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D.15.7.1 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
 -generators for the
 -filtration on
 truncated up to degree
 in
 .
- Note:
- activate the output ring with the
setring command.
In the output ring, the list Vfilt contains the
-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
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