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D.15.6.2 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 $f^\\ alpha$ up to level $p$, for a reduced hypersurface $f$.

Note:
activate the output ring with the setring command.
In the output ring, the list of ideals hodge contains the Hodge ideals of $f$.
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