Datasets:
Tasks:
Text Generation
Modalities:
Text
Sub-tasks:
language-modeling
Languages:
English
Size:
100K - 1M
License:
File size: 3,442 Bytes
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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;;
*)
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