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D.5.3.2 esIdeal
Procedure from library equising.lib (see equising_lib).
- Usage:
esIdeal(f); 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:
list of two ideals:
_[1]: equisingularity ideal of f (in sense of Wahl) _[2]: equisingularity ideal of f with fixed section- 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 degenerated ! → → // → // versal deformation with triv. section → // ===================================== → // → // → // Compute equisingular 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 degenerated ! → → // → // versal deformation with triv. section → // ===================================== → // → // → // Compute equisingular Stratum over Spec(C[t]/t^2) → // ================================================ → // → // finished → // vdim(std(K[1])); → 68 // the latter should be equal to: tau_es(f); → 68 |