D.5.5.18 separateHNE

Procedure from library hnoether.lib (see hnoether_lib).

Usage:

separateHNE(hne1,hne2); hne1, hne2 lists

Assume:

hne1, hne2 are HNEs (=output of develop(f), extdevelop(develop(f),n), or one entry in the list hne in the ring created by hnexpansion(f[,"ess"]).

Return:

number of quadratic transformations needed to separate both curves (branches).

Example:

LIB "hnoether.lib";
int p=printlevel; printlevel=-1;
ring r=0,(x,y),dp;
list hne1=develop(x);
list hne2=develop(x+y);
list hne3=develop(x+y2);
separateHNE(hne1,hne2);  // two transversal lines
→ 1
separateHNE(hne1,hne3);  // one quadratic transform. gives 1st example
→ 2
printlevel=p;

See also: develop; displayMultsequence; hnexpansion; multsequence.