#### D.6.12.2 esIdeal

Procedure from library `equising.lib` (see equising_lib).

Usage:
  esIdeal(f[,any]]); f poly

Assume:
  f is a reduced bivariate polynomial, the basering has precisely two variables, is local and no qring, and the characteristic of the ground field does not divide mult(f).

Return:
  if called with only one parameter: list of two ideals,

                _[1]:  equisingularity ideal of f (in sense of Wahl),
                _[2]:  ideal of equisingularity with fixed position of the
                       singularity;

  if called with more than one parameter: list of three ideals,

                _[1]:  equisingularity ideal of f (in sense of Wahl)
                _[2]:  ideal of equisingularity with fixed position of the
                       singularity;
                _[3]:  ideal of all g such that the deformation defined by f+eg
                       (e^2=0) is isomorphic to an equisingular deformation
                       of V(f) with all equimultiple sections being trivial.

Note:
  if some of the above condition is not satisfied then return value is list(0,0).

Example:

    LIB "equising.lib";
    ring r=0,(x,y),ds;
    poly f=x7+y7+(x-y)^2*x2y2;
    list K=esIdeal(f);
    ==> polynomial is Newton degenerate !
    ==>
    ==> //
    ==> // versal deformation with triv. section
    ==> // =====================================
    ==> //
    ==> //
    ==> // Compute equisingularity Stratum over Spec(C[t]/t^2)
    ==> // ===================================================
    ==> //
    ==> // finished
    ==> //
    option(redSB);
    // Wahl's equisingularity ideal:
    std(K[1]);
    ==> _[1]=4x4y-10x2y3+6xy4+21x6+14y6
    ==> _[2]=4x3y2-6x2y3+2xy4+7x6
    ==> _[3]=x2y4-xy5
    ==> _[4]=x7
    ==> _[5]=xy6
    ==> _[6]=y7
    ring rr=0,(x,y),ds;
    poly f=x4+4x3y+6x2y2+4xy3+y4+2x2y15+4xy16+2y17+xy23+y24+y30+y31;
    list K=esIdeal(f);
    ==> polynomial is Newton degenerate !
    ==>
    ==> //
    ==> // versal deformation with triv. section
    ==> // =====================================
    ==> //
    ==> //
    ==> // Compute equisingularity Stratum over Spec(C[t]/t^2)
    ==> // ===================================================
    ==> //
    ==> // finished
    ==> //
    vdim(std(K[1]));
    ==> 68
    // the latter should be equal to:
    tau_es(f);
    ==> 68

See also: esStratum; tau_es.

User manual for Singular version 4.4.1, 2025, generated by texi2html.