{ differential relation
  d(l) = (1-e*cos(E)) * d(E) 
  secular terms
  F_1*(1-e*cos(E)) without E in argument }
unit unfunons ; { to find secular terms from F_1 }
interface       { perturbation function prefon1.txt }
{ to select secular terms to prefos1.txt }
procedure secufone ;
implementation
uses
  untypvar , { types global variables }
  unrowmul , { proc MultForRow }
  unwrtext ; { proc texttorow rowtotext }
{ simple row for 1-e*cos(E) }
procedure sipmler ( var  mecone  : word ;      { two terms }
                    var  rowone  : TRowPtr ) ; { to rowone }
begin
  mecone:=2; { two terms }
  rowone^[1]:=recnul; { default untypvar but cosinus }
  rowone^[2]:=recnul; { default untypvar but cosinus }
  rowone^[1].amp[1]:=+1.0; { amplitude the first term }
  rowone^[2].amp[1]:=-1.0; { amplitude the second term }
  rowone^[2].mec[2]:=+1;   { power e^1 }
  rowone^[2].mar[2]:=+1;   { argument angle E }
end;
{ to select secular terms to prefol1.txt
  to obtain generating function S_1 to write to prefos1.txt }
procedure secufone ;
var
  m  : word ; { count for terms }
begin
  maxsum:=numsum; { for giant planet global untypvar } 
  sipmler(mecone,rowone); { simple row for 1-e*cos(E) }
  texttorow(1,'prefon',mectwo,rowtwo); { all terms for F_1 function }
  mectre:=0;        { initial nullo terms }
  MultForRow(+1.0); { rowone * rowtwo = rowtre result }
  mectmp:=0; { rowtmp^ to keep our secular terms }
  for m:=1 to mectre do              { for each term }
    if  rowtre^[m].mar[2] = 0  then  { now without E }
      begin
        mectmp:=mectmp+1; { the next secular term }
        rowtmp^[mectmp]:=rowtre^[m]; { to keep }
      end;
  writeln('there are',mectmp:10,'  secular terms');
  rowtotext(1,mectmp,rowtmp,'prefol'); { to this file secular }
  { to integrate current short periodic term
    Int [ a*cos(kE+b) ] = (1/k)*a*sin(kE+b)  thus
    to change cosinus by sinus and to divide amplitude by k }
  mectmp:=0; { rowtmp^ to obtain generating function S_1 by integration }
  for m:=1 to mectre do               { for each term }
    if  rowtre^[m].mar[2] <> 0  then  { now with E short periodic terms }
      begin                           { to integrate }
        mectmp:=mectmp+1; { the next term to function S_1 }
        rowtmp^[mectmp]:=rowtre^[m]; { to keep but with changing }
        with  rowtmp^[mectmp]  do    { with current term }
          begin                      { to change }
            amp[1]:=amp[1]/mar[2];   { amplitude by (1/k) mar[2]*E }
            mec[13]:=mec[13]-1;      { power for n (1/n) }
            if  fcs = 'S'            { to verify trigonometric }
              then          { may be terms with sinus function }
                begin              { to chanage    
                  amp[1]:=-amp[1]; { minus after integration }
                  fcs:='C';        { to change function }
                end         { may be sunus }
              else        { but only cosinus } 
                fcs:='S'; { only to change function }
          end;
      end;
  writeln('there are',mectmp:10,'  terms in generating function S_1');
  rowtotext(1,mectmp,rowtmp,'prefos'); { this file for function S_1 }
end;
end.