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D.15.6.1 Vfiltration

Procedure from library hodge.lib (see hodge_lib).

Usage:
Vfiltration(f, p [, eng]); f a poly, p a non-negative integer, eng an optional integer.

Return:
ring

Purpose:
compute $R$-generators for the $V$-filtration on $R_f f^s$ truncated up to degree $p$ in $\partial_t$.

Note:
activate the output ring with the setring command.
In the output ring, the list Vfilt contains the $V$-filtration.
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 D = Vfiltration(f, 1);
setring D; Vfilt;
==> [1]:
==>    [1]:
==>       [1]:
==>          -1
==>       [2]:
==>          -Dt*y
==>       [3]:
==>          -Dt*x
==>    [2]:
==>       1/6
==>    [3]:
==>       1
==> [2]:
==>    [1]:
==>       [1]:
==>          -Dt*y
==>       [2]:
==>          -1
==>       [3]:
==>          -Dt*x^2
==>    [2]:
==>       5/6
==>    [3]:
==>       1
==> [3]:
==>    [1]:
==>       [1]:
==>          -2*Dt*y^2+1
==>       [2]:
==>          -Dt*x*y
==>       [3]:
==>          -y
==>       [4]:
==>          -x
==>       [5]:
==>          -3*Dt*x^3-1
==>    [2]:
==>       1
==>    [3]:
==>       1