paramBpoly(RingElement,String) -- compute the list of all possible Bernstein-Sato polynomials for a polynomial with parametric coefficients

Synopsis

Usage:
paramBpoly(f,filename)
Function: paramBpoly
Inputs:
- f, a ring element, a polynomial in Weyl algebra A_n(Q)
- filename, a string, the base name for the output files
Optional inputs:
- GroundField => ..., -- characteristic for modular computation
Outputs:
- a list, all possible Bernstein-Sato polynomials

Description

i1 : A =  (QQ [a,b,c]) [x, y, Dx, Dy, WeylAlgebra => {x=>Dx, y=>Dy}]

o1 = A

o1 : PolynomialRing

i2 : paramBpoly(a*x^2 + b*x*y + c*y^2, "quadratic")
GC Warning: Finalization cycle involving 300c990
GC Warning: Finalization cycle involving 382b330
GC Warning: Finalization cycle involving 34b6770
GC Warning: Finalization cycle involving 1023110
GC Warning: Finalization cycle involving 4031550
GC Warning: Finalization cycle involving 3e1eaa0
GC Warning: Finalization cycle involving 3df2110
GC Warning: Finalization cycle involving 3e1e000
GC Warning: Finalization cycle involving 317fcc0
GC Warning: Finalization cycle involving 300c990
GC Warning: Finalization cycle involving 369dcc0
GC Warning: Finalization cycle involving 3481770
GC Warning: Finalization cycle involving 382b330
GC Warning: Finalization cycle involving 4034770
GC Warning: Finalization cycle involving 34b6770
GC Warning: Finalization cycle involving 1023110
GC Warning: Finalization cycle involving 4031550
GC Warning: Finalization cycle involving 3e1eaa0
GC Warning: Finalization cycle involving 3b02ee0
GC Warning: Finalization cycle involving 3df2110
GC Warning: Finalization cycle involving 3e1e000
GC Warning: Finalization cycle involving 34fb440
GC Warning: Finalization cycle involving 317fcc0
GC Warning: Finalization cycle involving 42de220
GC Warning: Finalization cycle involving 300c990
GC Warning: Finalization cycle involving 369dcc0
GC Warning: Finalization cycle involving 4677880
GC Warning: Finalization cycle involving 3481770
GC Warning: Finalization cycle involving 34a9660
GC Warning: Finalization cycle involving 382b330
GC Warning: Finalization cycle involving 4034770
GC Warning: Finalization cycle involving 34b6770
GC Warning: Finalization cycle involving 1023110
GC Warning: Finalization cycle involving 4031550
GC Warning: Finalization cycle involving 3e1e990
GC Warning: Finalization cycle involving 3e1eaa0
GC Warning: Finalization cycle involving 3b02ee0
GC Warning: Finalization cycle involving 3df2110
GC Warning: Finalization cycle involving 3e1e000
GC Warning: Finalization cycle involving 34fb440
GC Warning: Finalization cycle involving 317fcc0
GC Warning: Finalization cycle involving 42de220
GC Warning: Finalization cycle involving 300c990
GC Warning: Finalization cycle involving 369dcc0
GC Warning: Finalization cycle involving 4677880
GC Warning: Finalization cycle involving 3481770
GC Warning: Finalization cycle involving 34a9660
GC Warning: Finalization cycle involving 3c43880
GC Warning: Finalization cycle involving 4324770
GC Warning: Finalization cycle involving 382b330
GC Warning: Finalization cycle involving 4034770
GC Warning: Finalization cycle involving 34b6770
GC Warning: Finalization cycle involving 1023110
GC Warning: Finalization cycle involving 4031550
GC Warning: Finalization cycle involving 43d9220
GC Warning: Finalization cycle involving 3e1e990
GC Warning: Finalization cycle involving 3e1eaa0
GC Warning: Finalization cycle involving 42eddd0
GC Warning: Finalization cycle involving 3b02ee0
GC Warning: Finalization cycle involving 3df2110
GC Warning: Finalization cycle involving 3e1e000
GC Warning: Finalization cycle involving 34fb440
GC Warning: Finalization cycle involving 317fcc0
GC Warning: Finalization cycle involving 42de770
GC Warning: Finalization cycle involving 42de220
GC Warning: Finalization cycle involving 300c990
GC Warning: Finalization cycle involving 362dcc0
GC Warning: Finalization cycle involving 369dcc0
GC Warning: Finalization cycle involving 4677880
GC Warning: Finalization cycle involving 3481550
GC Warning: Finalization cycle involving 3481770
GC Warning: Finalization cycle involving 438b990
GC Warning: Finalization cycle involving 34a9660
GC Warning: Finalization cycle involving 3c43880
GC Warning: Finalization cycle involving 4324770
GC Warning: Finalization cycle involving 382b330
GC Warning: Finalization cycle involving 382b550
GC Warning: Finalization cycle involving 4034770
GC Warning: Finalization cycle involving 34b6770
GC Warning: Finalization cycle involving 1023110
GC Warning: Finalization cycle involving 4031550
GC Warning: Finalization cycle involving 43d9220
GC Warning: Finalization cycle involving 3e1e990
GC Warning: Finalization cycle involving 3e1eaa0
GC Warning: Finalization cycle involving 42eddd0
GC Warning: Finalization cycle involving 3b02ee0
GC Warning: Finalization cycle involving 3df2110
GC Warning: Finalization cycle involving 3e1e000
GC Warning: Finalization cycle involving 34fb440
GC Warning: Finalization cycle involving 317fcc0
GC Warning: Finalization cycle involving 42de770
GC Warning: Finalization cycle involving 42de220
GC Warning: Finalization cycle involving 300c990
GC Warning: Finalization cycle involving 362dcc0
GC Warning: Finalization cycle involving 369dcc0
GC Warning: Finalization cycle involving 4677880
GC Warning: Finalization cycle involving 3481550
GC Warning: Finalization cycle involving 3481770
GC Warning: Finalization cycle involving 438b990
GC Warning: Finalization cycle involving 34a9660
GC Warning: Finalization cycle involving 3c43880
GC Warning: Finalization cycle involving 4324770
GC Warning: Finalization cycle involving 382b330
GC Warning: Finalization cycle involving 4300220
GC Warning: Finalization cycle involving 382b550
GC Warning: Finalization cycle involving 4034770
GC Warning: Finalization cycle involving 34b6770
GC Warning: Finalization cycle involving 1023110
GC Warning: Finalization cycle involving 4031550
GC Warning: Finalization cycle involving 43d9220
GC Warning: Finalization cycle involving 3e1e990
GC Warning: Finalization cycle involving 3e1eaa0
GC Warning: Finalization cycle involving 42eddd0
GC Warning: Finalization cycle involving 3b02ee0
GC Warning: Finalization cycle involving 3df2110
GC Warning: Finalization cycle involving 3e1e000
GC Warning: Finalization cycle involving 34fb440
GC Warning: Finalization cycle involving 317fcc0
GC Warning: Finalization cycle involving 42de770
GC Warning: Finalization cycle involving 42de220
GC Warning: Finalization cycle involving 300c990
GC Warning: Finalization cycle involving 362dcc0
GC Warning: Finalization cycle involving 369dcc0
GC Warning: Finalization cycle involving 4677880
GC Warning: Finalization cycle involving 3481550
GC Warning: Finalization cycle involving 3481770
GC Warning: Finalization cycle involving 438b990
GC Warning: Finalization cycle involving 34a9660
GC Warning: Finalization cycle involving 3c43880
GC Warning: Finalization cycle involving 4300660
GC Warning: Finalization cycle involving 4324770
GC Warning: Finalization cycle involving 4300550
GC Warning: Finalization cycle involving 382b330
GC Warning: Finalization cycle involving 4300220
GC Warning: Finalization cycle involving 382b550
GC Warning: Finalization cycle involving 4034770
GC Warning: Finalization cycle involving 2004bb0
GC Warning: Finalization cycle involving 34b6770
GC Warning: Finalization cycle involving 1023110
GC Warning: Finalization cycle involving 4031550
GC Warning: Finalization cycle involving 43d9220
GC Warning: Finalization cycle involving 3e1e990
GC Warning: Finalization cycle involving 3e1eaa0
GC Warning: Finalization cycle involving 42eddd0
GC Warning: Finalization cycle involving 3b02ee0
GC Warning: Finalization cycle involving 3df2110
GC Warning: Finalization cycle involving 3e1e000
GC Warning: Finalization cycle involving 43d9aa0
GC Warning: Finalization cycle involving 34fb440
GC Warning: Finalization cycle involving 317fcc0
GC Warning: Finalization cycle involving 42de770
GC Warning: Finalization cycle involving 42de220
GC Warning: Finalization cycle involving 300c990
GC Warning: Finalization cycle involving 362dcc0
GC Warning: Finalization cycle involving 369dcc0
GC Warning: Finalization cycle involving 4677880
GC Warning: Finalization cycle involving 2bb2220
GC Warning: Finalization cycle involving 438bcc0
GC Warning: Finalization cycle involving 3481550
GC Warning: Finalization cycle involving 3481770
GC Warning: Finalization cycle involving 438b990
GC Warning: Finalization cycle involving 34a9660
GC Warning: Finalization cycle involving 3c43880
GC Warning: Finalization cycle involving 4300660
GC Warning: Finalization cycle involving 4324770
GC Warning: Finalization cycle involving 4300550
GC Warning: Finalization cycle involving 382b330
GC Warning: Finalization cycle involving 4300220
GC Warning: Finalization cycle involving 382b550
GC Warning: Finalization cycle involving 4034770
GC Warning: Finalization cycle involving 2004bb0
GC Warning: Finalization cycle involving 34b6770
GC Warning: Finalization cycle involving 1023110
GC Warning: Finalization cycle involving 4031550
GC Warning: Finalization cycle involving 43d9220
GC Warning: Finalization cycle involving 3e1e990
GC Warning: Finalization cycle involving 3e1eaa0
GC Warning: Finalization cycle involving 42eddd0
GC Warning: Finalization cycle involving 3b02ee0
GC Warning: Finalization cycle involving 3df2110
GC Warning: Finalization cycle involving 3e1e000
GC Warning: Finalization cycle involving 43d9aa0
GC Warning: Finalization cycle involving 34fb440
GC Warning: Finalization cycle involving 317fcc0
GC Warning: Finalization cycle involving 42de770
GC Warning: Finalization cycle involving 42de220
GC Warning: Finalization cycle involving 300c990
GC Warning: Finalization cycle involving 362dcc0
GC Warning: Finalization cycle involving 369dcc0
GC Warning: Finalization cycle involving 4677880
GC Warning: Finalization cycle involving 2bb2220
GC Warning: Finalization cycle involving 438bcc0
GC Warning: Finalization cycle involving 3481550
GC Warning: Finalization cycle involving 3481770
GC Warning: Finalization cycle involving 438b990
GC Warning: Finalization cycle involving 34a9660
GC Warning: Finalization cycle involving 3c43880
GC Warning: Finalization cycle involving 4300660
GC Warning: Finalization cycle involving 4324770
GC Warning: Finalization cycle involving 4300550
GC Warning: Finalization cycle involving 382b330
GC Warning: Finalization cycle involving 4300220
GC Warning: Finalization cycle involving 18d7550
GC Warning: Finalization cycle involving 382b550
GC Warning: Finalization cycle involving 4034770
GC Warning: Finalization cycle involving 2004bb0
GC Warning: Finalization cycle involving 34b6770
GC Warning: Finalization cycle involving 1023110
GC Warning: Finalization cycle involving 4031550
GC Warning: Finalization cycle involving 43d9220
GC Warning: Finalization cycle involving 3e1e990
GC Warning: Finalization cycle involving 3e1eaa0
GC Warning: Finalization cycle involving 42eddd0
GC Warning: Finalization cycle involving 3b02ee0
GC Warning: Finalization cycle involving 3df2110
GC Warning: Finalization cycle involving 3e1e000
GC Warning: Finalization cycle involving 43d9aa0
GC Warning: Finalization cycle involving 34fb440
GC Warning: Finalization cycle involving 317fcc0
GC Warning: Finalization cycle involving 46eedd0
GC Warning: Finalization cycle involving 42de770
GC Warning: Finalization cycle involving 46e6ee0
GC Warning: Finalization cycle involving 42de220
GC Warning: Finalization cycle involving 300c990
GC Warning: Finalization cycle involving 362dcc0
GC Warning: Finalization cycle involving 369dcc0
GC Warning: Finalization cycle involving 4677880
GC Warning: Finalization cycle involving 2bb2220
GC Warning: Finalization cycle involving 438bcc0
GC Warning: Finalization cycle involving 3481550
GC Warning: Finalization cycle involving 3481770
GC Warning: Finalization cycle involving 438b990
GC Warning: Finalization cycle involving 34a9660
GC Warning: Finalization cycle involving 3c43880
GC Warning: Finalization cycle involving 4300660
GC Warning: Finalization cycle involving 4324770
GC Warning: Finalization cycle involving 4300550
GC Warning: Finalization cycle involving 382b330
GC Warning: Finalization cycle involving 4300220
GC Warning: Finalization cycle involving 18d7550
GC Warning: Finalization cycle involving 382b550
GC Warning: Finalization cycle involving 4034770
GC Warning: Finalization cycle involving 2004bb0
GC Warning: Finalization cycle involving 34b6770
GC Warning: Finalization cycle involving 1023110
GC Warning: Finalization cycle involving 4031550
GC Warning: Finalization cycle involving 43d9220
GC Warning: Finalization cycle involving 3e1e990
GC Warning: Finalization cycle involving 3e1eaa0
GC Warning: Finalization cycle involving 42eddd0
GC Warning: Finalization cycle involving 3b02ee0
GC Warning: Finalization cycle involving 3df2110
GC Warning: Finalization cycle involving 3e1e000
GC Warning: Finalization cycle involving 43d9aa0
GC Warning: Finalization cycle involving 34fb440
GC Warning: Finalization cycle involving 317fcc0
GC Warning: Finalization cycle involving 46eedd0
GC Warning: Finalization cycle involving 42de770
GC Warning: Finalization cycle involving 46e6ee0
GC Warning: Finalization cycle involving 42de220
GC Warning: Finalization cycle involving 300c990
GC Warning: Finalization cycle involving 362dcc0
GC Warning: Finalization cycle involving 369dcc0
GC Warning: Finalization cycle involving 4677880
GC Warning: Finalization cycle involving 2bb2220
GC Warning: Finalization cycle involving 438bcc0
GC Warning: Finalization cycle involving 3481550
GC Warning: Finalization cycle involving 3481770
GC Warning: Finalization cycle involving 438b990
GC Warning: Finalization cycle involving 34a9660
GC Warning: Finalization cycle involving 3c43880
GC Warning: Finalization cycle involving 4300660
GC Warning: Finalization cycle involving 4324770
GC Warning: Finalization cycle involving 4300550
GC Warning: Finalization cycle involving 382b330
GC Warning: Finalization cycle involving 4300220
GC Warning: Finalization cycle involving 3c43cc0
GC Warning: Finalization cycle involving 18d7550
GC Warning: Finalization cycle involving 382b550
GC Warning: Finalization cycle involving 4034770
GC Warning: Finalization cycle involving 36f2550
GC Warning: Finalization cycle involving 4058aa0
GC Warning: Finalization cycle involving 2004bb0
GC Warning: Finalization cycle involving 34b6770
GC Warning: Finalization cycle involving 1023110
GC Warning: Finalization cycle involving 3b02770
GC Warning: Finalization cycle involving 4031550
GC Warning: Finalization cycle involving 43d9220
GC Warning: Finalization cycle involving 3e1e990
GC Warning: Finalization cycle involving 3e1eaa0
GC Warning: Finalization cycle involving 42eddd0
GC Warning: Finalization cycle involving 3b02ee0
GC Warning: Finalization cycle involving 3df2110
GC Warning: Finalization cycle involving 3e1e000
GC Warning: Finalization cycle involving 43d9aa0
GC Warning: Finalization cycle involving 34fb440
GC Warning: Finalization cycle involving 317fcc0
GC Warning: Finalization cycle involving 46eedd0
GC Warning: Finalization cycle involving 42de770
GC Warning: Finalization cycle involving 46e6ee0
GC Warning: Finalization cycle involving 42de220
GC Warning: Finalization cycle involving 300c990
GC Warning: Finalization cycle involving 362dcc0
GC Warning: Finalization cycle involving 4283440
GC Warning: Finalization cycle involving 369dcc0
GC Warning: Finalization cycle involving 4677880
GC Warning: Finalization cycle involving 4283000
GC Warning: Finalization cycle involving 2bb2220
GC Warning: Finalization cycle involving 4677990
GC Warning: Finalization cycle involving 438bcc0
GC Warning: Finalization cycle involving 3481550
GC Warning: Finalization cycle involving 3481770
GC Warning: Finalization cycle involving 438b990
GC Warning: Finalization cycle involving 34a9660
GC Warning: Finalization cycle involving 3c43880
GC Warning: Finalization cycle involving 4300660
GC Warning: Finalization cycle involving 351eaa0
GC Warning: Finalization cycle involving 4324770
GC Warning: Finalization cycle involving 4300550
GC Warning: Finalization cycle involving 382b330
GC Warning: Finalization cycle involving 4300220
GC Warning: Finalization cycle involving 3c43cc0
GC Warning: Finalization cycle involving 18d7550
GC Warning: Finalization cycle involving 382b550
GC Warning: Finalization cycle involving 4034770
GC Warning: Finalization cycle involving 36f2550
GC Warning: Finalization cycle involving 4058aa0
GC Warning: Finalization cycle involving 2004bb0
GC Warning: Finalization cycle involving 34b6770
GC Warning: Finalization cycle involving 1023110
GC Warning: Finalization cycle involving 3b02770
GC Warning: Finalization cycle involving 4031550
GC Warning: Finalization cycle involving 43d9220
GC Warning: Finalization cycle involving 3e1e990
GC Warning: Finalization cycle involving 3e1eaa0
GC Warning: Finalization cycle involving 42eddd0
GC Warning: Finalization cycle involving 3b02ee0
GC Warning: Finalization cycle involving 3df2110
GC Warning: Finalization cycle involving 3e1e000
GC Warning: Finalization cycle involving 43d9aa0
GC Warning: Finalization cycle involving 34fb440
GC Warning: Finalization cycle involving 317fcc0
GC Warning: Finalization cycle involving 46eedd0
GC Warning: Finalization cycle involving 42de770
GC Warning: Finalization cycle involving 46e6ee0
GC Warning: Finalization cycle involving 42de220
GC Warning: Finalization cycle involving 300c990
GC Warning: Finalization cycle involving 362dcc0
GC Warning: Finalization cycle involving 4283440
GC Warning: Finalization cycle involving 369dcc0
GC Warning: Finalization cycle involving 4677880
GC Warning: Finalization cycle involving 4283000
GC Warning: Finalization cycle involving 2bb2220
GC Warning: Finalization cycle involving 4677990
GC Warning: Finalization cycle involving 438bcc0
GC Warning: Finalization cycle involving 3481550
GC Warning: Finalization cycle involving 3481770
GC Warning: Finalization cycle involving 438b990
GC Warning: Finalization cycle involving 34a9660
GC Warning: Finalization cycle involving 3c43880
GC Warning: Finalization cycle involving 4300660
GC Warning: Finalization cycle involving 351eaa0
GC Warning: Finalization cycle involving 4324770
GC Warning: Finalization cycle involving 4300550
GC Warning: Finalization cycle involving 382b330
GC Warning: Finalization cycle involving 4300220
GC Warning: Finalization cycle involving 3c43cc0
GC Warning: Finalization cycle involving 18d7550
GC Warning: Finalization cycle involving 382b550
GC Warning: Finalization cycle involving 2004660
GC Warning: Finalization cycle involving 4034770
GC Warning: Finalization cycle involving 3b47110
GC Warning: Finalization cycle involving 3b47ee0
GC Warning: Finalization cycle involving 36f2550
GC Warning: Finalization cycle involving 4058aa0
GC Warning: Finalization cycle involving 2004bb0
GC Warning: Finalization cycle involving 34b6770
GC Warning: Finalization cycle involving 1023110
GC Warning: Finalization cycle involving 3b02770
GC Warning: Finalization cycle involving 4031550
GC Warning: Finalization cycle involving 43d9220
GC Warning: Finalization cycle involving 3e1e990
GC Warning: Finalization cycle involving 3e1eaa0
GC Warning: Finalization cycle involving 42eddd0
GC Warning: Finalization cycle involving 3b02ee0
GC Warning: Finalization cycle involving 3df2110
GC Warning: Finalization cycle involving 3e1e000
GC Warning: Finalization cycle involving 43d9aa0
GC Warning: Finalization cycle involving 34fb440
GC Warning: Finalization cycle involving 317fcc0
GC Warning: Finalization cycle involving 46eedd0
GC Warning: Finalization cycle involving 42de770
GC Warning: Finalization cycle involving 46e6ee0
GC Warning: Finalization cycle involving 42de220
GC Warning: Finalization cycle involving 42decc0
GC Warning: Finalization cycle involving 300c990
GC Warning: Finalization cycle involving 362dcc0
GC Warning: Finalization cycle involving 4283440
GC Warning: Finalization cycle involving 369dcc0
GC Warning: Finalization cycle involving 3481aa0
GC Warning: Finalization cycle involving 4677880
GC Warning: Finalization cycle involving 4283000
GC Warning: Finalization cycle involving 2bb2220
GC Warning: Finalization cycle involving 4677990
GC Warning: Finalization cycle involving 362dbb0
GC Warning: Finalization cycle involving 3481220
GC Warning: Finalization cycle involving 438bcc0
GC Warning: Finalization cycle involving 3481550
GC Warning: Finalization cycle involving 3481770
GC Warning: Finalization cycle involving 438b990
GC Warning: Finalization cycle involving 34a9660

             2              1
o2 = {(S + 1) , (S + 1)(S + -)}
                            2

o2 : List

Caveat

A finite field should be used in place of Q in order to speed up computations. This routine works only on relatively small examples.

paramBpoly(RingElement,String) -- compute the list of all possible Bernstein-Sato polynomials for a polynomial with parametric coefficients

Synopsis

Description

Caveat

See also