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

RngIntElt

379

pollard(

n: 0

)

>> R:= quo<Integers()|n>;

^

Runtime error in quo< ... >: Illegal empty quotient