Input: 
n=integer to be factored

Output:
A factorisation of n



pollard(n)=x=Mod(random,n);y=x;d=1;\
while(d==1,\
 for(j=1,10,x=x^2+2;y=y^2+2;y=y^2+2;d=d*(y-x));\
 d=gcd(lift(d),n));\
print(d,"*",n/d)





Input: 
n=integer to be factored
j=number of iterates 

Output: 
[j, 1] if no non trivial factor is found
[number of iterates which produced the first  non-trivial gcd, gcd]



pollard(n,j)=x=Mod(random,n);y=x;d=1;tel=0;t=j;\
while(tel<j,\
x=x^2+2;y=y^2+2;y=y^2+2;d= gcd(lift(y-x),n);tel=tel+1;\
if(d>1,t=tel;tel=j));\
print([t,d])






Input: 
n=integer to be factored

Output:
Initial point  
A factorisation of n
Number of iterates that produced the factorisation 

 
 
pollard2(n)=x=Mod(random,n);print("starting point is ", lift(x));y=x;d=1;ii=0;\
while(d==1,\
ii=ii+1;x=x^2+2;y=y^2+2;y=y^2+2;d=d*(y-x);\
   d=gcd(lift(d),n));\
print(ii," steps: ",d,"*",n/d)