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| (* ---------------------------------------------------------------------- *) | |
| (* PDIVIDES *) | |
| (* ---------------------------------------------------------------------- *) | |
| let PDIVIDES vars sgns p q = | |
| let s_thm = FINDSIGN vars sgns (head vars q) in | |
| let op,l1,r1 = get_binop (concl s_thm) in | |
| if op = req then failwith "PDIVIDES : head coefficient is zero" else | |
| let div_thm = PDIVIDE vars p q in | |
| let asx,pqr = dest_eq (concl div_thm) in | |
| let pq,r = dest_plus pqr in | |
| let p',q' = dest_mult pq in | |
| let ak,s = dest_mult asx in | |
| let a,k = dest_pow ak in | |
| let k' = dest_small_numeral k in | |
| if op = rgt || even k' then | |
| r,div_thm | |
| else if odd k' && op = rlt then | |
| let par_thm = PARITY_CONV k in | |
| let mp_thm = MATCH_MPL[neg_odd_lem;div_thm;par_thm] in | |
| let mp_thm1 = (CONV_RULE (LAND_CONV (LAND_CONV (LAND_CONV POLY_NEG_CONV)))) mp_thm in | |
| let mp_thm2 = (CONV_RULE (RAND_CONV (LAND_CONV (LAND_CONV (POLY_NEG_CONV))))) mp_thm1 in | |
| let mp_thm3 = (CONV_RULE (RAND_CONV (RAND_CONV POLY_NEG_CONV))) mp_thm2 in | |
| let ret = (snd o dest_plus o rhs o concl) mp_thm3 in | |
| ret,mp_thm3 | |
| else if odd k' && op = rneq then | |
| let par_thm = PARITY_CONV k in | |
| let mp_thm = MATCH_MPL[mul_odd_lem;div_thm;par_thm] in | |
| let mp_thm1 = (CONV_RULE (LAND_CONV (LAND_CONV (LAND_CONV (POLYNATE_CONV vars))))) mp_thm in | |
| let mp_thm2 = (CONV_RULE (RAND_CONV (LAND_CONV (POLYNATE_CONV vars)))) mp_thm1 in | |
| let mp_thm3 = (CONV_RULE (RAND_CONV (RAND_CONV (POLY_MUL_CONV vars)))) mp_thm2 in | |
| let ret = (snd o dest_plus o rhs o concl) mp_thm3 in | |
| ret,mp_thm3 | |
| else failwith "PDIVIDES: 1";; | |
| (* ---------------------------------------------------------------------- *) | |
| (* Timing *) | |
| (* ---------------------------------------------------------------------- *) | |
| let PDIVIDES vars sgns mat_thm div_thms = | |
| let start_time = Sys.time() in | |
| let res = PDIVIDES vars sgns mat_thm div_thms in | |
| pdivides_timer +.= (Sys.time() -. start_time); | |
| res;; | |
| (* | |
| PDIVIDES vars sgns p | |
| let q = (ith 2 qs) | |
| let vars = [`x:real`;`y:real`];; | |
| let sgns = [ARITH_RULE `&1 > &0`;ASSUME `&0 + y * &1 < &0`];; | |
| let q = rhs(concl (POLYNATE_CONV vars `x * y`));; | |
| let p = rhs(concl (POLYNATE_CONV vars `&1 + y * x * x + x * x * x * &5 * y`));; | |
| PDIVIDE vars p q;; | |
| PDIVIDES vars sgns p q;; | |
| let vars = [`x:real`;`y:real`];; | |
| let sgns = [ARITH_RULE `&1 > &0`;ASSUME `&0 + y * &1 > &0`];; | |
| let q = rhs(concl (POLYNATE_CONV vars `x * x * y`));; | |
| let p = rhs(concl (POLYNATE_CONV vars `&1 + x * x + x * x * x * y`));; | |
| PDIVIDE vars p q;; | |
| PDIVIDES vars sgns p q;; | |
| let vars = [`x:real`;`y:real`];; | |
| let sgns = [ARITH_RULE `&1 > &0`;ASSUME `&0 + y * &1 < &0`];; | |
| let q = rhs(concl (POLYNATE_CONV vars `x * x * y`));; | |
| let p = rhs(concl (POLYNATE_CONV vars `&1 + x * x + x * x * x * y`));; | |
| PDIVIDE vars p q;; | |
| PDIVIDES vars sgns p q;; | |
| let vars = [`x:real`;`y:real`];; | |
| let sgns = [ASSUME `&0 + y * &1 < &0`];; | |
| let q = rhs(concl (POLYNATE_CONV vars `-- x:real`));; | |
| let p = rhs(concl (POLYNATE_CONV vars `x * x * y`));; | |
| PDIVIDE vars p q;; | |
| PDIVIDES vars sgns p q | |
| let vars = [`x:real`;`y:real`];; | |
| let sgns = [ARITH_RULE `&1 > &0`;ASSUME `&0 + y * &1 <> &0`];; | |
| let q = rhs(concl (POLYNATE_CONV vars `x * x * y`));; | |
| let p = rhs(concl (POLYNATE_CONV vars `&1 + x * x + x * x * x * y`));; | |
| PDIVIDE vars p q;; | |
| PDIVIDES vars sgns p q;; | |
| *) | |