NTL library

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(I am continuously losing comments... "This comment is forbidden...)

It seems that the C++ NTL library is called by default from sage.

http://doc.sagemath.org/html/en/constructions/polynomials.html

(There is an incomplete sentence using the abbreviation NTL.)

For instance, no my machine, the following code

R.<x> = PolynomialRing( GF(2) )
f = x^15910 + x^7 + x^2 + 1
print "f =", f
for k in range( 1, 100 ):
    for l in range( k, 100 ):
        g = x^k + x^l + 1
        if f.gcd(g) != 1:
            print "g = %s (f,g) = %s" % ( g, f.gcd(g) )

gives a quick result.