/*
*  Primality with Fractions (Gaussian)
*
*  Author	: Rosario Turco
*  Date		: 23/12/2009 
*  Revision	: 1.0           
*/


/*
*  Period of a fraction with
*  gaussian function
*
*
*/
GaussN(n)= local(g=0, r=1); { 

 while( Mod(n,2) == 0, n = n/2;);
 while( Mod(n,5) == 0, n = n/5;);

 while( g == 0 | r != 1, 
        r = Mod(( 10 * r), n);
        g = g + 1;
        
 ); 

 return(g);  

}

/*
*  IsComposite ?
*  -1 Boh
*   1 Yes
*   0 No (it's a prime number)
*   
*
*/
isCompN(n)= local(g=0, status=-1); { 

 g = GaussN(n);
 print("gaussiano(",n,") = ", g);

 if( g == n-1, 
     status=0; 
     print("No, it's a prime number!");
     return(status);
 ); 
 if( g != 1,
     if( frac((n-1)/g) != 0.0, status = 1;);
 );      

 if( status == 1, print("Yes, it's a composite number!"););
 

 return(status);  

}


/*
*  IsMyPrime ?
*   1 Yes
*   0 No 
*   
*
*/
isMyPrime(n)= local(status=0); { 

 if( eulerphi(n) == n-1, status=1;);
 return(status);  

}

/*
*
*  AntiPeriod of a fraction with  
*
*/
AntPerN(n)= local(d2=0, d5=0); { 

 while( Mod(n,2) == 0, n = n/2; d2=d2+1);
 while( Mod(n,5) == 0, n = n/5; d5=d5+1);

 return(max(d2,d5));  

}