Hamburger Noether Expansion in the case of several branches
LIB "hnoether.lib";
ring r=0,(x,y),ls;
poly f=(x2-y3)*(x3-y2)*(y2-x2-x3);
list hn=reddevelop(f);
=> // result: 4 branch(es) successfully computed
displayHNE(hn);
=> // Hamburger-Noether development of branch nr.1:
=> HNE[1]=-y+z(0)+1/2*z(0)^2
=> HNE[2]=-x+z(0)
=> // Hamburger-Noether development of branch nr.2:
=> HNE[1]=-y-z(0)-1/2*z(0)^2
=> HNE[2]=-x+z(0)
=> // Hamburger-Noether development of branch nr.3:
=> HNE[1]=-y+z(0)*z(1)
=> HNE[2]=-x+z(1)^2
=> // Hamburger-Noether development of branch nr.4:
=> HNE[1]=-x+z(0)*z(1)
=> HNE[2]=-y+z(1)^2
We can have a closer look on the branches, e.g. on branch nr.4, by
displayInvariants(hn[4]);
==> characteristic exponents : 2,3
==> generators of semigroup : 2,3
==> Puiseux pairs : (3,2)
==> degree of the conductor : 2
==> delta invariant : 1
==> sequence of multiplicities: 2,1