ceiling

349 days ago by raraavis

m=2 q=2^(2*m+1) q0=2^m n=q^4+1+2*q^2*q0*(q-1)-(q^2+1) print "n = ",n print "l k d t R" for h in range(q^2-1): l=h+1 k=l*(q^2+1)-q0*(q-1)+1 d=n-l*(q^2+1) t=((d-1)/2).floor() R=float(k/n) print l," ",k ," ",d," ",t," ",R 
        
WARNING: Output truncated!  
full_output.txt



n =  1301504
l   k    d   t   R
1     902     1300479     650239     0.000693044354839
2     1927     1299454     649726     0.00148059475806
3     2952     1298429     649214     0.00226814516129
4     3977     1297404     648701     0.00305569556452
5     5002     1296379     648189     0.00384324596774
6     6027     1295354     647676     0.00463079637097
7     7052     1294329     647164     0.00541834677419
8     8077     1293304     646651     0.00620589717742
9     9102     1292279     646139     0.00699344758065
10     10127     1291254     645626     0.00778099798387
11     11152     1290229     645114     0.0085685483871
12     12177     1289204     644601     0.00935609879032
13     13202     1288179     644089     0.0101436491935
14     14227     1287154     643576     0.0109311995968
15     15252     1286129     643064     0.01171875
16     16277     1285104     642551     0.0125063004032
17     17302     1284079     642039     0.0132938508065
18     18327     1283054     641526     0.0140814012097
19     19352     1282029     641014     0.0148689516129
20     20377     1281004     640501     0.0156565020161
21     21402     1279979     639989     0.0164440524194
22     22427     1278954     639476     0.0172316028226
23     23452     1277929     638964     0.0180191532258
24     24477     1276904     638451     0.018806703629
25     25502     1275879     637939     0.0195942540323
26     26527     1274854     637426     0.0203818044355
27     27552     1273829     636914     0.0211693548387
28     28577     1272804     636401     0.0219569052419
29     29602     1271779     635889     0.0227444556452
30     30627     1270754     635376     0.0235320060484
31     31652     1269729     634864     0.0243195564516
32     32677     1268704     634351     0.0251071068548
33     33702     1267679     633839     0.0258946572581
34     34727     1266654     633326     0.0266822076613
35     35752     1265629     632814     0.0274697580645
36     36777     1264604     632301     0.0282573084677
37     37802     1263579     631789     0.029044858871
38     38827     1262554     631276     0.0298324092742
39     39852     1261529     630764     0.0306199596774
40     40877     1260504     630251     0.0314075100806
41     41902     1259479     629739     0.0321950604839
42     42927     1258454     629226     0.0329826108871
43     43952     1257429     628714     0.0337701612903
44     44977     1256404     628201     0.0345577116935
45     46002     1255379     627689     0.0353452620968
46     47027     1254354     627176     0.0361328125
47     48052     1253329     626664     0.0369203629032
48     49077     1252304     626151     0.0377079133065
49     50102     1251279     625639     0.0384954637097
50     51127     1250254     625126     0.0392830141129
51     52152     1249229     624614     0.0400705645161
52     53177     1248204     624101     0.0408581149194
53     54202     1247179     623589     0.0416456653226
54     55227     1246154     623076     0.0424332157258
55     56252     1245129     622564     0.043220766129
56     57277     1244104     622051     0.0440083165323
57     58302     1243079     621539     0.0447958669355

...

964     987977     313404     156701     0.759104082661
965     989002     312379     156189     0.759891633065
966     990027     311354     155676     0.760679183468
967     991052     310329     155164     0.761466733871
968     992077     309304     154651     0.762254284274
969     993102     308279     154139     0.763041834677
970     994127     307254     153626     0.763829385081
971     995152     306229     153114     0.764616935484
972     996177     305204     152601     0.765404485887
973     997202     304179     152089     0.76619203629
974     998227     303154     151576     0.766979586694
975     999252     302129     151064     0.767767137097
976     1000277     301104     150551     0.7685546875
977     1001302     300079     150039     0.769342237903
978     1002327     299054     149526     0.770129788306
979     1003352     298029     149014     0.77091733871
980     1004377     297004     148501     0.771704889113
981     1005402     295979     147989     0.772492439516
982     1006427     294954     147476     0.773279989919
983     1007452     293929     146964     0.774067540323
984     1008477     292904     146451     0.774855090726
985     1009502     291879     145939     0.775642641129
986     1010527     290854     145426     0.776430191532
987     1011552     289829     144914     0.777217741935
988     1012577     288804     144401     0.778005292339
989     1013602     287779     143889     0.778792842742
990     1014627     286754     143376     0.779580393145
991     1015652     285729     142864     0.780367943548
992     1016677     284704     142351     0.781155493952
993     1017702     283679     141839     0.781943044355
994     1018727     282654     141326     0.782730594758
995     1019752     281629     140814     0.783518145161
996     1020777     280604     140301     0.784305695565
997     1021802     279579     139789     0.785093245968
998     1022827     278554     139276     0.785880796371
999     1023852     277529     138764     0.786668346774
1000     1024877     276504     138251     0.787455897177
1001     1025902     275479     137739     0.788243447581
1002     1026927     274454     137226     0.789030997984
1003     1027952     273429     136714     0.789818548387
1004     1028977     272404     136201     0.79060609879
1005     1030002     271379     135689     0.791393649194
1006     1031027     270354     135176     0.792181199597
1007     1032052     269329     134664     0.79296875
1008     1033077     268304     134151     0.793756300403
1009     1034102     267279     133639     0.794543850806
1010     1035127     266254     133126     0.79533140121
1011     1036152     265229     132614     0.796118951613
1012     1037177     264204     132101     0.796906502016
1013     1038202     263179     131589     0.797694052419
1014     1039227     262154     131076     0.798481602823
1015     1040252     261129     130564     0.799269153226
1016     1041277     260104     130051     0.800056703629
1017     1042302     259079     129539     0.800844254032
1018     1043327     258054     129026     0.801631804435
1019     1044352     257029     128514     0.802419354839
1020     1045377     256004     128001     0.803206905242
1021     1046402     254979     127489     0.803994455645
1022     1047427     253954     126976     0.804782006048
1023     1048452     252929     126464     0.805569556452
WARNING: Output truncated!  
full_output.txt



n =  1301504
l   k    d   t   R
1     902     1300479     650239     0.000693044354839
2     1927     1299454     649726     0.00148059475806
3     2952     1298429     649214     0.00226814516129
4     3977     1297404     648701     0.00305569556452
5     5002     1296379     648189     0.00384324596774
6     6027     1295354     647676     0.00463079637097
7     7052     1294329     647164     0.00541834677419
8     8077     1293304     646651     0.00620589717742
9     9102     1292279     646139     0.00699344758065
10     10127     1291254     645626     0.00778099798387
11     11152     1290229     645114     0.0085685483871
12     12177     1289204     644601     0.00935609879032
13     13202     1288179     644089     0.0101436491935
14     14227     1287154     643576     0.0109311995968
15     15252     1286129     643064     0.01171875
16     16277     1285104     642551     0.0125063004032
17     17302     1284079     642039     0.0132938508065
18     18327     1283054     641526     0.0140814012097
19     19352     1282029     641014     0.0148689516129
20     20377     1281004     640501     0.0156565020161
21     21402     1279979     639989     0.0164440524194
22     22427     1278954     639476     0.0172316028226
23     23452     1277929     638964     0.0180191532258
24     24477     1276904     638451     0.018806703629
25     25502     1275879     637939     0.0195942540323
26     26527     1274854     637426     0.0203818044355
27     27552     1273829     636914     0.0211693548387
28     28577     1272804     636401     0.0219569052419
29     29602     1271779     635889     0.0227444556452
30     30627     1270754     635376     0.0235320060484
31     31652     1269729     634864     0.0243195564516
32     32677     1268704     634351     0.0251071068548
33     33702     1267679     633839     0.0258946572581
34     34727     1266654     633326     0.0266822076613
35     35752     1265629     632814     0.0274697580645
36     36777     1264604     632301     0.0282573084677
37     37802     1263579     631789     0.029044858871
38     38827     1262554     631276     0.0298324092742
39     39852     1261529     630764     0.0306199596774
40     40877     1260504     630251     0.0314075100806
41     41902     1259479     629739     0.0321950604839
42     42927     1258454     629226     0.0329826108871
43     43952     1257429     628714     0.0337701612903
44     44977     1256404     628201     0.0345577116935
45     46002     1255379     627689     0.0353452620968
46     47027     1254354     627176     0.0361328125
47     48052     1253329     626664     0.0369203629032
48     49077     1252304     626151     0.0377079133065
49     50102     1251279     625639     0.0384954637097
50     51127     1250254     625126     0.0392830141129
51     52152     1249229     624614     0.0400705645161
52     53177     1248204     624101     0.0408581149194
53     54202     1247179     623589     0.0416456653226
54     55227     1246154     623076     0.0424332157258
55     56252     1245129     622564     0.043220766129
56     57277     1244104     622051     0.0440083165323
57     58302     1243079     621539     0.0447958669355

...

964     987977     313404     156701     0.759104082661
965     989002     312379     156189     0.759891633065
966     990027     311354     155676     0.760679183468
967     991052     310329     155164     0.761466733871
968     992077     309304     154651     0.762254284274
969     993102     308279     154139     0.763041834677
970     994127     307254     153626     0.763829385081
971     995152     306229     153114     0.764616935484
972     996177     305204     152601     0.765404485887
973     997202     304179     152089     0.76619203629
974     998227     303154     151576     0.766979586694
975     999252     302129     151064     0.767767137097
976     1000277     301104     150551     0.7685546875
977     1001302     300079     150039     0.769342237903
978     1002327     299054     149526     0.770129788306
979     1003352     298029     149014     0.77091733871
980     1004377     297004     148501     0.771704889113
981     1005402     295979     147989     0.772492439516
982     1006427     294954     147476     0.773279989919
983     1007452     293929     146964     0.774067540323
984     1008477     292904     146451     0.774855090726
985     1009502     291879     145939     0.775642641129
986     1010527     290854     145426     0.776430191532
987     1011552     289829     144914     0.777217741935
988     1012577     288804     144401     0.778005292339
989     1013602     287779     143889     0.778792842742
990     1014627     286754     143376     0.779580393145
991     1015652     285729     142864     0.780367943548
992     1016677     284704     142351     0.781155493952
993     1017702     283679     141839     0.781943044355
994     1018727     282654     141326     0.782730594758
995     1019752     281629     140814     0.783518145161
996     1020777     280604     140301     0.784305695565
997     1021802     279579     139789     0.785093245968
998     1022827     278554     139276     0.785880796371
999     1023852     277529     138764     0.786668346774
1000     1024877     276504     138251     0.787455897177
1001     1025902     275479     137739     0.788243447581
1002     1026927     274454     137226     0.789030997984
1003     1027952     273429     136714     0.789818548387
1004     1028977     272404     136201     0.79060609879
1005     1030002     271379     135689     0.791393649194
1006     1031027     270354     135176     0.792181199597
1007     1032052     269329     134664     0.79296875
1008     1033077     268304     134151     0.793756300403
1009     1034102     267279     133639     0.794543850806
1010     1035127     266254     133126     0.79533140121
1011     1036152     265229     132614     0.796118951613
1012     1037177     264204     132101     0.796906502016
1013     1038202     263179     131589     0.797694052419
1014     1039227     262154     131076     0.798481602823
1015     1040252     261129     130564     0.799269153226
1016     1041277     260104     130051     0.800056703629
1017     1042302     259079     129539     0.800844254032
1018     1043327     258054     129026     0.801631804435
1019     1044352     257029     128514     0.802419354839
1020     1045377     256004     128001     0.803206905242
1021     1046402     254979     127489     0.803994455645
1022     1047427     253954     126976     0.804782006048
1023     1048452     252929     126464     0.805569556452
 
       
n.ceiling() 
        
8
8
type(n) 
        
<type 'sage.rings.integer.Integer'>
<type 'sage.rings.integer.Integer'>
n=2.3 
       
type(n) 
        
<type 'sage.rings.real_mpfr.RealLiteral'>
<type 'sage.rings.real_mpfr.RealLiteral'>
n=2/3 
       
type(n) 
        
<type 'sage.rings.rational.Rational'>
<type 'sage.rings.rational.Rational'>
for i in range(5): print i," ", i+1 
        
0        1
1        2
2        3
3        4
4        5
0        1
1        2
2        3
3        4
4        5