type mail.txt
22-Jul-83 06:14:43-PDT,3739;000000000001
Mail-From: P.PING created at 22-Jul-83 06:14:42
Date: Fri 22 Jul 83 06:14:42-PDT
From: P.PING@SU-LOTS-A
Subject: rotation number
To: m.mccarthy@SU-LOTS-A


        I have now a pascal program that finds the interval of lambda
efficiently giving any value of the rotation number.  Below is the 
output for the case alpha = .5, p = 1, and q from 2 to 50.  The numbers
should be good for at least 6 significant figures, and have been checked
against results obtained previously by other means.  It took roughly 
half a minute of CPU time to generate the output.

        Do you have any suggestions for the next step?

↑L
 alpha =    0.50000 ,       p =  1


  q      rot           d lam        lo lam        hi lam

  2  5.000000E-01  3.255175E-02  4.058954E-01  4.384471E-01
  3  3.333333E-01  1.456860E-02  2.472978E-01  2.618664E-01
  4  2.500000E-01  8.161433E-03  1.681416E-01  1.763030E-01
  5  2.000000E-01  5.144555E-03  1.211526E-01  1.262971E-01

  6  1.666667E-01  3.492706E-03  9.035709E-02  9.384980E-02
  7  1.428571E-01  2.497143E-03  6.887032E-02  7.136746E-02
  8  1.250000E-01  1.845208E-03  5.324557E-02  5.509077E-02
  9  1.111111E-01  1.399724E-03  4.154381E-02  4.294353E-02
 10  1.000000E-01  1.074322E-03  3.260864E-02  3.368296E-02

 11  9.090909E-02  8.342206E-04  2.568300E-02  2.651722E-02
 12  8.333333E-02  6.531645E-04  2.026251E-02  2.091568E-02
 13  7.692308E-02  5.200347E-04  1.598757E-02  1.650760E-02
 14  7.142857E-02  4.122551E-04  1.261251E-02  1.302477E-02
 15  6.666667E-02  3.238050E-04  9.943608E-03  1.026741E-02

 16  6.250000E-02  2.584304E-04  7.824816E-03  8.083246E-03
 17  5.882353E-02  2.039664E-04  6.150015E-03  6.353981E-03
 18  5.555556E-02  1.601574E-04  4.826389E-03  4.986547E-03
 19  5.263158E-02  1.268682E-04  3.780179E-03  3.907047E-03
 20  5.000000E-02  1.003890E-04  2.956070E-03  3.056459E-03

 21  4.761905E-02  7.870028E-05  2.308890E-03  2.387591E-03
 22  4.545455E-02  6.137780E-05  1.801260E-03  1.862638E-03
 23  4.347826E-02  4.837656E-05  1.403019E-03  1.451395E-03
 24  4.166667E-02  3.774457E-05  1.092039E-03  1.129784E-03
 25  4.000000E-02  2.884858E-05  8.498058E-04  8.786544E-04

 26  3.846154E-02  2.294030E-05  6.598979E-04  6.828382E-04
 27  3.703704E-02  1.789251E-05  5.124174E-04  5.303100E-04
 28  3.571429E-02  1.390275E-05  3.977195E-04  4.116222E-04
 29  3.448276E-02  1.074371E-05  3.086254E-04  3.193691E-04
 30  3.333333E-02  8.389343E-06  2.392903E-04  2.476796E-04

 31  3.225806E-02  6.511797E-06  1.855269E-04  1.920387E-04
 32  3.125000E-02  5.051483E-06  1.438037E-04  1.488551E-04
 33  3.030303E-02  3.904100E-06  1.114532E-04  1.153573E-04
 34  2.941176E-02  3.039833E-06  8.634478E-05  8.938461E-05
 35  2.857143E-02  2.343202E-06  6.689504E-05  6.923824E-05

 36  2.777778E-02  1.817940E-06  5.181879E-05  5.363673E-05
 37  2.702703E-02  1.415609E-06  4.013628E-05  4.155189E-05
 38  2.631579E-02  1.087783E-06  3.109127E-05  3.217906E-05
 39  2.564103E-02  8.493657E-07  2.407283E-05  2.492219E-05
 40  2.500000E-02  6.556502E-07  1.864880E-05  1.930445E-05

 41  2.439024E-02  5.029140E-07  1.443550E-05  1.493841E-05
 42  2.380952E-02  3.874295E-07  1.118332E-05  1.157075E-05
 43  2.325581E-02  2.980229E-07  8.665026E-06  8.963048E-06
 44  2.272727E-02  2.235170E-07  6.712973E-06  6.936490E-06
 45  2.222222E-02  1.788137E-07  5.193055E-06  5.371868E-06

 46  2.173913E-02  1.490114E-07  4.015863E-06  4.164875E-06
 47  2.127660E-02  1.154839E-07  3.110618E-06  3.226101E-06
 48  2.083333E-02  8.568145E-08  2.410263E-06  2.495944E-06
 49  2.040816E-02  5.960452E-08  1.870096E-06  1.929700E-06
 50  2.000000E-02  5.215396E-08  1.445413E-06  1.497567E-06

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