Type conversion (RngIntResElt to RngIntElt)

Open discussion for MAGMA library (Matrix Algebra on GPU and Multicore Architectures)

Type conversion (RngIntResElt to RngIntElt)

Postby Lioth2 » Sat Nov 04, 2017 7:14 am

Hi guys,
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);

This is the actual output I get:
RngIntResElt
RngIntElt
379

pollard(
n: 0
)
>> R:= quo<Integers()|n>;
^
Runtime error in quo< ... >: Illegal empty quotient

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.
Lioth2
 
Posts: 1
Joined: Sat Nov 04, 2017 6:37 am

Re: Type conversion (RngIntResElt to RngIntElt)

Postby mgates3 » Sat Nov 04, 2017 8:44 am

It appears that you are using the MAGMA algebra system:
http://magma.maths.usyd.edu.au/magma/

This forum is for the MAGMA linear algebra library for GPUs and Accelerators:
http://icl.utk.edu/magma/

-mark
mgates3
 
Posts: 753
Joined: Fri Jan 06, 2012 2:13 pm


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