Singular Manual: nextHodgeIdeal

| #### 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 -th Hodge ideal of compute the -th Hodge ideal assuming that the Hodge filtration of the underlying mixed Hodge module is generated at level less than or equal to . 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

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