AuTra.cin

// AuTra.cin is C++ implementation of function AuTra, id est, the Abel function dor the Trappmann function

/* using namespace std; typedef complex z_type;
 * 1) include 
 * 2) include 
 * 3) include 
 * 4) define DB double
 * 5) define DO(x,y) for(x=0;x<y;x++)
 * 1) include
 * 1) define Re(x) x.real
 * 2) define Im(x) x.imag
 * 3) define I z_type(0.,1.)

z_type arctra(z_type z){return z-Tania(z-1.);} z_type tra(z_type z) {return z+exp(z);}
 * 1) include "tania.cin"
 * 2) include "LambertW.cin"
 * 3) include "SuZex.cin"
 * 4) include "AuZex.cin"

z_type sutra0(z_type z){ return log(suzex(z));} z_type sutra(z_type z){ if( Re(z)<2. ) return sutra0(z); if( Re(z)<3. ) return tra(sutra0(z-1.)); if( Re(z)<4. ) return tra(tra(sutra0(z-2.))); return tra(tra(tra(sutra0(z-3.)))); }

z_type autra0(z_type z) {return auzex(exp(z));} z_type autra(z_type z) { DB x,y,t; x=Re(z); y=fabs(Im(z)); if(y>=M_PI) return autra(arctra(z)) + 1. ;                         if(x<-2.2 ) { t=-1.-x; if( y > M_PI*t/sqrt(1+t*t) ) return autra(arctra(z))+1.; } return auzex(exp(z));}