D.5.5.6 displayHNE

Procedure from library hnoether.lib (see hnoether_lib).

Usage:

displayHNE(L[,n]); L list, n int

Assume:

L is the output of develop(f), or of exdevelop(f,n), or of hnexpansion(f[,"ess"]), or (one entry in) the list hne in the ring created by hnexpansion(f[,"ess"]).

Return:

- if only one argument is given, no return value, but display an ideal HNE of the following form:

HNE[1]=-y+[]*z(0)^1+[]*z(0)^2+...+z(0)^<>*z(1) HNE[2]=-x+ []*z(1)^2+...+z(1)^<>*z(2) HNE[3]= []*z(2)^2+...+z(2)^<>*z(3) ....... .......................... HNE[r+1]= []*z(r)^2+[]*z(r)^3+......

where x,y are the first 2 variables of the basering. The values of [] are the coefficients of the Hamburger-Noether matrix, the values of <> are represented by x in the HN-matrix.
- if a second argument is given, create and export a new ring with name displayring containing an ideal HNE as described above.
- if L corresponds to the output of hnexpansion(f[,"ess"]) or to the list hne in the ring created by hnexpansion(f[,"ess"]), displayHNE(L[,n]) shows the HNE’s of all branches of f in the form described above. The optional parameter is then ignored.

Note:

The 1st line of the above ideal (i.e., HNE[1]) means that y=[]*z(0)^1+..., the 2nd line (HNE[2]) means that x=[]*z(1)^2+..., so you can see which indeterminate corresponds to which line (it’s also possible that x corresponds to the 1st line and y to the 2nd).

Example:

LIB "hnoether.lib";
ring r=0,(x,y),dp;
poly f=x3+2xy2+y2;
list hn=develop(f);
displayHNE(hn);
→ HNE[1]=-y+z(0)*z(1)
→ HNE[2]=-x-z(1)^2

See also: develop; hnexpansion.