_coeff and
wenzelm@60286	428	complete_square = complete_square and
wenzelm@60286	429	PolyEq_erls = PolyEq_erls and
wenzelm@60286	430	polyeq_simplify = polyeq_simplify
wneuper@59472	431	ML\<open>
neuper@37954	432
neuper@37954	433	(* ------------- polySolve ------------------ *)
neuper@37954	434	(* -- d0 -- *)
neuper@37954	435	(isolate the bound variable in an d0 equation; 'bdv' is a meta-constant)
s1210629013@55444	436	val d0_polyeq_simplify = prep_rls'(
walther@59851	437	Rule_Def.Repeat {id = "d0_polyeq_simplify", preconds = [],
walther@59857	438	rew_ord = ("e_rew_ord",Rewrite_Ord.e_rew_ord),
neuper@37954	439	erls = PolyEq_erls,
walther@59851	440	srls = Rule_Set.Empty,
neuper@42451	441	calc = [], errpatts = [],
wenzelm@60297	442	rules = [\<^rule_thm>\<open>d0_true\<close>,
walther@59871	443	Rule.Thm("d0_false",ThmC.numerals_to_Free @{thm d0_false})
neuper@37954	444	],
walther@59878	445	scr = Rule.Empty_Prog
wneuper@59406	446	});
neuper@37954	447
neuper@37954	448	(* -- d1 -- *)
neuper@37954	449	(isolate the bound variable in an d1 equation; 'bdv' is a meta-constant)
s1210629013@55444	450	val d1_polyeq_simplify = prep_rls'(
walther@59851	451	Rule_Def.Repeat {id = "d1_polyeq_simplify", preconds = [],
walther@59857	452	rew_ord = ("e_rew_ord",Rewrite_Ord.e_rew_ord),
neuper@37954	453	erls = PolyEq_erls,
walther@59851	454	srls = Rule_Set.Empty,
neuper@42451	455	calc = [], errpatts = [],
neuper@37954	456	rules = [
wenzelm@60297	457	\<^rule_thm>\<open>d1_isolate_add1\<close>,
neuper@37954	458	(* a+bx=0 -> bx=-a *)
wenzelm@60297	459	\<^rule_thm>\<open>d1_isolate_add2\<close>,
neuper@37954	460	(* a+ x=0 -> x=-a *)
wenzelm@60297	461	\<^rule_thm>\<open>d1_isolate_div\<close>
neuper@37954	462	(* bx=c -> x=c/b *)
neuper@37954	463	],
walther@59878	464	scr = Rule.Empty_Prog
wneuper@59406	465	});
neuper@37954	466
wneuper@59472	467	\<close>
wneuper@59472	468	subsection \<open>degree 2\<close>
wneuper@59472	469	ML\<open>
neuper@42394	470	(* isolate the bound variable in an d2 equation with bdv only;
neuper@42394	471	"bdv" is a meta-constant substituted for the "x" below by isac's rewriter. *)
s1210629013@55444	472	val d2_polyeq_bdv_only_simplify = prep_rls'(
walther@59857	473	Rule_Def.Repeat {id = "d2_polyeq_bdv_only_simplify", preconds = [], rew_ord = ("e_rew_ord",Rewrite_Ord.e_rew_ord),
walther@59851	474	erls = PolyEq_erls, srls = Rule_Set.Empty, calc = [], errpatts = [],
neuper@42394	475	rules =
wenzelm@60297	476	[\<^rule_thm>\<open>d2_prescind1\<close>, (* ax+bx^2=0 -> x(a+bx)=0 *)
wenzelm@60297	477	\<^rule_thm>\<open>d2_prescind2\<close>, (* ax+ x^2=0 -> x(a+ x)=0 *)
wenzelm@60297	478	\<^rule_thm>\<open>d2_prescind3\<close>, (* x+bx^2=0 -> x(1+bx)=0 *)
wenzelm@60297	479	\<^rule_thm>\<open>d2_prescind4\<close>, (* x+ x^2=0 -> x(1+ x)=0 *)
wenzelm@60297	480	\<^rule_thm>\<open>d2_sqrt_equation1\<close>, (* x^2=c -> x=+-sqrt(c) *)
wenzelm@60297	481	\<^rule_thm>\<open>d2_sqrt_equation1_neg\<close>, (* [0<c] x^2=c -> []*)
wenzelm@60297	482	\<^rule_thm>\<open>d2_sqrt_equation2\<close>, (* x^2=0 -> x=0 *)
wenzelm@60297	483	\<^rule_thm>\<open>d2_reduce_equation1\<close>,(* x(a+bx)=0 -> x=0 \|a+bx=0*)
wenzelm@60297	484	\<^rule_thm>\<open>d2_reduce_equation2\<close>,(* x(a+ x)=0 -> x=0 \|a+ x=0*)
wenzelm@60297	485	\<^rule_thm>\<open>d2_isolate_div\<close> (* bx^2=c -> x^2=c/b *)
neuper@42394	486	],
walther@59878	487	scr = Rule.Empty_Prog
wneuper@59406	488	});
wneuper@59472	489	\<close>
wneuper@59472	490	ML\<open>
neuper@37954	491	(* isolate the bound variable in an d2 equation with sqrt only;
neuper@37954	492	'bdv' is a meta-constant*)
s1210629013@55444	493	val d2_polyeq_sq_only_simplify = prep_rls'(
walther@59851	494	Rule_Def.Repeat {id = "d2_polyeq_sq_only_simplify", preconds = [],
walther@59857	495	rew_ord = ("e_rew_ord",Rewrite_Ord.e_rew_ord),
neuper@37954	496	erls = PolyEq_erls,
walther@59851	497	srls = Rule_Set.Empty,
neuper@42451	498	calc = [], errpatts = [],
walther@59997	499	(*asm_thm = [("d2_sqrt_equation1", ""),("d2_sqrt_equation1_neg", ""),
walther@59997	500	("d2_isolate_div", "")],*)
wenzelm@60297	501	rules = [\<^rule_thm>\<open>d2_isolate_add1\<close>,
neuper@37954	502	(* a+ bx^2=0 -> bx^2=(-1)a*)
wenzelm@60297	503	\<^rule_thm>\<open>d2_isolate_add2\<close>,
neuper@37954	504	(* a+ x^2=0 -> x^2=(-1)a*)
wenzelm@60297	505	\<^rule_thm>\<open>d2_sqrt_equation2\<close>,
neuper@37954	506	(* x^2=0 -> x=0 *)
wenzelm@60297	507	\<^rule_thm>\<open>d2_sqrt_equation1\<close>,
neuper@37954	508	(* x^2=c -> x=+-sqrt(c)*)
wenzelm@60297	509	\<^rule_thm>\<open>d2_sqrt_equation1_neg\<close>,
neuper@37954	510	(* [c<0] x^2=c -> x=[] *)
wenzelm@60297	511	\<^rule_thm>\<open>d2_isolate_div\<close>
neuper@37954	512	(* bx^2=c -> x^2=c/b*)
neuper@37954	513	],
walther@59878	514	scr = Rule.Empty_Prog
wneuper@59406	515	});
wneuper@59472	516	\<close>
wneuper@59472	517	ML\<open>
neuper@37954	518	(* isolate the bound variable in an d2 equation with pqFormula;
neuper@37954	519	'bdv' is a meta-constant*)
s1210629013@55444	520	val d2_polyeq_pqFormula_simplify = prep_rls'(
walther@59851	521	Rule_Def.Repeat {id = "d2_polyeq_pqFormula_simplify", preconds = [],
walther@59857	522	rew_ord = ("e_rew_ord",Rewrite_Ord.e_rew_ord), erls = PolyEq_erls,
walther@59851	523	srls = Rule_Set.Empty, calc = [], errpatts = [],
wenzelm@60297	524	rules = [\<^rule_thm>\<open>d2_pqformula1\<close>,
neuper@37954	525	(* q+px+ x^2=0 *)
wenzelm@60297	526	\<^rule_thm>\<open>d2_pqformula1_neg\<close>,
neuper@37954	527	(* q+px+ x^2=0 *)
wenzelm@60297	528	\<^rule_thm>\<open>d2_pqformula2\<close>,
neuper@37954	529	(* q+px+1x^2=0 *)
wenzelm@60297	530	\<^rule_thm>\<open>d2_pqformula2_neg\<close>,
neuper@37954	531	(* q+px+1x^2=0 *)
wenzelm@60297	532	\<^rule_thm>\<open>d2_pqformula3\<close>,
neuper@37954	533	(* q+ x+ x^2=0 *)
wenzelm@60297	534	\<^rule_thm>\<open>d2_pqformula3_neg\<close>,
neuper@37954	535	(* q+ x+ x^2=0 *)
wenzelm@60297	536	\<^rule_thm>\<open>d2_pqformula4\<close>,
neuper@37954	537	(* q+ x+1x^2=0 *)
wenzelm@60297	538	\<^rule_thm>\<open>d2_pqformula4_neg\<close>,
neuper@37954	539	(* q+ x+1x^2=0 *)
wenzelm@60297	540	\<^rule_thm>\<open>d2_pqformula5\<close>,
neuper@37954	541	(* qx+ x^2=0 *)
wenzelm@60297	542	\<^rule_thm>\<open>d2_pqformula6\<close>,
neuper@37954	543	(* qx+1x^2=0 *)
wenzelm@60297	544	\<^rule_thm>\<open>d2_pqformula7\<close>,
neuper@37954	545	(* x+ x^2=0 *)
wenzelm@60297	546	\<^rule_thm>\<open>d2_pqformula8\<close>,
neuper@37954	547	(* x+1x^2=0 *)
wenzelm@60297	548	\<^rule_thm>\<open>d2_pqformula9\<close>,
neuper@37954	549	(* q +1x^2=0 *)
wenzelm@60297	550	\<^rule_thm>\<open>d2_pqformula9_neg\<close>,
neuper@37954	551	(* q +1x^2=0 *)
wenzelm@60297	552	\<^rule_thm>\<open>d2_pqformula10\<close>,
neuper@37954	553	(* q + x^2=0 *)
wenzelm@60297	554	\<^rule_thm>\<open>d2_pqformula10_neg\<close>,
neuper@37954	555	(* q + x^2=0 *)
wenzelm@60297	556	\<^rule_thm>\<open>d2_sqrt_equation2\<close>,
neuper@37954	557	(* x^2=0 *)
wenzelm@60297	558	\<^rule_thm>\<open>d2_sqrt_equation3\<close>
neuper@37954	559	(* 1x^2=0 *)
walther@59878	560	],scr = Rule.Empty_Prog
wneuper@59406	561	});
wneuper@59472	562	\<close>
wneuper@59472	563	ML\<open>
neuper@37954	564	(* isolate the bound variable in an d2 equation with abcFormula;
neuper@37954	565	'bdv' is a meta-constant*)
s1210629013@55444	566	val d2_polyeq_abcFormula_simplify = prep_rls'(
walther@59851	567	Rule_Def.Repeat {id = "d2_polyeq_abcFormula_simplify", preconds = [],
walther@59857	568	rew_ord = ("e_rew_ord",Rewrite_Ord.e_rew_ord), erls = PolyEq_erls,
walther@59851	569	srls = Rule_Set.Empty, calc = [], errpatts = [],
wenzelm@60297	570	rules = [\<^rule_thm>\<open>d2_abcformula1\<close>,
neuper@37954	571	(c+bx+cx^2=0 )
wenzelm@60297	572	\<^rule_thm>\<open>d2_abcformula1_neg\<close>,
neuper@37954	573	(c+bx+cx^2=0 )
wenzelm@60297	574	\<^rule_thm>\<open>d2_abcformula2\<close>,
neuper@37954	575	(c+ x+cx^2=0 )
wenzelm@60297	576	\<^rule_thm>\<open>d2_abcformula2_neg\<close>,
neuper@37954	577	(c+ x+cx^2=0 )
wenzelm@60297	578	\<^rule_thm>\<open>d2_abcformula3\<close>,
neuper@37954	579	(c+bx+ x^2=0 )
wenzelm@60297	580	\<^rule_thm>\<open>d2_abcformula3_neg\<close>,
neuper@37954	581	(c+bx+ x^2=0 )
wenzelm@60297	582	\<^rule_thm>\<open>d2_abcformula4\<close>,
neuper@37954	583	(c+ x+ x^2=0 )
wenzelm@60297	584	\<^rule_thm>\<open>d2_abcformula4_neg\<close>,
neuper@37954	585	(c+ x+ x^2=0 )
wenzelm@60297	586	\<^rule_thm>\<open>d2_abcformula5\<close>,
neuper@37954	587	(c+ cx^2=0 )
wenzelm@60297	588	\<^rule_thm>\<open>d2_abcformula5_neg\<close>,
neuper@37954	589	(c+ cx^2=0 )
wenzelm@60297	590	\<^rule_thm>\<open>d2_abcformula6\<close>,
neuper@37954	591	(c+ x^2=0 )
wenzelm@60297	592	\<^rule_thm>\<open>d2_abcformula6_neg\<close>,
neuper@37954	593	(c+ x^2=0 )
wenzelm@60297	594	\<^rule_thm>\<open>d2_abcformula7\<close>,
neuper@37954	595	(* bx+ax^2=0 *)
wenzelm@60297	596	\<^rule_thm>\<open>d2_abcformula8\<close>,
neuper@37954	597	(* bx+ x^2=0 *)
wenzelm@60297	598	\<^rule_thm>\<open>d2_abcformula9\<close>,
neuper@37954	599	(* x+ax^2=0 *)
wenzelm@60297	600	\<^rule_thm>\<open>d2_abcformula10\<close>,
neuper@37954	601	(* x+ x^2=0 *)
wenzelm@60297	602	\<^rule_thm>\<open>d2_sqrt_equation2\<close>,
neuper@37954	603	(* x^2=0 *)
wenzelm@60297	604	\<^rule_thm>\<open>d2_sqrt_equation3\<close>
neuper@37954	605	(* bx^2=0 *)
neuper@37954	606	],
walther@59878	607	scr = Rule.Empty_Prog
wneuper@59406	608	});
wneuper@59472	609	\<close>
wneuper@59472	610	ML\<open>
neuper@37954	611
neuper@37954	612	(* isolate the bound variable in an d2 equation;
neuper@37954	613	'bdv' is a meta-constant*)
s1210629013@55444	614	val d2_polyeq_simplify = prep_rls'(
walther@59851	615	Rule_Def.Repeat {id = "d2_polyeq_simplify", preconds = [],
walther@59857	616	rew_ord = ("e_rew_ord",Rewrite_Ord.e_rew_ord), erls = PolyEq_erls,
walther@59851	617	srls = Rule_Set.Empty, calc = [], errpatts = [],
wenzelm@60297	618	rules = [\<^rule_thm>\<open>d2_pqformula1\<close>,
neuper@37954	619	(* p+qx+ x^2=0 *)
wenzelm@60297	620	\<^rule_thm>\<open>d2_pqformula1_neg\<close>,
neuper@37954	621	(* p+qx+ x^2=0 *)
wenzelm@60297	622	\<^rule_thm>\<open>d2_pqformula2\<close>,
neuper@37954	623	(* p+qx+1x^2=0 *)
wenzelm@60297	624	\<^rule_thm>\<open>d2_pqformula2_neg\<close>,
neuper@37954	625	(* p+qx+1x^2=0 *)
wenzelm@60297	626	\<^rule_thm>\<open>d2_pqformula3\<close>,
neuper@37954	627	(* p+ x+ x^2=0 *)
wenzelm@60297	628	\<^rule_thm>\<open>d2_pqformula3_neg\<close>,
neuper@37954	629	(* p+ x+ x^2=0 *)
wenzelm@60297	630	\<^rule_thm>\<open>d2_pqformula4\<close>,
neuper@37954	631	(* p+ x+1x^2=0 *)
wenzelm@60297	632	\<^rule_thm>\<open>d2_pqformula4_neg\<close>,
neuper@37954	633	(* p+ x+1x^2=0 *)
wenzelm@60297	634	\<^rule_thm>\<open>d2_abcformula1\<close>,
neuper@37954	635	(* c+bx+cx^2=0 *)
wenzelm@60297	636	\<^rule_thm>\<open>d2_abcformula1_neg\<close>,
neuper@37954	637	(* c+bx+cx^2=0 *)
wenzelm@60297	638	\<^rule_thm>\<open>d2_abcformula2\<close>,
neuper@37954	639	(* c+ x+cx^2=0 *)
wenzelm@60297	640	\<^rule_thm>\<open>d2_abcformula2_neg\<close>,
neuper@37954	641	(* c+ x+cx^2=0 *)
wenzelm@60297	642	\<^rule_thm>\<open>d2_prescind1\<close>,
neuper@37954	643	(* ax+bx^2=0 -> x(a+bx)=0 *)
wenzelm@60297	644	\<^rule_thm>\<open>d2_prescind2\<close>,
neuper@37954	645	(* ax+ x^2=0 -> x(a+ x)=0 *)
wenzelm@60297	646	\<^rule_thm>\<open>d2_prescind3\<close>,
neuper@37954	647	(* x+bx^2=0 -> x(1+bx)=0 *)
wenzelm@60297	648	\<^rule_thm>\<open>d2_prescind4\<close>,
neuper@37954	649	(* x+ x^2=0 -> x(1+ x)=0 *)
wenzelm@60297	650	\<^rule_thm>\<open>d2_isolate_add1\<close>,
neuper@37954	651	(* a+ bx^2=0 -> bx^2=(-1)a*)
wenzelm@60297	652	\<^rule_thm>\<open>d2_isolate_add2\<close>,
neuper@37954	653	(* a+ x^2=0 -> x^2=(-1)a*)
wenzelm@60297	654	\<^rule_thm>\<open>d2_sqrt_equation1\<close>,
neuper@37954	655	(* x^2=c -> x=+-sqrt(c)*)
wenzelm@60297	656	\<^rule_thm>\<open>d2_sqrt_equation1_neg\<close>,
neuper@37954	657	(* [c<0] x^2=c -> x=[]*)
wenzelm@60297	658	\<^rule_thm>\<open>d2_sqrt_equation2\<close>,
neuper@37954	659	(* x^2=0 -> x=0 *)
wenzelm@60297	660	\<^rule_thm>\<open>d2_reduce_equation1\<close>,
neuper@37954	661	(* x(a+bx)=0 -> x=0 \| a+bx=0*)
wenzelm@60297	662	\<^rule_thm>\<open>d2_reduce_equation2\<close>,
neuper@37954	663	(* x(a+ x)=0 -> x=0 \| a+ x=0*)
wenzelm@60297	664	\<^rule_thm>\<open>d2_isolate_div\<close>
neuper@37954	665	(* bx^2=c -> x^2=c/b*)
neuper@37954	666	],
walther@59878	667	scr = Rule.Empty_Prog
wneuper@59406	668	});
wneuper@59472	669	\<close>
wneuper@59472	670	ML\<open>
neuper@37954	671
neuper@37954	672	(* -- d3 -- *)
neuper@37954	673	(* isolate the bound variable in an d3 equation; 'bdv' is a meta-constant *)
s1210629013@55444	674	val d3_polyeq_simplify = prep_rls'(
walther@59851	675	Rule_Def.Repeat {id = "d3_polyeq_simplify", preconds = [],
walther@59857	676	rew_ord = ("e_rew_ord",Rewrite_Ord.e_rew_ord), erls = PolyEq_erls,
walther@59851	677	srls = Rule_Set.Empty, calc = [], errpatts = [],
neuper@37954	678	rules =
wenzelm@60297	679	[\<^rule_thm>\<open>d3_reduce_equation1\<close>,
walther@60242	680	(abdv + bbdv \<up> 2 + cbdv \<up> 3=0) =
walther@60242	681	(bdv=0 \| (a + bbdv + cbdv \<up> 2=0)*)
wenzelm@60297	682	\<^rule_thm>\<open>d3_reduce_equation2\<close>,
walther@60242	683	(* bdv + bbdv \<up> 2 + cbdv \<up> 3=0) =
walther@60242	684	(bdv=0 \| (1 + bbdv + cbdv \<up> 2=0)*)
wenzelm@60297	685	\<^rule_thm>\<open>d3_reduce_equation3\<close>,
walther@60242	686	(abdv + bdv \<up> 2 + c*bdv \<up> 3=0) =
walther@60242	687	(bdv=0 \| (a + bdv + cbdv \<up> 2=0))
wenzelm@60297	688	\<^rule_thm>\<open>d3_reduce_equation4\<close>,
walther@60242	689	(* bdv + bdv \<up> 2 + c*bdv \<up> 3=0) =
walther@60242	690	(bdv=0 \| (1 + bdv + cbdv \<up> 2=0))
wenzelm@60297	691	\<^rule_thm>\<open>d3_reduce_equation5\<close>,
walther@60242	692	(abdv + b*bdv \<up> 2 + bdv \<up> 3=0) =
walther@60242	693	(bdv=0 \| (a + bbdv + bdv \<up> 2=0))
wenzelm@60297	694	\<^rule_thm>\<open>d3_reduce_equation6\<close>,
walther@60242	695	(* bdv + b*bdv \<up> 2 + bdv \<up> 3=0) =
walther@60242	696	(bdv=0 \| (1 + bbdv + bdv \<up> 2=0))
wenzelm@60297	697	\<^rule_thm>\<open>d3_reduce_equation7\<close>,
walther@60242	698	(abdv + bdv \<up> 2 + bdv \<up> 3=0) =
walther@60242	699	(bdv=0 \| (1 + bdv + bdv \<up> 2=0)*)
wenzelm@60297	700	\<^rule_thm>\<open>d3_reduce_equation8\<close>,
walther@60242	701	(* bdv + bdv \<up> 2 + bdv \<up> 3=0) =
walther@60242	702	(bdv=0 \| (1 + bdv + bdv \<up> 2=0)*)
wenzelm@60297	703	\<^rule_thm>\<open>d3_reduce_equation9\<close>,
walther@60242	704	(abdv + c*bdv \<up> 3=0) =
walther@60242	705	(bdv=0 \| (a + cbdv \<up> 2=0))
wenzelm@60297	706	\<^rule_thm>\<open>d3_reduce_equation10\<close>,
walther@60242	707	(* bdv + c*bdv \<up> 3=0) =
walther@60242	708	(bdv=0 \| (1 + cbdv \<up> 2=0))
wenzelm@60297	709	\<^rule_thm>\<open>d3_reduce_equation11\<close>,
walther@60242	710	(abdv + bdv \<up> 3=0) =
walther@60242	711	(bdv=0 \| (a + bdv \<up> 2=0)*)
wenzelm@60297	712	\<^rule_thm>\<open>d3_reduce_equation12\<close>,
walther@60242	713	(* bdv + bdv \<up> 3=0) =
walther@60242	714	(bdv=0 \| (1 + bdv \<up> 2=0)*)
wenzelm@60297	715	\<^rule_thm>\<open>d3_reduce_equation13\<close>,
walther@60242	716	(* bbdv \<up> 2 + cbdv \<up> 3=0) =
walther@60242	717	(bdv=0 \| ( bbdv + cbdv \<up> 2=0)*)
wenzelm@60297	718	\<^rule_thm>\<open>d3_reduce_equation14\<close>,
walther@60242	719	(* bdv \<up> 2 + c*bdv \<up> 3=0) =
walther@60242	720	(bdv=0 \| ( bdv + cbdv \<up> 2=0))
wenzelm@60297	721	\<^rule_thm>\<open>d3_reduce_equation15\<close>,
walther@60242	722	(* b*bdv \<up> 2 + bdv \<up> 3=0) =
walther@60242	723	(bdv=0 \| ( bbdv + bdv \<up> 2=0))
wenzelm@60297	724	\<^rule_thm>\<open>d3_reduce_equation16\<close>,
walther@60242	725	(* bdv \<up> 2 + bdv \<up> 3=0) =
walther@60242	726	(bdv=0 \| ( bdv + bdv \<up> 2=0)*)
wenzelm@60297	727	\<^rule_thm>\<open>d3_isolate_add1\<close>,
walther@60242	728	([\|Not(bdv occurs_in a)\|] ==> (a + bbdv \<up> 3=0) =
walther@60242	729	(bdv=0 \| (bbdv \<up> 3=a))
wenzelm@60297	730	\<^rule_thm>\<open>d3_isolate_add2\<close>,
walther@60242	731	(*[\|Not(bdv occurs_in a)\|] ==> (a + bdv \<up> 3=0) =
walther@60242	732	(bdv=0 \| ( bdv \<up> 3=a)*)
wenzelm@60297	733	\<^rule_thm>\<open>d3_isolate_div\<close>,
walther@60242	734	([\|Not(b=0)\|] ==> (bbdv \<up> 3=c) = (bdv \<up> 3=c/b*)
wenzelm@60297	735	\<^rule_thm>\<open>d3_root_equation2\<close>,
walther@60242	736	((bdv \<up> 3=0) = (bdv=0) )
wenzelm@60297	737	\<^rule_thm>\<open>d3_root_equation1\<close>
walther@60242	738	(bdv \<up> 3=c) = (bdv = nroot 3 c)
neuper@37954	739	],
walther@59878	740	scr = Rule.Empty_Prog
wneuper@59406	741	});
wneuper@59472	742	\<close>
wneuper@59472	743	ML\<open>
neuper@37954	744
neuper@37954	745	(* -- d4 -- *)
neuper@37954	746	(isolate the bound variable in an d4 equation; 'bdv' is a meta-constant)
s1210629013@55444	747	val d4_polyeq_simplify = prep_rls'(
walther@59851	748	Rule_Def.Repeat {id = "d4_polyeq_simplify", preconds = [],
walther@59857	749	rew_ord = ("e_rew_ord",Rewrite_Ord.e_rew_ord), erls = PolyEq_erls,
walther@59851	750	srls = Rule_Set.Empty, calc = [], errpatts = [],
neuper@37954	751	rules =
wenzelm@60297	752	[\<^rule_thm>\<open>d4_sub_u1\<close>
neuper@37954	753	(* ax^4+bx^2+c=0 -> x=+-sqrt(ax^2+bx^+c) *)
neuper@37954	754	],
walther@59878	755	scr = Rule.Empty_Prog
wneuper@59406	756	});
wneuper@59472	757	\<close>
wenzelm@60289	758	rule_set_knowledge
wenzelm@60286	759	d0_polyeq_simplify = d0_polyeq_simplify and
wenzelm@60286	760	d1_polyeq_simplify = d1_polyeq_simplify and
wenzelm@60286	761	d2_polyeq_simplify = d2_polyeq_simplify and
wenzelm@60286	762	d2_polyeq_bdv_only_simplify = d2_polyeq_bdv_only_simplify and
wenzelm@60286	763	d2_polyeq_sq_only_simplify = d2_polyeq_sq_only_simplify and
neuper@52125	764
wenzelm@60286	765	d2_polyeq_pqFormula_simplify = d2_polyeq_pqFormula_simplify and
wenzelm@60286	766	d2_polyeq_abcFormula_simplify = d2_polyeq_abcFormula_simplify and
wenzelm@60286	767	d3_polyeq_simplify = d3_polyeq_simplify and
wenzelm@60286	768	d4_polyeq_simplify = d4_polyeq_simplify
walther@60258	769
wneuper@59472	770	setup \<open>KEStore_Elems.add_pbts
wenzelm@60290	771	[(Problem.prep_input @{theory} "pbl_equ_univ_poly" [] Problem.id_empty
walther@59997	772	(["polynomial", "univariate", "equation"],
walther@59997	773	[("#Given" ,["equality e_e", "solveFor v_v"]),
s1210629013@55339	774	("#Where" ,["~((e_e::bool) is_ratequation_in (v_v::real))",
s1210629013@55339	775	"~((lhs e_e) is_rootTerm_in (v_v::real))",
s1210629013@55339	776	"~((rhs e_e) is_rootTerm_in (v_v::real))"]),
s1210629013@55339	777	("#Find" ,["solutions v_v'i'"])],
s1210629013@55339	778	PolyEq_prls, SOME "solve (e_e::bool, v_v)", [])),
s1210629013@55339	779	(--- d0 ---)
wenzelm@60290	780	(Problem.prep_input @{theory} "pbl_equ_univ_poly_deg0" [] Problem.id_empty
walther@59997	781	(["degree_0", "polynomial", "univariate", "equation"],
walther@59997	782	[("#Given" ,["equality e_e", "solveFor v_v"]),
s1210629013@55339	783	("#Where" ,["matches (?a = 0) e_e",
s1210629013@55339	784	"(lhs e_e) is_poly_in v_v",
s1210629013@55339	785	"((lhs e_e) has_degree_in v_v ) = 0"]),
s1210629013@55339	786	("#Find" ,["solutions v_v'i'"])],
walther@59997	787	PolyEq_prls, SOME "solve (e_e::bool, v_v)", [["PolyEq", "solve_d0_polyeq_equation"]])),
s1210629013@55339	788	(--- d1 ---)
wenzelm@60290	789	(Problem.prep_input @{theory} "pbl_equ_univ_poly_deg1" [] Problem.id_empty
walther@59997	790	(["degree_1", "polynomial", "univariate", "equation"],
walther@59997	791	[("#Given" ,["equality e_e", "solveFor v_v"]),
s1210629013@55339	792	("#Where" ,["matches (?a = 0) e_e",
s1210629013@55339	793	"(lhs e_e) is_poly_in v_v",
s1210629013@55339	794	"((lhs e_e) has_degree_in v_v ) = 1"]),
s1210629013@55339	795	("#Find" ,["solutions v_v'i'"])],
walther@59997	796	PolyEq_prls, SOME "solve (e_e::bool, v_v)", [["PolyEq", "solve_d1_polyeq_equation"]])),
s1210629013@55339	797	(--- d2 ---)
wenzelm@60290	798	(Problem.prep_input @{theory} "pbl_equ_univ_poly_deg2" [] Problem.id_empty
walther@59997	799	(["degree_2", "polynomial", "univariate", "equation"],
walther@59997	800	[("#Given" ,["equality e_e", "solveFor v_v"]),
s1210629013@55339	801	("#Where" ,["matches (?a = 0) e_e",
s1210629013@55339	802	"(lhs e_e) is_poly_in v_v ",
s1210629013@55339	803	"((lhs e_e) has_degree_in v_v ) = 2"]),
s1210629013@55339	804	("#Find" ,["solutions v_v'i'"])],
walther@59997	805	PolyEq_prls, SOME "solve (e_e::bool, v_v)", [["PolyEq", "solve_d2_polyeq_equation"]])),
wenzelm@60290	806	(Problem.prep_input @{theory} "pbl_equ_univ_poly_deg2_sqonly" [] Problem.id_empty
walther@59997	807	(["sq_only", "degree_2", "polynomial", "univariate", "equation"],
walther@59997	808	[("#Given" ,["equality e_e", "solveFor v_v"]),
walther@60242	809	("#Where" ,["matches ( ?a + ?v_ \<up> 2 = 0) e_e \| " ^
walther@60242	810	"matches ( ?a + ?b*?v_ \<up> 2 = 0) e_e \| " ^
walther@60242	811	"matches ( ?v_ \<up> 2 = 0) e_e \| " ^
walther@60242	812	"matches ( ?b*?v_ \<up> 2 = 0) e_e" ,
walther@60242	813	"Not (matches (?a + ?v_ + ?v_ \<up> 2 = 0) e_e) &" ^
walther@60242	814	"Not (matches (?a + ?b*?v_ + ?v_ \<up> 2 = 0) e_e) &" ^
walther@60242	815	"Not (matches (?a + ?v_ + ?c*?v_ \<up> 2 = 0) e_e) &" ^
walther@60242	816	"Not (matches (?a + ?b?v_ + ?c?v_ \<up> 2 = 0) e_e) &" ^
walther@60242	817	"Not (matches ( ?v_ + ?v_ \<up> 2 = 0) e_e) &" ^
walther@60242	818	"Not (matches ( ?b*?v_ + ?v_ \<up> 2 = 0) e_e) &" ^
walther@60242	819	"Not (matches ( ?v_ + ?c*?v_ \<up> 2 = 0) e_e) &" ^
walther@60242	820	"Not (matches ( ?b?v_ + ?c?v_ \<up> 2 = 0) e_e)"]),
s1210629013@55339	821	("#Find" ,["solutions v_v'i'"])],
s1210629013@55339	822	PolyEq_prls, SOME "solve (e_e::bool, v_v)",
walther@59997	823	[["PolyEq", "solve_d2_polyeq_sqonly_equation"]])),
wenzelm@60290	824	(Problem.prep_input @{theory} "pbl_equ_univ_poly_deg2_bdvonly" [] Problem.id_empty
walther@59997	825	(["bdv_only", "degree_2", "polynomial", "univariate", "equation"],
walther@59997	826	[("#Given", ["equality e_e", "solveFor v_v"]),
walther@60242	827	("#Where", ["matches (?a*?v_ + ?v_ \<up> 2 = 0) e_e \| " ^
walther@60242	828	"matches ( ?v_ + ?v_ \<up> 2 = 0) e_e \| " ^
walther@60242	829	"matches ( ?v_ + ?b*?v_ \<up> 2 = 0) e_e \| " ^
walther@60242	830	"matches (?a?v_ + ?b?v_ \<up> 2 = 0) e_e \| " ^
walther@60242	831	"matches ( ?v_ \<up> 2 = 0) e_e \| " ^
walther@60242	832	"matches ( ?b*?v_ \<up> 2 = 0) e_e "]),
s1210629013@55339	833	("#Find", ["solutions v_v'i'"])],
s1210629013@55339	834	PolyEq_prls, SOME "solve (e_e::bool, v_v)",
walther@59997	835	[["PolyEq", "solve_d2_polyeq_bdvonly_equation"]])),
wenzelm@60290	836	(Problem.prep_input @{theory} "pbl_equ_univ_poly_deg2_pq" [] Problem.id_empty
walther@59997	837	(["pqFormula", "degree_2", "polynomial", "univariate", "equation"],
walther@59997	838	[("#Given", ["equality e_e", "solveFor v_v"]),
walther@60242	839	("#Where", ["matches (?a + 1*?v_ \<up> 2 = 0) e_e \| " ^
walther@60242	840	"matches (?a + ?v_ \<up> 2 = 0) e_e"]),
s1210629013@55339	841	("#Find", ["solutions v_v'i'"])],
walther@59997	842	PolyEq_prls, SOME "solve (e_e::bool, v_v)", [["PolyEq", "solve_d2_polyeq_pq_equation"]])),
wenzelm@60290	843	(Problem.prep_input @{theory} "pbl_equ_univ_poly_deg2_abc" [] Problem.id_empty
walther@59997	844	(["abcFormula", "degree_2", "polynomial", "univariate", "equation"],
walther@59997	845	[("#Given", ["equality e_e", "solveFor v_v"]),
walther@60242	846	("#Where", ["matches (?a + ?v_ \<up> 2 = 0) e_e \| " ^
walther@60242	847	"matches (?a + ?b*?v_ \<up> 2 = 0) e_e"]),
s1210629013@55339	848	("#Find", ["solutions v_v'i'"])],
walther@59997	849	PolyEq_prls, SOME "solve (e_e::bool, v_v)", [["PolyEq", "solve_d2_polyeq_abc_equation"]])),
s1210629013@55339	850	(--- d3 ---)
wenzelm@60290	851	(Problem.prep_input @{theory} "pbl_equ_univ_poly_deg3" [] Problem.id_empty
walther@59997	852	(["degree_3", "polynomial", "univariate", "equation"],
walther@59997	853	[("#Given", ["equality e_e", "solveFor v_v"]),
s1210629013@55339	854	("#Where", ["matches (?a = 0) e_e",
s1210629013@55339	855	"(lhs e_e) is_poly_in v_v ",
s1210629013@55339	856	"((lhs e_e) has_degree_in v_v) = 3"]),
s1210629013@55339	857	("#Find", ["solutions v_v'i'"])],
walther@59997	858	PolyEq_prls, SOME "solve (e_e::bool, v_v)", [["PolyEq", "solve_d3_polyeq_equation"]])),
s1210629013@55339	859	(--- d4 ---)
wenzelm@60290	860	(Problem.prep_input @{theory} "pbl_equ_univ_poly_deg4" [] Problem.id_empty
walther@59997	861	(["degree_4", "polynomial", "univariate", "equation"],
walther@59997	862	[("#Given", ["equality e_e", "solveFor v_v"]),
s1210629013@55339	863	("#Where", ["matches (?a = 0) e_e",
s1210629013@55339	864	"(lhs e_e) is_poly_in v_v ",
s1210629013@55339	865	"((lhs e_e) has_degree_in v_v) = 4"]),
s1210629013@55339	866	("#Find", ["solutions v_v'i'"])],
walther@59997	867	PolyEq_prls, SOME "solve (e_e::bool, v_v)", [(["PolyEq", "solve_d4_polyeq_equation"])])),
wneuper@59370	868	(--- normalise ---)
wenzelm@60290	869	(Problem.prep_input @{theory} "pbl_equ_univ_poly_norm" [] Problem.id_empty
walther@59997	870	(["normalise", "polynomial", "univariate", "equation"],
walther@59997	871	[("#Given", ["equality e_e", "solveFor v_v"]),
s1210629013@55339	872	("#Where", ["(Not((matches (?a = 0 ) e_e ))) \|" ^
s1210629013@55339	873	"(Not(((lhs e_e) is_poly_in v_v)))"]),
s1210629013@55339	874	("#Find", ["solutions v_v'i'"])],
walther@59842	875	PolyEq_prls, SOME "solve (e_e::bool, v_v)", [["PolyEq", "normalise_poly"]])),
s1210629013@55339	876	(-------------------------expanded-----------------------)
wenzelm@60290	877	(Problem.prep_input @{theory} "pbl_equ_univ_expand" [] Problem.id_empty
walther@59997	878	(["expanded", "univariate", "equation"],
walther@59997	879	[("#Given", ["equality e_e", "solveFor v_v"]),
s1210629013@55339	880	("#Where", ["matches (?a = 0) e_e",
s1210629013@55339	881	"(lhs e_e) is_expanded_in v_v "]),
s1210629013@55339	882	("#Find", ["solutions v_v'i'"])],
s1210629013@55339	883	PolyEq_prls, SOME "solve (e_e::bool, v_v)", [])),
s1210629013@55339	884	(--- d2 ---)
wenzelm@60290	885	(Problem.prep_input @{theory} "pbl_equ_univ_expand_deg2" [] Problem.id_empty
walther@59997	886	(["degree_2", "expanded", "univariate", "equation"],
walther@59997	887	[("#Given", ["equality e_e", "solveFor v_v"]),
s1210629013@55339	888	("#Where", ["((lhs e_e) has_degree_in v_v) = 2"]),
s1210629013@55339	889	("#Find", ["solutions v_v'i'"])],
walther@59997	890	PolyEq_prls, SOME "solve (e_e::bool, v_v)", [["PolyEq", "complete_square"]]))]\<close>
neuper@37954	891
wneuper@59472	892	text \<open>"-------------------------methods-----------------------"\<close>
wneuper@59472	893	setup \<open>KEStore_Elems.add_mets
wenzelm@60290	894	[MethodC.prep_input @{theory} "met_polyeq" [] MethodC.id_empty
s1210629013@55373	895	(["PolyEq"], [],
walther@59852	896	{rew_ord'="tless_true",rls'=Atools_erls,calc = [], srls = Rule_Set.empty, prls=Rule_Set.empty,
s1210629013@55373	897	crls=PolyEq_crls, errpats = [], nrls = norm_Rational},
wneuper@59545	898	@{thm refl})]
wneuper@59473	899	\<close>
wneuper@59545	900
wneuper@59504	901	partial_function (tailrec) normalize_poly_eq :: "bool \<Rightarrow> real \<Rightarrow> bool"
wneuper@59504	902	where
walther@59635	903	"normalize_poly_eq e_e v_v = (
walther@59635	904	let
walther@59635	905	e_e = (
walther@59637	906	(Try (Rewrite ''all_left'')) #>
walther@59637	907	(Try (Repeat (Rewrite ''makex1_x''))) #>
walther@59637	908	(Try (Repeat (Rewrite_Set ''expand_binoms''))) #>
walther@59637	909	(Try (Repeat (Rewrite_Set_Inst [(''bdv'', v_v)] ''make_ratpoly_in''))) #>
walther@59635	910	(Try (Repeat (Rewrite_Set ''polyeq_simplify''))) ) e_e
walther@59635	911	in
walther@59635	912	SubProblem (''PolyEq'', [''polynomial'', ''univariate'', ''equation''], [''no_met''])
wneuper@59504	913	[BOOL e_e, REAL v_v])"
wneuper@59473	914	setup \<open>KEStore_Elems.add_mets
wenzelm@60290	915	[MethodC.prep_input @{theory} "met_polyeq_norm" [] MethodC.id_empty
walther@59842	916	(["PolyEq", "normalise_poly"],
walther@59997	917	[("#Given" ,["equality e_e", "solveFor v_v"]),
walther@59842	918	("#Where" ,["(Not((matches (?a = 0 ) e_e ))) \| (Not(((lhs e_e) is_poly_in v_v)))"]),
s1210629013@55373	919	("#Find" ,["solutions v_v'i'"])],
walther@59852	920	{rew_ord'="termlessI", rls'=PolyEq_erls, srls=Rule_Set.empty, prls=PolyEq_prls, calc=[],
s1210629013@55373	921	crls=PolyEq_crls, errpats = [], nrls = norm_Rational},
wneuper@59551	922	@{thm normalize_poly_eq.simps})]
wneuper@59473	923	\<close>
wneuper@59545	924
wneuper@59504	925	partial_function (tailrec) solve_poly_equ :: "bool \<Rightarrow> real \<Rightarrow> bool list"
wneuper@59504	926	where
walther@59635	927	"solve_poly_equ e_e v_v = (
walther@59635	928	let
walther@59635	929	e_e = (Try (Rewrite_Set_Inst [(''bdv'', v_v)] ''d0_polyeq_simplify'')) e_e
walther@59635	930	in
walther@59635	931	Or_to_List e_e)"
wneuper@59473	932	setup \<open>KEStore_Elems.add_mets
wenzelm@60290	933	[MethodC.prep_input @{theory} "met_polyeq_d0" [] MethodC.id_empty
walther@59997	934	(["PolyEq", "solve_d0_polyeq_equation"],
walther@59997	935	[("#Given" ,["equality e_e", "solveFor v_v"]),
s1210629013@55373	936	("#Where" ,["(lhs e_e) is_poly_in v_v ", "((lhs e_e) has_degree_in v_v) = 0"]),
s1210629013@55373	937	("#Find" ,["solutions v_v'i'"])],
walther@59852	938	{rew_ord'="termlessI", rls'=PolyEq_erls, srls=Rule_Set.empty, prls=PolyEq_prls,
s1210629013@55373	939	calc=[("sqrt", ("NthRoot.sqrt", eval_sqrt "#sqrt_"))], crls=PolyEq_crls, errpats = [],
s1210629013@55373	940	nrls = norm_Rational},
wneuper@59551	941	@{thm solve_poly_equ.simps})]
wneuper@59473	942	\<close>
wneuper@59545	943
wneuper@59504	944	partial_function (tailrec) solve_poly_eq1 :: "bool \<Rightarrow> real \<Rightarrow> bool list"
walther@59635	945	where
walther@59635	946	"solve_poly_eq1 e_e v_v = (
walther@59635	947	let
walther@59635	948	e_e = (
walther@59637	949	(Try (Rewrite_Set_Inst [(''bdv'', v_v)] ''d1_polyeq_simplify'')) #>
walther@59637	950	(Try (Rewrite_Set ''polyeq_simplify'')) #>
walther@59635	951	(Try (Rewrite_Set ''norm_Rational_parenthesized'')) ) e_e;
walther@59635	952	L_L = Or_to_List e_e
walther@59635	953	in
walther@59635	954	Check_elementwise L_L {(v_v::real). Assumptions})"
wneuper@59473	955	setup \<open>KEStore_Elems.add_mets
wenzelm@60290	956	[MethodC.prep_input @{theory} "met_polyeq_d1" [] MethodC.id_empty
walther@59997	957	(["PolyEq", "solve_d1_polyeq_equation"],
walther@59997	958	[("#Given" ,["equality e_e", "solveFor v_v"]),
s1210629013@55373	959	("#Where" ,["(lhs e_e) is_poly_in v_v ", "((lhs e_e) has_degree_in v_v) = 1"]),
s1210629013@55373	960	("#Find" ,["solutions v_v'i'"])],
walther@59852	961	{rew_ord'="termlessI", rls'=PolyEq_erls, srls=Rule_Set.empty, prls=PolyEq_prls,
s1210629013@55373	962	calc=[("sqrt", ("NthRoot.sqrt", eval_sqrt "#sqrt_"))], crls=PolyEq_crls, errpats = [],
s1210629013@55373	963	nrls = norm_Rational},
wneuper@59551	964	@{thm solve_poly_eq1.simps})]
wneuper@59473	965	\<close>
wneuper@59545	966
wneuper@59504	967	partial_function (tailrec) solve_poly_equ2 :: "bool \<Rightarrow> real \<Rightarrow> bool list"
wneuper@59504	968	where
walther@59635	969	"solve_poly_equ2 e_e v_v = (
walther@59635	970	let
walther@59635	971	e_e = (
walther@59637	972	(Try (Rewrite_Set_Inst [(''bdv'', v_v)] ''d2_polyeq_simplify'')) #>
walther@59637	973	(Try (Rewrite_Set ''polyeq_simplify'')) #>
walther@59637	974	(Try (Rewrite_Set_Inst [(''bdv'', v_v)] ''d1_polyeq_simplify'')) #>
walther@59637	975	(Try (Rewrite_Set ''polyeq_simplify'')) #>
walther@59635	976	(Try (Rewrite_Set ''norm_Rational_parenthesized'')) ) e_e;
walther@59635	977	L_L = Or_to_List e_e
walther@59635	978	in
walther@59635	979	Check_elementwise L_L {(v_v::real). Assumptions})"
wneuper@59473	980	setup \<open>KEStore_Elems.add_mets
wenzelm@60290	981	[MethodC.prep_input @{theory} "met_polyeq_d22" [] MethodC.id_empty
walther@59997	982	(["PolyEq", "solve_d2_polyeq_equation"],
walther@59997	983	[("#Given" ,["equality e_e", "solveFor v_v"]),
s1210629013@55373	984	("#Where" ,["(lhs e_e) is_poly_in v_v ", "((lhs e_e) has_degree_in v_v) = 2"]),
s1210629013@55373	985	("#Find" ,["solutions v_v'i'"])],
walther@59852	986	{rew_ord'="termlessI", rls'=PolyEq_erls, srls=Rule_Set.empty, prls=PolyEq_prls,
s1210629013@55373	987	calc=[("sqrt", ("NthRoot.sqrt", eval_sqrt "#sqrt_"))], crls=PolyEq_crls, errpats = [],
s1210629013@55373	988	nrls = norm_Rational},
wneuper@59551	989	@{thm solve_poly_equ2.simps})]
wneuper@59473	990	\<close>
wneuper@59545	991
wneuper@59504	992	partial_function (tailrec) solve_poly_equ0 :: "bool \<Rightarrow> real \<Rightarrow> bool list"
walther@59635	993	where
walther@59635	994	"solve_poly_equ0 e_e v_v = (
walther@59635	995	let
walther@59635	996	e_e = (
walther@59637	997	(Try (Rewrite_Set_Inst [(''bdv'', v_v)] ''d2_polyeq_bdv_only_simplify'')) #>
walther@59637	998	(Try (Rewrite_Set ''polyeq_simplify'')) #>
walther@59637	999	(Try (Rewrite_Set_Inst [(''bdv'',v_v::real)] ''d1_polyeq_simplify'')) #>
walther@59637	1000	(Try (Rewrite_Set ''polyeq_simplify'')) #>
walther@59635	1001	(Try (Rewrite_Set ''norm_Rational_parenthesized'')) ) e_e;
wneuper@59504	1002	L_L = Or_to_List e_e
walther@59635	1003	in
walther@59635	1004	Check_elementwise L_L {(v_v::real). Assumptions})"
wneuper@59473	1005	setup \<open>KEStore_Elems.add_mets
wenzelm@60290	1006	[MethodC.prep_input @{theory} "met_polyeq_d2_bdvonly" [] MethodC.id_empty
walther@59997	1007	(["PolyEq", "solve_d2_polyeq_bdvonly_equation"],
walther@59997	1008	[("#Given" ,["equality e_e", "solveFor v_v"]),
s1210629013@55373	1009	("#Where" ,["(lhs e_e) is_poly_in v_v ", "((lhs e_e) has_degree_in v_v) = 2"]),
s1210629013@55373	1010	("#Find" ,["solutions v_v'i'"])],
walther@59852	1011	{rew_ord'="termlessI", rls'=PolyEq_erls, srls=Rule_Set.empty, prls=PolyEq_prls,
s1210629013@55373	1012	calc=[("sqrt", ("NthRoot.sqrt", eval_sqrt "#sqrt_"))], crls=PolyEq_crls, errpats = [],
s1210629013@55373	1013	nrls = norm_Rational},
wneuper@59551	1014	@{thm solve_poly_equ0.simps})]
wneuper@59473	1015	\<close>
wneuper@59545	1016
wneuper@59504	1017	partial_function (tailrec) solve_poly_equ_sqrt :: "bool \<Rightarrow> real \<Rightarrow> bool list"
wneuper@59504	1018	where
walther@59635	1019	"solve_poly_equ_sqrt e_e v_v = (
walther@59635	1020	let
walther@59635	1021	e_e = (
walther@59637	1022	(Try (Rewrite_Set_Inst [(''bdv'', v_v)] ''d2_polyeq_sq_only_simplify'')) #>
walther@59637	1023	(Try (Rewrite_Set ''polyeq_simplify'')) #>
walther@59635	1024	(Try (Rewrite_Set ''norm_Rational_parenthesized'')) ) e_e;
wneuper@59504	1025	L_L = Or_to_List e_e
walther@59635	1026	in
walther@59635	1027	Check_elementwise L_L {(v_v::real). Assumptions})"
wneuper@59473	1028	setup \<open>KEStore_Elems.add_mets
wenzelm@60290	1029	[MethodC.prep_input @{theory} "met_polyeq_d2_sqonly" [] MethodC.id_empty
walther@59997	1030	(["PolyEq", "solve_d2_polyeq_sqonly_equation"],
walther@59997	1031	[("#Given" ,["equality e_e", "solveFor v_v"]),
s1210629013@55373	1032	("#Where" ,["(lhs e_e) is_poly_in v_v ", "((lhs e_e) has_degree_in v_v) = 2"]),
s1210629013@55373	1033	("#Find" ,["solutions v_v'i'"])],
walther@59852	1034	{rew_ord'="termlessI", rls'=PolyEq_erls, srls=Rule_Set.empty, prls=PolyEq_prls,
s1210629013@55373	1035	calc=[("sqrt", ("NthRoot.sqrt", eval_sqrt "#sqrt_"))], crls=PolyEq_crls, errpats = [],
s1210629013@55373	1036	nrls = norm_Rational},
wneuper@59551	1037	@{thm solve_poly_equ_sqrt.simps})]
wneuper@59473	1038	\<close>
wneuper@59545	1039
wneuper@59504	1040	partial_function (tailrec) solve_poly_equ_pq :: "bool \<Rightarrow> real \<Rightarrow> bool list"
walther@59635	1041	where
walther@59635	1042	"solve_poly_equ_pq e_e v_v = (
walther@59635	1043	let
walther@59635	1044	e_e = (
walther@59637	1045	(Try (Rewrite_Set_Inst [(''bdv'', v_v)] ''d2_polyeq_pqFormula_simplify'')) #>
walther@59637	1046	(Try (Rewrite_Set ''polyeq_simplify'')) #>
walther@59635	1047	(Try (Rewrite_Set ''norm_Rational_parenthesized'')) ) e_e;
walther@59635	1048	L_L = Or_to_List e_e
walther@59635	1049	in
walther@59635	1050	Check_elementwise L_L {(v_v::real). Assumptions})"
wneuper@59473	1051	setup \<open>KEStore_Elems.add_mets
wenzelm@60290	1052	[MethodC.prep_input @{theory} "met_polyeq_d2_pq" [] MethodC.id_empty
walther@59997	1053	(["PolyEq", "solve_d2_polyeq_pq_equation"],
walther@59997	1054	[("#Given" ,["equality e_e", "solveFor v_v"]),
s1210629013@55373	1055	("#Where" ,["(lhs e_e) is_poly_in v_v ", "((lhs e_e) has_degree_in v_v) = 2"]),
s1210629013@55373	1056	("#Find" ,["solutions v_v'i'"])],
walther@59852	1057	{rew_ord'="termlessI", rls'=PolyEq_erls, srls=Rule_Set.empty, prls=PolyEq_prls,
s1210629013@55373	1058	calc=[("sqrt", ("NthRoot.sqrt", eval_sqrt "#sqrt_"))], crls=PolyEq_crls, errpats = [],
s1210629013@55373	1059	nrls = norm_Rational},
wneuper@59551	1060	@{thm solve_poly_equ_pq.simps})]
wneuper@59473	1061	\<close>
wneuper@59545	1062
wneuper@59504	1063	partial_function (tailrec) solve_poly_equ_abc :: "bool \<Rightarrow> real \<Rightarrow> bool list"
wneuper@59504	1064	where
walther@59635	1065	"solve_poly_equ_abc e_e v_v = (
walther@59635	1066	let
walther@59635	1067	e_e = (
walther@59637	1068	(Try (Rewrite_Set_Inst [(''bdv'', v_v)] ''d2_polyeq_abcFormula_simplify'')) #>
walther@59637	1069	(Try (Rewrite_Set ''polyeq_simplify'')) #>
walther@59635	1070	(Try (Rewrite_Set ''norm_Rational_parenthesized'')) ) e_e;
walther@59635	1071	L_L = Or_to_List e_e
wneuper@59504	1072	in Check_elementwise L_L {(v_v::real). Assumptions})"
wneuper@59473	1073	setup \<open>KEStore_Elems.add_mets
wenzelm@60290	1074	[MethodC.prep_input @{theory} "met_polyeq_d2_abc" [] MethodC.id_empty
walther@59997	1075	(["PolyEq", "solve_d2_polyeq_abc_equation"],
walther@59997	1076	[("#Given" ,["equality e_e", "solveFor v_v"]),
s1210629013@55373	1077	("#Where" ,["(lhs e_e) is_poly_in v_v ", "((lhs e_e) has_degree_in v_v) = 2"]),
s1210629013@55373	1078	("#Find" ,["solutions v_v'i'"])],
walther@59852	1079	{rew_ord'="termlessI", rls'=PolyEq_erls,srls=Rule_Set.empty, prls=PolyEq_prls,
s1210629013@55373	1080	calc=[("sqrt", ("NthRoot.sqrt", eval_sqrt "#sqrt_"))], crls=PolyEq_crls, errpats = [],
s1210629013@55373	1081	nrls = norm_Rational},
wneuper@59551	1082	@{thm solve_poly_equ_abc.simps})]
wneuper@59473	1083	\<close>
wneuper@59545	1084
wneuper@59504	1085	partial_function (tailrec) solve_poly_equ3 :: "bool \<Rightarrow> real \<Rightarrow> bool list"
walther@59635	1086	where
walther@59635	1087	"solve_poly_equ3 e_e v_v = (
walther@59635	1088	let
walther@59635	1089	e_e = (
walther@59637	1090	(Try (Rewrite_Set_Inst [(''bdv'', v_v)] ''d3_polyeq_simplify'')) #>
walther@59637	1091	(Try (Rewrite_Set ''polyeq_simplify'')) #>
walther@59637	1092	(Try (Rewrite_Set_Inst [(''bdv'', v_v)] ''d2_polyeq_simplify'')) #>
walther@59637	1093	(Try (Rewrite_Set ''polyeq_simplify'')) #>
walther@59637	1094	(Try (Rewrite_Set_Inst [(''bdv'',v_v)] ''d1_polyeq_simplify'')) #>
walther@59637	1095	(Try (Rewrite_Set ''polyeq_simplify'')) #>
walther@59635	1096	(Try (Rewrite_Set ''norm_Rational_parenthesized''))) e_e;
walther@59635	1097	L_L = Or_to_List e_e
walther@59635	1098	in
walther@59635	1099	Check_elementwise L_L {(v_v::real). Assumptions})"
wneuper@59473	1100	setup \<open>KEStore_Elems.add_mets
wenzelm@60290	1101	[MethodC.prep_input @{theory} "met_polyeq_d3" [] MethodC.id_empty
walther@59997	1102	(["PolyEq", "solve_d3_polyeq_equation"],
walther@59997	1103	[("#Given" ,["equality e_e", "solveFor v_v"]),
s1210629013@55373	1104	("#Where" ,["(lhs e_e) is_poly_in v_v ", "((lhs e_e) has_degree_in v_v) = 3"]),
s1210629013@55373	1105	("#Find" ,["solutions v_v'i'"])],
walther@59852	1106	{rew_ord'="termlessI", rls'=PolyEq_erls, srls=Rule_Set.empty, prls=PolyEq_prls,
s1210629013@55373	1107	calc=[("sqrt", ("NthRoot.sqrt", eval_sqrt "#sqrt_"))], crls=PolyEq_crls, errpats = [],
s1210629013@55373	1108	nrls = norm_Rational},
wneuper@59551	1109	@{thm solve_poly_equ3.simps})]
wneuper@59473	1110	\<close>
wneuper@59370	1111	(.solves all expanded (ie. normalised) terms of degree 2.)
s1210629013@55373	1112	(*Oct.02 restriction: 'eval_true 0 =< discriminant' ony for integer values
s1210629013@55373	1113	by 'PolyEq_erls'; restricted until Float.thy is implemented*)
wneuper@59504	1114	partial_function (tailrec) solve_by_completing_square :: "bool \<Rightarrow> real \<Rightarrow> bool list"
wneuper@59504	1115	where
walther@59635	1116	"solve_by_completing_square e_e v_v = (
walther@59635	1117	let e_e = (
walther@59637	1118	(Try (Rewrite_Set_Inst [(''bdv'', v_v)] ''cancel_leading_coeff'')) #>
walther@59637	1119	(Try (Rewrite_Set_Inst [(''bdv'', v_v)] ''complete_square'')) #>
walther@59637	1120	(Try (Rewrite ''square_explicit1'')) #>
walther@59637	1121	(Try (Rewrite ''square_explicit2'')) #>
walther@59637	1122	(Rewrite ''root_plus_minus'') #>
walther@59637	1123	(Try (Repeat (Rewrite_Inst [(''bdv'', v_v)] ''bdv_explicit1''))) #>
walther@59637	1124	(Try (Repeat (Rewrite_Inst [(''bdv'', v_v)] ''bdv_explicit2''))) #>
walther@59637	1125	(Try (Repeat (Rewrite_Inst [(''bdv'', v_v)] ''bdv_explicit3''))) #>
walther@59637	1126	(Try (Rewrite_Set ''calculate_RootRat'')) #>
walther@59635	1127	(Try (Repeat (Calculate ''SQRT'')))) e_e
walther@59635	1128	in
walther@59635	1129	Or_to_List e_e)"
wneuper@59473	1130	setup \<open>KEStore_Elems.add_mets
wenzelm@60290	1131	[MethodC.prep_input @{theory} "met_polyeq_complsq" [] MethodC.id_empty
walther@59997	1132	(["PolyEq", "complete_square"],
walther@59997	1133	[("#Given" ,["equality e_e", "solveFor v_v"]),
s1210629013@55373	1134	("#Where" ,["matches (?a = 0) e_e", "((lhs e_e) has_degree_in v_v) = 2"]),
s1210629013@55373	1135	("#Find" ,["solutions v_v'i'"])],
walther@59852	1136	{rew_ord'="termlessI",rls'=PolyEq_erls,srls=Rule_Set.empty,prls=PolyEq_prls,
s1210629013@55373	1137	calc=[("sqrt", ("NthRoot.sqrt", eval_sqrt "#sqrt_"))], crls=PolyEq_crls, errpats = [],
s1210629013@55373	1138	nrls = norm_Rational},
wneuper@59551	1139	@{thm solve_by_completing_square.simps})]
wneuper@59472	1140	\<close>
s1210629013@55373	1141
wneuper@59472	1142	ML\<open>
neuper@37954	1143
neuper@37954	1144	(* termorder hacked by MG *)
neuper@37954	1145	local (. for make_polynomial_in .)
neuper@37954	1146
neuper@37954	1147	open Term; (* for type order = EQUAL \| LESS \| GREATER *)
neuper@37954	1148
neuper@37954	1149	fun pr_ord EQUAL = "EQUAL"
neuper@37954	1150	\| pr_ord LESS = "LESS"
neuper@37954	1151	\| pr_ord GREATER = "GREATER";
neuper@37954	1152
walther@60263	1153	fun dest_hd' _ (Const (a, T)) = (((a, 0), T), 0)
neuper@37954	1154	\| dest_hd' x (t as Free (a, T)) =
neuper@37954	1155	if x = t then ((("\|\|\|\|\|\|\|\|\|\|\|\|\|", 0), T), 0) (WN)
neuper@37954	1156	else (((a, 0), T), 1)
walther@60263	1157	\| dest_hd' _ (Var v) = (v, 2)
walther@60263	1158	\| dest_hd' _ (Bound i) = ((("", i), dummyT), 3)
walther@60263	1159	\| dest_hd' _ (Abs (_, T, _)) = ((("", 0), T), 4)
walther@60263	1160	\| dest_hd' _ _ = raise ERROR "dest_hd': uncovered case in fun.def.";
neuper@37954	1161
walther@60275	1162	fun size_of_term' x (Const ("Transcendental.powr",_) $ Free (var,_) $ Free (pot,_)) =
neuper@37954	1163	(case x of (WN)
neuper@37954	1164	(Free (xstr,_)) =>
walther@59875	1165	(if xstr = var then 1000*(the (TermC.int_opt_of_string pot)) else 3)
walther@59962	1166	\| _ => raise ERROR ("size_of_term' called with subst = "^
walther@59868	1167	(UnparseC.term x)))
neuper@37954	1168	\| size_of_term' x (Free (subst,_)) =
neuper@37954	1169	(case x of
neuper@37954	1170	(Free (xstr,_)) => (if xstr = subst then 1000 else 1)
walther@59962	1171	\| _ => raise ERROR ("size_of_term' called with subst = "^
walther@59868	1172	(UnparseC.term x)))
neuper@37954	1173	\| size_of_term' x (Abs (_,_,body)) = 1 + size_of_term' x body
neuper@37954	1174	\| size_of_term' x (f$t) = size_of_term' x f + size_of_term' x t
walther@60263	1175	\| size_of_term' _ _ = 1;
neuper@37954	1176
neuper@37989	1177	fun term_ord' x pr thy (Abs (_, T, t), Abs(_, U, u)) = (* ~ term.ML *)
neuper@52070	1178	(case term_ord' x pr thy (t, u) of EQUAL => Term_Ord.typ_ord (T, U) \| ord => ord)
neuper@37989	1179	\| term_ord' x pr thy (t, u) =
neuper@52070	1180	(if pr
neuper@52070	1181	then
neuper@52070	1182	let
neuper@52070	1183	val (f, ts) = strip_comb t and (g, us) = strip_comb u;
walther@59870	1184	val _ = tracing ("t= f@ts= \"" ^ UnparseC.term_in_thy thy f ^ "\" @ \"[" ^
walther@59870	1185	commas (map (UnparseC.term_in_thy thy) ts) ^ "]\"");
walther@59870	1186	val _ = tracing ("u= g@us= \"" ^ UnparseC.term_in_thy thy g ^ "\" @ \"[" ^
walther@59870	1187	commas(map (UnparseC.term_in_thy thy) us) ^ "]\"");
neuper@52070	1188	val _ = tracing ("size_of_term(t,u)= (" ^ string_of_int (size_of_term' x t) ^ ", " ^
neuper@52070	1189	string_of_int (size_of_term' x u) ^ ")");
neuper@52070	1190	val _ = tracing ("hd_ord(f,g) = " ^ (pr_ord o (hd_ord x)) (f,g));
neuper@52070	1191	val _ = tracing ("terms_ord(ts,us) = " ^ (pr_ord o (terms_ord x) str false) (ts, us));
neuper@52070	1192	val _ = tracing ("-------");
neuper@52070	1193	in () end
neuper@52070	1194	else ();
neuper@52070	1195	case int_ord (size_of_term' x t, size_of_term' x u) of
neuper@52070	1196	EQUAL =>
neuper@52070	1197	let val (f, ts) = strip_comb t and (g, us) = strip_comb u
neuper@52070	1198	in
neuper@52070	1199	(case hd_ord x (f, g) of
neuper@52070	1200	EQUAL => (terms_ord x str pr) (ts, us)
neuper@52070	1201	\| ord => ord)
neuper@52070	1202	end
neuper@37954	1203	\| ord => ord)
neuper@37954	1204	and hd_ord x (f, g) = (* ~ term.ML *)
neuper@37989	1205	prod_ord (prod_ord Term_Ord.indexname_ord Term_Ord.typ_ord)
neuper@37989	1206	int_ord (dest_hd' x f, dest_hd' x g)
walther@60263	1207	and terms_ord x _ pr (ts, us) =
walther@59881	1208	list_ord (term_ord' x pr (ThyC.get_theory "Isac_Knowledge"))(ts, us);
neuper@52070	1209
neuper@37954	1210	in
neuper@37954	1211
walther@60263	1212	fun ord_make_polynomial_in (pr:bool) thy subst tu =
walther@60263	1213	(()tracing ("* subs variable is: " ^ (Env.subst2str subst)); (**)
neuper@37954	1214	case subst of
walther@60263	1215	(_, x) :: _ => (term_ord' x pr thy tu = LESS)
walther@60263	1216	\| _ => raise ERROR ("ord_make_polynomial_in called with subst = " ^ Env.subst2str subst))
walther@60263	1217
neuper@37989	1218	end;(local)
neuper@37954	1219
wneuper@59472	1220	\<close>
wneuper@59472	1221	ML\<open>
s1210629013@55444	1222	val order_add_mult_in = prep_rls'(
walther@59851	1223	Rule_Def.Repeat{id = "order_add_mult_in", preconds = [],
neuper@37954	1224	rew_ord = ("ord_make_polynomial_in",
neuper@52139	1225	ord_make_polynomial_in false @{theory "Poly"}),
walther@59852	1226	erls = Rule_Set.empty,srls = Rule_Set.Empty,
neuper@42451	1227	calc = [], errpatts = [],
wenzelm@60297	1228	rules = [\<^rule_thm>\<open>mult.commute\<close>,
neuper@37954	1229	(* z * w = w * z *)
wenzelm@60297	1230	\<^rule_thm>\<open>real_mult_left_commute\<close>,
neuper@37954	1231	(z1.0 (z2.0 * z3.0) = z2.0 * (z1.0 * z3.0)*)
wenzelm@60297	1232	\<^rule_thm>\<open>mult.assoc\<close>,
neuper@37954	1233	(z1.0 z2.0 * z3.0 = z1.0 * (z2.0 * z3.0)*)
wenzelm@60297	1234	\<^rule_thm>\<open>add.commute\<close>,
neuper@37954	1235	(z + w = w + z)
wenzelm@60297	1236	\<^rule_thm>\<open>add.left_commute\<close>,
neuper@37954	1237	(x + (y + z) = y + (x + z))
wenzelm@60297	1238	\<^rule_thm>\<open>add.assoc\<close>
neuper@37954	1239	(z1.0 + z2.0 + z3.0 = z1.0 + (z2.0 + z3.0))
walther@59878	1240	], scr = Rule.Empty_Prog});
neuper@37954	1241
wneuper@59472	1242	\<close>
wneuper@59472	1243	ML\<open>
s1210629013@55444	1244	val collect_bdv = prep_rls'(
walther@59851	1245	Rule_Def.Repeat{id = "collect_bdv", preconds = [],
walther@59857	1246	rew_ord = ("dummy_ord", Rewrite_Ord.dummy_ord),
walther@59852	1247	erls = Rule_Set.empty,srls = Rule_Set.Empty,
neuper@42451	1248	calc = [], errpatts = [],
wenzelm@60297	1249	rules = [\<^rule_thm>\<open>bdv_collect_1\<close>,
wenzelm@60297	1250	\<^rule_thm>\<open>bdv_collect_2\<close>,
wenzelm@60297	1251	\<^rule_thm>\<open>bdv_collect_3\<close>,
neuper@37954	1252
wenzelm@60297	1253	\<^rule_thm>\<open>bdv_collect_assoc1_1\<close>,
wenzelm@60297	1254	\<^rule_thm>\<open>bdv_collect_assoc1_2\<close>,
wenzelm@60297	1255	\<^rule_thm>\<open>bdv_collect_assoc1_3\<close>,
neuper@37954	1256
wenzelm@60297	1257	\<^rule_thm>\<open>bdv_collect_assoc2_1\<close>,
wenzelm@60297	1258	\<^rule_thm>\<open>bdv_collect_assoc2_2\<close>,
wenzelm@60297	1259	\<^rule_thm>\<open>bdv_collect_assoc2_3\<close>,
neuper@37954	1260
neuper@37954	1261
wenzelm@60297	1262	\<^rule_thm>\<open>bdv_n_collect_1\<close>,
wenzelm@60297	1263	\<^rule_thm>\<open>bdv_n_collect_2\<close>,
wenzelm@60297	1264	\<^rule_thm>\<open>bdv_n_collect_3\<close>,
neuper@37954	1265
wenzelm@60297	1266	\<^rule_thm>\<open>bdv_n_collect_assoc1_1\<close>,
wenzelm@60297	1267	\<^rule_thm>\<open>bdv_n_collect_assoc1_2\<close>,
wenzelm@60297	1268	\<^rule_thm>\<open>bdv_n_collect_assoc1_3\<close>,
neuper@37954	1269
wenzelm@60297	1270	\<^rule_thm>\<open>bdv_n_collect_assoc2_1\<close>,
wenzelm@60297	1271	\<^rule_thm>\<open>bdv_n_collect_assoc2_2\<close>,
wenzelm@60297	1272	\<^rule_thm>\<open>bdv_n_collect_assoc2_3\<close>
walther@59878	1273	], scr = Rule.Empty_Prog});
neuper@37954	1274
wneuper@59472	1275	\<close>
wneuper@59472	1276	ML\<open>
neuper@37954	1277	(*.transforms an arbitrary term without roots to a polynomial [4]
neuper@37954	1278	according to knowledge/Poly.sml.*)
s1210629013@55444	1279	val make_polynomial_in = prep_rls'(
walther@59878	1280	Rule_Set.Sequence {id = "make_polynomial_in", preconds = []:term list,
walther@59857	1281	rew_ord = ("dummy_ord", Rewrite_Ord.dummy_ord),
walther@59851	1282	erls = Atools_erls, srls = Rule_Set.Empty,
neuper@42451	1283	calc = [], errpatts = [],
wneuper@59416	1284	rules = [Rule.Rls_ expand_poly,
wneuper@59416	1285	Rule.Rls_ order_add_mult_in,
wneuper@59416	1286	Rule.Rls_ simplify_power,
wneuper@59416	1287	Rule.Rls_ collect_numerals,
wneuper@59416	1288	Rule.Rls_ reduce_012,
wenzelm@60297	1289	\<^rule_thm>\<open>realpow_oneI\<close>,
wneuper@59416	1290	Rule.Rls_ discard_parentheses,
wneuper@59416	1291	Rule.Rls_ collect_bdv
neuper@37954	1292	],
walther@59878	1293	scr = Rule.Empty_Prog
wneuper@59406	1294	});
neuper@37954	1295
wneuper@59472	1296	\<close>
wneuper@59472	1297	ML\<open>
neuper@37954	1298	val separate_bdvs =
walther@59852	1299	Rule_Set.append_rules "separate_bdvs"
neuper@37954	1300	collect_bdv
wenzelm@60297	1301	[\<^rule_thm>\<open>separate_bdv\<close>,
neuper@37954	1302	("?a ?bdv / ?b = ?a / ?b * ?bdv"*)
wenzelm@60297	1303	\<^rule_thm>\<open>separate_bdv_n\<close>,
wenzelm@60297	1304	\<^rule_thm>\<open>separate_1_bdv\<close>,
neuper@37954	1305	("?bdv / ?b = (1 / ?b) ?bdv"*)
wenzelm@60297	1306	\<^rule_thm>\<open>separate_1_bdv_n\<close>,
walther@60242	1307	("?bdv \<up> ?n / ?b = 1 / ?b ?bdv \<up> ?n"*)
wneuper@59416	1308	Rule.Thm ("add_divide_distrib",
walther@59871	1309	ThmC.numerals_to_Free @{thm add_divide_distrib})
neuper@37954	1310	(*"(?x + ?y) / ?z = ?x / ?z + ?y / ?z"
neuper@37954	1311	WN051031 DOES NOT BELONG TO HERE*)
neuper@37954	1312	];
wneuper@59472	1313	\<close>
wneuper@59472	1314	ML\<open>
s1210629013@55444	1315	val make_ratpoly_in = prep_rls'(
walther@59878	1316	Rule_Set.Sequence {id = "make_ratpoly_in", preconds = []:term list,
walther@59857	1317	rew_ord = ("dummy_ord", Rewrite_Ord.dummy_ord),
walther@59851	1318	erls = Atools_erls, srls = Rule_Set.Empty,
neuper@42451	1319	calc = [], errpatts = [],
wneuper@59416	1320	rules = [Rule.Rls_ norm_Rational,
wneuper@59416	1321	Rule.Rls_ order_add_mult_in,
wneuper@59416	1322	Rule.Rls_ discard_parentheses,
wneuper@59416	1323	Rule.Rls_ separate_bdvs,
wneuper@59416	1324	(* Rule.Rls_ rearrange_assoc, WN060916 why does cancel_p not work?*)
wneuper@59416	1325	Rule.Rls_ cancel_p
wenzelm@60294	1326	(\<^rule_eval>\<open>divide\<close> (eval_cancel "#divide_e") too weak!)
neuper@37954	1327	],
walther@59878	1328	scr = Rule.Empty_Prog});
wneuper@59472	1329	\<close>
wenzelm@60289	1330	rule_set_knowledge
wenzelm@60286	1331	order_add_mult_in = order_add_mult_in and
wenzelm@60286	1332	collect_bdv = collect_bdv and
wenzelm@60286	1333	make_polynomial_in = make_polynomial_in and
wenzelm@60286	1334	make_ratpoly_in = make_ratpoly_in and
wenzelm@60286	1335	separate_bdvs = separate_bdvs
wenzelm@60286	1336	ML \<open>
walther@60278	1337	\<close> ML \<open>
walther@60278	1338	\<close> ML \<open>
walther@60278	1339	\<close>
neuper@37906	1340	end
neuper@37906	1341
neuper@37906	1342
neuper@37906	1343
neuper@37906	1344
neuper@37906	1345
neuper@37906	1346

author	wenzelm
	Sat, 12 Jun 2021 18:06:27 +0200
changeset 60297	73e7175a7d3f
parent 60294	6623f5cdcb19
child 60298	09106b85d3b4
permissions	-rw-r--r--