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D.15.7.4 nextHodgeIdeal

Procedure from library hodge.lib (see hodge_lib).

Usage:
nextHodgeIdeal(f, I, p); f a poly, I an ideal, p a non-negative integer

Return:
ideal

Purpose:
given the $p$-th Hodge ideal $I$ of $f^\alpha$ compute the $p+1$-th Hodge ideal assuming that
the Hodge filtration of the underlying mixed Hodge module is generated at level less than or equal to $p$.

Example:
 
LIB "hodge.lib";
ring R = 0,(x,y),dp;
poly f = y^2-x^3;
def Ra = hodgeIdeals(f, 2);
setring(Ra);
int p = 1;
nextHodgeIdeal(y^2-x^3, hodge[3][1][p+1], p);
==> _[1]=x^2*y^2
==> _[2]=y^3
==> _[3]=x^3*y
==> _[4]=x^4+(2*a+1)*x*y^2