These functions represent just a possible solution to the exercise.

EXERCISE 2
---------------------------

---------------------------
Point (1)
---------------------------

PrimitiveRoot(a,n) = {  my(primroot=0,nprimes=0);
				forprime(p=1,n,
					nprimes=nprimes+1;
					if(a%p!=0 && znorder(Mod(a,p))==p-1,
						primroot=primroot+1);
				);
				return(primroot/nprimes*1.0);

}

---------------------------
Point (2)
---------------------------

findIntersection( f1 , f2 ) = {
    subfieldsOfKPols = nfsubfields(f1);
    if(poldegree(f1) > poldegree(f2), return(findIntersection(f2, f1)));
    myAnswer = x;
    for(i=1, #subfieldsOfKPols, 
        currentSubfieldPol = subfieldsOfKPols[i][1];
        isSubfieldOfL = nfisincl(currentSubfieldPol, f2);
        if( #isSubfieldOfL != 0,
          myAnswer = currentSubfieldPol;
        );
    );
    return(myAnswer);
}


---------------------------
Point (3)
---------------------------


SplittingType(K1,K2,n) = {forprime(p=1,n,
					v1=[];
					v2=[];
					dec1=idealprimedec(K1,p);
					dec2=idealprimedec(K2,p);
					for(i=1,#dec1,v1=concat(v1,[dec1[i].f]));
					for(i=1,#dec2,v2=concat(v2,[dec2[i].f]));
					print(p,vecsort(v1),vecsort(v2));
					);
}