D.6.12.4 isEquising

Usage:

isEquising(F[,m,L]); F poly, m int, L list

Assume:

F defines a deformation of a reduced bivariate polynomial f and the characteristic of the basering does not divide mult(f).
If nv is the number of variables of the basering, then the first nv-2 variables are the deformation parameters.
If the basering is a qring, ideal(basering) must only depend on the deformation parameters.

Compute:

tests if the given family is equisingular along the trivial section.

Return:

int: 1 if the family is equisingular, 0 otherwise.

Note:

L is supposed to be the output of hnexpansion (with the given ordering of the variables appearing in f).
If m is given, the family is considered over A/maxideal(m).
This procedure uses execute or calls a procedure using execute. printlevel>=2 displays additional information.

LIB "equising.lib";
ring r = 0,(a,b,x,y),ds;
poly F = (x2+2xy+y2+x5)+ay3+bx5;
isEquising(F);
==> 0
ideal I = ideal(a);
qring q = std(I);
poly F = imap(r,F);
isEquising(F);
==> 1
ring rr=0,(A,B,C,x,y),ls;
poly f=x7+y7+(x-y)^2*x2y2;
poly F=f+A*y*diff(f,x)+B*x*diff(f,x);
isEquising(F);
==> 0
isEquising(F,2);    // computation over  Q[a,b] / <a,b>^2
==> 1