I'm very very new to Magma and I'm having some troubles with division between different types. My task is to implement the Pollard p-1 method (factorization method) in Magma in order to find all the prime factors of a given integer.
Basically what I want to do is to find the first prime factor, divide my given integer n by the prime number I just found and repeat the cycle until I found all the prime factors. The problem is that n (my integer) is RngIntElt while t (the prime factor) is RngIntResElt and the division "n div t" always gives me 0 (which is wrong), blocking the next cycle.
This is my code:
Code: Select all
E := 1; B:=17; for j in [2..B] do E:=LCM(E,j); end for; pollard:= function(n) R:= quo<Integers()|n>; a := 2; if (IsPrime(n) eq false) then for j in [1..100] do a := NextPrime(a); if (n mod a) eq 0 then return a; else b := (R!a)^E; g := GCD(n,b-1); if not (g eq 1) and not (g eq n) then t := g; return g; end if; end if; end for; else return n; end if; end function; n := 2*3^40+1; repeat t := pollard(n); Type(t); Type(n); t; n := n div t; until (n eq 1);
Is there some kind of conversion I can make so that the division is performed correctly? I think mine is a noob problem, but I just can't find a working solution. Let me know if you need any more info or if I did some mistakes in posting the discussion.RngIntResElt
>> R:= quo<Integers()|n>;
Runtime error in quo< ... >: Illegal empty quotient