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def as_ogf(f, prec):
    pari.set_series_precision(prec)
    C = pari("Vec(serlaplace(" + repr(f(x)) + "))")
    S.<z> = PowerSeriesRing(ZZ)
    return S(C)

f(x) = ((3*x + 8)*sinh(2*x) + (2*x^2 + 16*(x + 1))*cosh(2*x))/16    
as_ogf(f, 4) returns 1 + 2*z + 5*z^2 + 16*z^3 + 28*z^4 and is of the required type.

It seems to me it would be worthwhile to include such a function in Sage.

def as_ogf(f, prec): pari.set_series_precision(prec) C = pari("Vec(serlaplace(" + repr(f(x)) + "))") S.<z> = PowerSeriesRing(ZZ) return S(C) S(C) f(x) = ((3*x + 8)*sinh(2*x) + (2*x^2 + 16*(x + 1))*cosh(2*x))/16 as_ogf(f, 4) returns 1 + 2*z + 5*z^2 + 16*z^3 + 28*z^4 and is of the required type. It seems to me it would be worthwhile to include such a function in Sage. EDIT: Unfortunately this does not work. f(x) = (3*x + 8)*sinh(2*x)/4; as_ogf(f, 4) returns 4 + 3z + 16z^2 + 24z^3 istead of the correct 4z + 3z^2 + 16z^3 + 24*z^4. Pari seems to swallow the constant coefficient if it is '0'? How can this be corrected?

          3    No.3 Revision 
      
    
        
        updated 2019-10-20 14:48:03 +0100  
 
 
  
 
 
 
  def as_ogf(f, prec):
        pari.set_series_precision(prec)
        C = pari("Vec(serlaplace(" + repr(f(x)) + "))")
        S.<z> = PowerSeriesRing(ZZ)
        return S(C)
 f(x) = ((3*x + 8)*sinh(2*x) + (2*x^2 + 16*(x + 1))*cosh(2*x))/16    
as_ogf(f, 4) returns 1 + 2*z + 5*z^2 + 16*z^3 + 28*z^4 and is of the required type.
 It seems to me it would be worthwhile to include such a function in Sage.
 EDIT:
 EDIT: Unfortunately this does not work. 
 f(x) = (3*x + 8)*sinh(2*x)/4; as_ogf(f, 4)
 returns 4 + 3z + 16z^2 + 24z^3 istead of the correct 4z + 3z^2 + 16z^3 + 24*z^4. Pari seems to swallow the constant coefficient if it is '0'? How can this be corrected?
 
 
          4    No.4 Revision 
      
    
        
        updated 2019-10-20 14:48:37 +0100  
 
 
  
 
 
 
  def as_ogf(f, prec):
        pari.set_series_precision(prec)
        C = pari("Vec(serlaplace(" + repr(f(x)) + "))")
        S.<z> = PowerSeriesRing(ZZ)
        return S(C)
 f(x) = ((3*x + 8)*sinh(2*x) + (2*x^2 + 16*(x + 1))*cosh(2*x))/16    
as_ogf(f, 4) returns 1 + 2*z + 5*z^2 + 16*z^3 + 28*z^4 and is of the required type.
 It seems to me it would be worthwhile to include such a function in Sage.
 EDIT: Unfortunately this does not work. 
 f(x) = (3*x + 8)*sinh(2*x)/4; as_ogf(f, 4)
 returns 4 + 3z + 16z^2 + 24z^3 istead of the correct 4z + 3z^2 + 16z^3 + 24*z^4. Pari seems to swallow the constant coefficient if it is '0'? How can this be corrected?
 
 
          5    No.5 Revision 
      
    
        
        updated 2019-10-20 14:49:33 +0100  
 
 
  
 
 
 
  Here a potential solution:
 def as_ogf(f, prec):
     pari.set_series_precision(prec)
     C = pari("Vec(serlaplace(" + repr(f(x)) + "))")
     S.<z> = PowerSeriesRing(ZZ)
     return S(C)S(C)
  f(x) = ((3*x + 8)*sinh(2*x) + (2*x^2 + 16*(x + 1))*cosh(2*x))/16    
as_ogf(f, 4) returns 1 + 2*z + 5*z^2 + 16*z^3 + 28*z^4 and is of the required type.
 It seems to me it would be worthwhile to include such a function in Sage.
 EDIT: Unfortunately this does not work. 
 f(x) = (3*x + 8)*sinh(2*x)/4; as_ogf(f, 4)
 returns 4 + 3z + 16z^2 + 24z^3 istead of the correct 4z + 3z^2 + 16z^3 + 24*z^4. Pari seems to swallow the constant coefficient if it is '0'? How can this be corrected?
 
 
          6    No.6 Revision 
      
    
        
        updated 2019-10-20 19:36:05 +0100  
 
 
  
 
 
 
  Here a potential solution:
 def as_ogf(f, prec):
    S.<z> = PowerSeriesRing(ZZ)
    pari.set_series_precision(prec)
    C = pari("Vec(serlaplace(" pari("serlaplace(" + repr(f(x)) str(f(x)) + "))")
    S.<z> = PowerSeriesRing(ZZ)
")")
    return S(C)

f(x) = ((3*x + 8)*sinh(2*x) + (2*x^2 + 16*(x + 1))*cosh(2*x))/16    
as_ogf(f, 4) returns 1 + 2*z + 5*z^2 + 16*z^3 + 28*z^4 and is of the required type.
 It seems to me it would be worthwhile to include such a function in Sage.
 EDIT: Unfortunately After an edit this does not work. now works also with
 f(x) = (3*x + 8)*sinh(2*x)/4; as_ogf(f, 4)
 and returns 4 + 34z + 163z^2 + 2416z^3 istead of the correct 4+ 24z z^4 + 3z^2 + 16z^3 + 24*z^4. Pari seems to swallow the constant coefficient if it is '0'? How can this be corrected?O(z^5), as desired.