Singular Manual: hodgeIdeals

| #### D.15.9.2 hodgeIdeals Procedure from library `hodge.lib` (see hodge_lib). Usage: hodgeIdeals(f, p [, eng]); f a reduced poly, p a non-negative integer, eng an optional integer. Return: ring Purpose: compute the Hodge ideals of 1070#1070 up to level 23#23, for a reduced hypersurface 267#267. Note: activate the output ring with the `setring` command. In the output ring, the list of ideals `hodge` contains the Hodge ideals of 267#267. The value of `eng` controls the algorithm used for Groebner basis computations. See the `engine` procedure from dmodapp_lib for the available algorithms. Display: If `printlevel`=1, progress debug messages will be printed. Example:
    LIB "hodge.lib";
    ring R = 0,(x,y),dp;
    poly f = y^2-x^3;
    def Ra = hodgeIdeals(f, 2);
    setring Ra; hodge;
    ==> [1]:
    ==>    [1]:
    ==>       [1]:
    ==>          _[1]=1
    ==>       [2]:
    ==>          _[1]=y
    ==>          _[2]=x
    ==>       [3]:
    ==>          _[1]=y^2
    ==>          _[2]=x*y
    ==>          _[3]=x^3
    ==>    [2]:
    ==>       1/6
    ==>    [3]:
    ==>       1
    ==> [2]:
    ==>    [1]:
    ==>       [1]:
    ==>          _[1]=1
    ==>       [2]:
    ==>          _[1]=y
    ==>          _[2]=x^2
    ==>       [3]:
    ==>          _[1]=y^3
    ==>          _[2]=x*y^2
    ==>          _[3]=x^2*y
    ==>          _[4]=x^3+(2*a+1)*y^2
    ==>    [2]:
    ==>       5/6
    ==>    [3]:
    ==>       1
    ==> [3]:
    ==>    [1]:
    ==>       [1]:
    ==>          _[1]=y
    ==>          _[2]=x
    ==>       [2]:
    ==>          _[1]=y^2
    ==>          _[2]=x*y
    ==>          _[3]=x^3
    ==>       [3]:
    ==>          _[1]=y^3
    ==>          _[2]=x^2*y^2
    ==>          _[3]=x^3*y
    ==>          _[4]=x^4+(2*a+1)*x*y^2
    ==>    [2]:
    ==>       1
    ==>    [3]:
    ==>       1

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