Comparision: 4 different methods of interpolation

[Gottfried]

Code:

stitchsexp(z) = {
  print(z);
  if (imag(z)>=1, return (riemaprx(z)));
  if (imag(z)<=-1, return (conj(riemaprx(conj(z)))));
  return(sexp(z));
}
pc = vectorv(65,r,stitchsexp(2*Pi*I*(r-1)/64))

Code:

for (s=1,65,print(pc[s]));
1.0000000000000000000000000000000 + 0.E-105*I
0.99411091497356251121660334054347 + 0.12727677792455698141545403455080*I
0.97672654305998578305917759789250 +
(...)
0.063853734876755975181544200369394 + 1.0910178122849990427062282998385*I

Hi Sheldon -

upps - I think my Pari/GP-vector-call was meaningless.
Of course I wanted, that the "height" parameter circles 1 time in the complex plane, thus the last value of sexp should equal the first one in the vectorial output. Sorry. I should have written it in this way:

pc = vectorv(65,r,stitchsexp(exp(2*Pi*I*(r-1)/64)))

Then I get

Code:

4.00000000000+0.E-67*I
      3.87336468717+0.686320949087*I
       3.53286632591+1.25400277240*I
       3.07245040887+1.63627353165*I
       2.59063527737+1.83193139680*I
       2.15456857774+1.88240761546*I
       1.79318667065+1.84024780663*I
       1.50843156756+1.74933262494*I
       1.28927607041+1.63906429915*I
       1.12129007339+1.52628683915*I
      0.991249900203+1.41932158308*I
      0.888608334316+1.32147766690*I
      0.805497695424+1.23341451594*I
      0.736235931369+1.15453275928*I
      0.676770912155+1.08372321281*I
      0.624213185339+1.01973965792*I
     0.576484729285+0.961366385498*I
     0.532068845117+0.907479289431*I
     0.489837394148+0.857054039805*I
     0.448934299533+0.809148995558*I
     0.408699813497+0.762876526969*I
     0.368625526510+0.717369262745*I
     0.328334760078+0.671744585062*I
     0.287586855613+0.625070110831*I
     0.246306948051+0.576334576435*I
     0.204644547462+0.524432811667*I
     0.163062886522+0.468180840110*I
     0.122452775427+0.406386947333*I
    0.0842439806503+0.338012004684*I
    0.0504505580843+0.262443576481*I
    0.0235466506798+0.179859514724*I
  0.00607381145893+0.0915545538344*I
                  -9.01293432323E-55
  0.00607381145893-0.0915545538344*I
    0.0235466506798-0.179859514724*I
    0.0504505580843-0.262443576481*I
    0.0842439806503-0.338012004684*I
     0.122452775427-0.406386947333*I
     0.163062886522-0.468180840110*I
     0.204644547462-0.524432811667*I
     0.246306948051-0.576334576435*I
     0.287586855613-0.625070110831*I
     0.328334760078-0.671744585062*I
     0.368625526510-0.717369262745*I
     0.408699813497-0.762876526969*I
     0.448934299533-0.809148995558*I
     0.489837394148-0.857054039805*I
     0.532068845117-0.907479289431*I
     0.576484729285-0.961366385498*I
      0.624213185339-1.01973965792*I
      0.676770912155-1.08372321281*I
      0.736235931369-1.15453275928*I
      0.805497695424-1.23341451594*I
      0.888608334316-1.32147766690*I
      0.991249900203-1.41932158308*I
       1.12129007339-1.52628683915*I
       1.28927607041-1.63906429915*I
       1.50843156756-1.74933262494*I
       1.79318667065-1.84024780663*I
       2.15456857774-1.88240761546*I
       2.59063527737-1.83193139680*I
       3.07245040887-1.63627353165*I
       3.53286632591-1.25400277240*I
      3.87336468717-0.686320949087*I
              4.00000000000+0.E-67*I

which is at least by the general pattern what was expected. This looks much better... :-)

Gottfried