// File: primitiv_s.tst
// Short tests for primitiv lib
LIB "tst.lib";
tst_init();
LIB "primitiv.lib";
// ------------ test of primitive: -------------------
printlevel=3;
ring r=0,x,dp;
primitive(ideal(x2+1));
kill r;
ring r=0,(x,y),dp;
ideal i=x2-2,y2-3;
ideal j=primitive(i);
factorize(j[1]);
ring r1=(0,a),x,lp;
map phi=r,x,a;
string s=string(phi(j)[1]);
execute("minpoly="+s+";");
ideal v=phi(j)[1],phi(j)[2]^2-2,phi(j)[3]^2-3;
v;
if (size(v)>0)
  { "ERROR!!! Result of primitive(i) is not a primitive element!"; }
// else minpoly(a)==0, g_1(a) is squareroot of 2, g_2(a) is squareroot of 3
// as it should be
setring r;
i=x2-3,y2-x;
primitive(i);
kill r;
ring r=3,(x,y,z),dp;
ideal i=x2+1,y3-y-1,z2+yz-1;
primitive(i);
// ------------ test of primitive_extra: -------------
primitive_extra(i);
primitive_extra(ideal(i[1],i[2]));
kill r;
// ------------ test of splitring: -------------------
ring r=0,(x,y),ds;
def R1=splitring(x2-5);
R1;
setring R1;
def R2=splitring(x2-7,a);
setring R2;
erg[1]^2;
R2;
def RR=splitring(y2+1,a);
RR;
kill r,R1,R2,RR;
ring r=(2003,j),(a,b,c,d),dp;
minpoly=j2-2;
def R1=splitring(b3+b2+b-2,list(a,b,c,d,j));
setring R1;
erg;
number(erg[5])^2;
factorize(b3+b2+b-2);
def RR=splitring(c2-2j,list(a2+ja,j,erg[5]));
setring RR;
erg[3]^2;
kill R1,r,RR;
// example by Bernd Martin
LIB"zeroset.lib";
ring R=(0,a),x,lp;
poly f=x4+2;
def T=roots(f);
setring T;
map F;
F[1] = theRoots[1];
F(f);
tst_status(1);$