How can you check if a polynomial is invertible with NTL?

Question

I've searched for hours and have not found an answer. I am working with polynomials modulo another polynomial (so ZZ_pE objects). When I use the method inv(ZZ_pE poly), the result is either the inverse (if it exists), or the following error message:

ZZ_p: division by non-invertible element
Abort trap: 6

I tried using a try/catch:

    while(1)
    {
    random(f);
    f = 2*f + 1;    
        try{
            inv(fi, f);
            break;
        }
        catch(...) {
            // f not invertible
            // Do nothing
        }
    }

but the error message still stops the program. As far as I know there is no isInvertible or similar method. How can I check if a polynomial is invertible?

@Peter Not if the software library being used provides a way to do it. — aschepler, Jul 01 '18 at 02:54
@aschepler - the OP mentioned there is no such method in NTL. That means he's seeking an algorithm. That makes it a math question. — Peter, Jul 01 '18 at 03:48

score 1 · Accepted Answer · answered Jul 03 '18 at 11:50

Checking if a polynomial is invertible in ZZ_pE highly depends on your choice of p and polynomial you use for the modulo. In NTL p don't have to be prime, so ZZ_p does not need to be a field and the polynomial does not need to be irreducable, so ZZ_pE can be anything.

Your solution don't work because NTL throws errors instead of exceptions by default. But you can change this if you compile NTL using the option NTL_EXCEPTIONS=on.
See http://www.shoup.net/ntl/doc/tour-unix.html for more details.

How can you check if a polynomial is invertible with NTL?

1 Answers1