LIB "tst.lib"; tst_init();
  ring r=0,(x,y,z),ds;
  ideal i=x^4-y*z^2,x*y-z^3,y^2-x^3*z;  // the space curve singularity
  qhweight(i);
  // The given space curve singularity is quasihomogeneous. Hence we can pass
  // to the polynomial ring.
  ring rr=0,(x,y,z),dp;
  ideal i=imap(r,i);
  resolution ires=mres(i,0);
  ires;
  // From the structure of the resolution, we see that the Cohen-Macaulay
  // type of the given singularity is 2
  //
  // Let us now look for the branches using the primdec library.
  LIB "primdec.lib";
  primdecSY(i);
  def li=_[2];
  ideal i2=li[2];       // call the second ideal i2
  // The curve seems to have 2 branches by what we computed using the
  // algorithm of Shimoyama-Yokoyama.
  // Now the same computation by the Gianni-Trager-Zacharias algorithm:
  primdecGTZ(i);
  // Having computed the primary decomposition in 2 different ways and
  // having obtained the same number of branches, we might expect that the
  // number of branches is really 2, but we can check this by formulae
  // for the invariants of space curve singularities:
  //
  // mu = tau - t + 1 (for quasihomogeneous curve singularities)
  // where mu denotes the Milnor number, tau the Tjurina number and
  // t the Cohen-Macaulay type
  //
  // mu = 2 delta - r + 1
  // where delta denotes the delta-Invariant and r the number of branches
  //
  // tau can be computed by using the corresponding procedure T1 from
  // sing.lib.
  setring r;
  LIB "sing.lib";
  T_1(i);
  setring rr;
  // Hence tau is 13 and therefore mu is 12. But then it is impossible that
  // the singularity has two branches, since mu is even and delta is an
  // integer!
  // So obviously, we did not decompose completely. Because the first branch
  // is smooth, only the second ideal can be the one which can be decomposed
  // further.
  // Let us now consider the normalization of this second ideal i2.
  LIB "normal.lib";
  normal(i2);
  def rno=_[1][1];
  setring rno;
  norid;
  // The ideal is generated by a polynomial in one variable of degree 4 which
  // factors completely into 4 polynomials of type T(2)+a.
  // From this, we know that the ring of the normalization is the direct sum of
  // 4 polynomial rings in one variable.
  // Hence our original curve has these 4 branches plus a smooth one
  // which we already determined by primary decomposition.
  // Our final result is therefore: 5 branches.
tst_status(1);$