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 283caa0
GC Warning: Finalization cycle involving 3024cc0
GC Warning: Finalization cycle involving 2553990
GC Warning: Finalization cycle involving 2c48bb0
GC Warning: Finalization cycle involving 373e220
GC Warning: Finalization cycle involving 2c48bb0
GC Warning: Finalization cycle involving 2c48cc0
GC Warning: Finalization cycle involving 283caa0
GC Warning: Finalization cycle involving 3024cc0
GC Warning: Finalization cycle involving 2553990
GC Warning: Finalization cycle involving 373eaa0
GC Warning: Finalization cycle involving 3d23110
GC Warning: Finalization cycle involving 373e220
GC Warning: Finalization cycle involving 2c48bb0
GC Warning: Finalization cycle involving 2c48cc0
GC Warning: Finalization cycle involving 283caa0
GC Warning: Finalization cycle involving 3024cc0
GC Warning: Finalization cycle involving 2553990
GC Warning: Finalization cycle involving 3d00220
GC Warning: Finalization cycle involving 373eaa0
GC Warning: Finalization cycle involving 3d23110
GC Warning: Finalization cycle involving 373e220
GC Warning: Finalization cycle involving 2c48bb0
GC Warning: Finalization cycle involving 2c48cc0
GC Warning: Finalization cycle involving 283caa0
GC Warning: Finalization cycle involving 3024cc0
GC Warning: Finalization cycle involving 2553990
GC Warning: Finalization cycle involving 3d00220
GC Warning: Finalization cycle involving 373eaa0
GC Warning: Finalization cycle involving 3d23110
GC Warning: Finalization cycle involving 373e220
GC Warning: Finalization cycle involving 3dff660
GC Warning: Finalization cycle involving 2c48bb0
GC Warning: Finalization cycle involving 2c48cc0
GC Warning: Finalization cycle involving 283caa0
GC Warning: Finalization cycle involving 3d76110
GC Warning: Finalization cycle involving 4075cc0
GC Warning: Finalization cycle involving 3024cc0
GC Warning: Finalization cycle involving 3dc4aa0
GC Warning: Finalization cycle involving 2553990
GC Warning: Finalization cycle involving 32d5220
GC Warning: Finalization cycle involving 3d00220
GC Warning: Finalization cycle involving 404fdd0
GC Warning: Finalization cycle involving 373eaa0
GC Warning: Finalization cycle involving 3d23110
GC Warning: Finalization cycle involving 373e220
GC Warning: Finalization cycle involving 3dff660
GC Warning: Finalization cycle involving 38ee110
GC Warning: Finalization cycle involving 2c48bb0
GC Warning: Finalization cycle involving 2c48cc0
GC Warning: Finalization cycle involving 283caa0
GC Warning: Finalization cycle involving 3d76110
GC Warning: Finalization cycle involving 4075cc0
GC Warning: Finalization cycle involving 2c48660
GC Warning: Finalization cycle involving 3024cc0
GC Warning: Finalization cycle involving 3dc4aa0
GC Warning: Finalization cycle involving 2553990
GC Warning: Finalization cycle involving 32d5220
GC Warning: Finalization cycle involving 3d00220
GC Warning: Finalization cycle involving 404fdd0
GC Warning: Finalization cycle involving 373eaa0
GC Warning: Finalization cycle involving 3d23110
GC Warning: Finalization cycle involving 373e220
GC Warning: Finalization cycle involving 3dff660
GC Warning: Finalization cycle involving 38ee110
GC Warning: Finalization cycle involving 2c48bb0
GC Warning: Finalization cycle involving 2c48cc0
GC Warning: Finalization cycle involving 283caa0
GC Warning: Finalization cycle involving 3d76110
GC Warning: Finalization cycle involving 4075cc0
GC Warning: Finalization cycle involving 2c48660
GC Warning: Finalization cycle involving 3024cc0
GC Warning: Finalization cycle involving 3dc4aa0
GC Warning: Finalization cycle involving 2553990
GC Warning: Finalization cycle involving 32d5220
GC Warning: Finalization cycle involving 3d00220
GC Warning: Finalization cycle involving 404fdd0
GC Warning: Finalization cycle involving 343a990
GC Warning: Finalization cycle involving 373eaa0
GC Warning: Finalization cycle involving 2e39880
GC Warning: Finalization cycle involving 40bc660
GC Warning: Finalization cycle involving 2ea9440
GC Warning: Finalization cycle involving 3d23110
GC Warning: Finalization cycle involving 373e220
GC Warning: Finalization cycle involving 3dff660
GC Warning: Finalization cycle involving 38ee110
GC Warning: Finalization cycle involving 2c48bb0
GC Warning: Finalization cycle involving 2c48cc0
GC Warning: Finalization cycle involving 283caa0
GC Warning: Finalization cycle involving 3d76110
GC Warning: Finalization cycle involving 4075cc0
GC Warning: Finalization cycle involving 2c48660
GC Warning: Finalization cycle involving 277a900
GC Warning: Finalization cycle involving 3024aa0
GC Warning: Finalization cycle involving 3024cc0
GC Warning: Finalization cycle involving 3dc4aa0
GC Warning: Finalization cycle involving 2553990
GC Warning: Finalization cycle involving 32d5220
GC Warning: Finalization cycle involving 404f770
GC Warning: Finalization cycle involving 3d00220
GC Warning: Finalization cycle involving 404fdd0
GC Warning: Finalization cycle involving 343a990
GC Warning: Finalization cycle involving 373eaa0
GC Warning: Finalization cycle involving 2e39880
GC Warning: Finalization cycle involving 40bc660
GC Warning: Finalization cycle involving 2ea9440
GC Warning: Finalization cycle involving 3d23110
GC Warning: Finalization cycle involving 373e220
GC Warning: Finalization cycle involving 3dff660
GC Warning: Finalization cycle involving 38ee110
GC Warning: Finalization cycle involving 2c48bb0
GC Warning: Finalization cycle involving 2c48cc0
GC Warning: Finalization cycle involving 283caa0
GC Warning: Finalization cycle involving 3d76110
GC Warning: Finalization cycle involving 4075cc0
GC Warning: Finalization cycle involving 2c48660
GC Warning: Finalization cycle involving 277a900
GC Warning: Finalization cycle involving 3024aa0
GC Warning: Finalization cycle involving 3024cc0
GC Warning: Finalization cycle involving 3dc4aa0
GC Warning: Finalization cycle involving 2553990
GC Warning: Finalization cycle involving 32d5220
GC Warning: Finalization cycle involving 404f770
GC Warning: Finalization cycle involving 3d00220
GC Warning: Finalization cycle involving 404fdd0
GC Warning: Finalization cycle involving 343a990
GC Warning: Finalization cycle involving 373eaa0
GC Warning: Finalization cycle involving 2e39880
GC Warning: Finalization cycle involving 40bc660
GC Warning: Finalization cycle involving 2ea9440
GC Warning: Finalization cycle involving 3d23110
GC Warning: Finalization cycle involving 373e220
GC Warning: Finalization cycle involving 3dff660
GC Warning: Finalization cycle involving 38ee110
GC Warning: Finalization cycle involving 4311770
GC Warning: Finalization cycle involving 405d110
GC Warning: Finalization cycle involving 2c48bb0
GC Warning: Finalization cycle involving 2c48cc0
GC Warning: Finalization cycle involving 283caa0
GC Warning: Finalization cycle involving 3d76110
GC Warning: Finalization cycle involving 4075cc0
GC Warning: Finalization cycle involving 2c48660
GC Warning: Finalization cycle involving 277a900
GC Warning: Finalization cycle involving 40f6880
GC Warning: Finalization cycle involving 1f8d660
GC Warning: Finalization cycle involving 3024aa0
GC Warning: Finalization cycle involving 3024cc0
GC Warning: Finalization cycle involving 4132cc0
GC Warning: Finalization cycle involving 2553aa0
GC Warning: Finalization cycle involving 3dc4aa0
GC Warning: Finalization cycle involving 2553990
GC Warning: Finalization cycle involving 2da6880
GC Warning: Finalization cycle involving 32d5220
GC Warning: Finalization cycle involving 404f770
GC Warning: Finalization cycle involving 3d00220
GC Warning: Finalization cycle involving 404fdd0
GC Warning: Finalization cycle involving 343a990
GC Warning: Finalization cycle involving 373eaa0
GC Warning: Finalization cycle involving 2e39880
GC Warning: Finalization cycle involving 3dffee0
GC Warning: Finalization cycle involving 40bc660
GC Warning: Finalization cycle involving 2ea9440
GC Warning: Finalization cycle involving 3d23110
GC Warning: Finalization cycle involving 373e220
GC Warning: Finalization cycle involving 3dff660
GC Warning: Finalization cycle involving 38ee110
GC Warning: Finalization cycle involving 4311770
GC Warning: Finalization cycle involving 405d110
GC Warning: Finalization cycle involving 2c48bb0
GC Warning: Finalization cycle involving 2c48cc0
GC Warning: Finalization cycle involving 283caa0
GC Warning: Finalization cycle involving 3d76110
GC Warning: Finalization cycle involving 4075cc0
GC Warning: Finalization cycle involving 2c48660
GC Warning: Finalization cycle involving 277a900
GC Warning: Finalization cycle involving 40f6880
GC Warning: Finalization cycle involving 1f8d660
GC Warning: Finalization cycle involving 3024aa0
GC Warning: Finalization cycle involving 3024cc0
GC Warning: Finalization cycle involving 4132cc0
GC Warning: Finalization cycle involving 2553aa0
GC Warning: Finalization cycle involving 3dc4aa0
GC Warning: Finalization cycle involving 2553990
GC Warning: Finalization cycle involving 2da6880
GC Warning: Finalization cycle involving 32d5220
GC Warning: Finalization cycle involving 404f770
GC Warning: Finalization cycle involving 3d00220
GC Warning: Finalization cycle involving 404f990
GC Warning: Finalization cycle involving 404fdd0
GC Warning: Finalization cycle involving 3336770
GC Warning: Finalization cycle involving 343a990
GC Warning: Finalization cycle involving 4328440
GC Warning: Finalization cycle involving 373eaa0
GC Warning: Finalization cycle involving 2e39880
GC Warning: Finalization cycle involving 3dffee0
GC Warning: Finalization cycle involving 40bc660
GC Warning: Finalization cycle involving 2ea9440
GC Warning: Finalization cycle involving 2ea9660
GC Warning: Finalization cycle involving 3d23110
GC Warning: Finalization cycle involving 373e220
GC Warning: Finalization cycle involving 3dff660
GC Warning: Finalization cycle involving 38ee110
GC Warning: Finalization cycle involving 4311770
GC Warning: Finalization cycle involving 405d110
GC Warning: Finalization cycle involving 2c48bb0
GC Warning: Finalization cycle involving 2c48cc0
GC Warning: Finalization cycle involving 283caa0
GC Warning: Finalization cycle involving 3d76110
GC Warning: Finalization cycle involving 4075cc0
GC Warning: Finalization cycle involving 2c48660
GC Warning: Finalization cycle involving 4132770
GC Warning: Finalization cycle involving 277a900
GC Warning: Finalization cycle involving 40f6880
GC Warning: Finalization cycle involving 1f8d660
GC Warning: Finalization cycle involving 3210ee0
GC Warning: Finalization cycle involving 3024aa0
GC Warning: Finalization cycle involving 3024cc0
GC Warning: Finalization cycle involving 4132cc0
GC Warning: Finalization cycle involving 2553aa0
GC Warning: Finalization cycle involving 3dc4aa0
GC Warning: Finalization cycle involving 2553990
GC Warning: Finalization cycle involving 2da6880
GC Warning: Finalization cycle involving 32d5220
GC Warning: Finalization cycle involving 404f770
GC Warning: Finalization cycle involving 3d00220
GC Warning: Finalization cycle involving 404f990
GC Warning: Finalization cycle involving 404fdd0
GC Warning: Finalization cycle involving 43d3990
GC Warning: Finalization cycle involving 3336770
GC Warning: Finalization cycle involving 343a990
GC Warning: Finalization cycle involving 4328440
GC Warning: Finalization cycle involving 373eaa0
GC Warning: Finalization cycle involving 2e39880
GC Warning: Finalization cycle involving 3dffee0
GC Warning: Finalization cycle involving 373e880
GC Warning: Finalization cycle involving 40bc660
GC Warning: Finalization cycle involving 4248330
GC Warning: Finalization cycle involving 2ea9440
GC Warning: Finalization cycle involving 4228ee0
GC Warning: Finalization cycle involving 2ea9660
GC Warning: Finalization cycle involving 3d23110
GC Warning: Finalization cycle involving 373e220
GC Warning: Finalization cycle involving 3dff660
GC Warning: Finalization cycle involving 38ee110
GC Warning: Finalization cycle involving 4311770
GC Warning: Finalization cycle involving 405d110
GC Warning: Finalization cycle involving 2c48bb0
GC Warning: Finalization cycle involving 2c48cc0
GC Warning: Finalization cycle involving 2d08ee0
GC Warning: Finalization cycle involving 283caa0
GC Warning: Finalization cycle involving 3d76110
GC Warning: Finalization cycle involving 4075cc0
GC Warning: Finalization cycle involving 4311880
GC Warning: Finalization cycle involving 2c48660
GC Warning: Finalization cycle involving 4132770
GC Warning: Finalization cycle involving 277a900
GC Warning: Finalization cycle involving 40f6880
GC Warning: Finalization cycle involving 1f8d660
GC Warning: Finalization cycle involving 3210ee0
GC Warning: Finalization cycle involving 3024aa0
GC Warning: Finalization cycle involving 3024cc0
GC Warning: Finalization cycle involving 4132cc0
GC Warning: Finalization cycle involving 2553aa0
GC Warning: Finalization cycle involving 3dc4aa0
GC Warning: Finalization cycle involving 2553990
GC Warning: Finalization cycle involving 2da6880
GC Warning: Finalization cycle involving 32d5220
GC Warning: Finalization cycle involving 404f770
GC Warning: Finalization cycle involving 3d00220
GC Warning: Finalization cycle involving 404f990
GC Warning: Finalization cycle involving 2553110
GC Warning: Finalization cycle involving 404fdd0
GC Warning: Finalization cycle involving 43d3990
GC Warning: Finalization cycle involving 2da2440
GC Warning: Finalization cycle involving 3336770
GC Warning: Finalization cycle involving 343a990
GC Warning: Finalization cycle involving 4328440
GC Warning: Finalization cycle involving 3933110
GC Warning: Finalization cycle involving 373eaa0
GC Warning: Finalization cycle involving 2e39880
GC Warning: Finalization cycle involving 3dffee0
GC Warning: Finalization cycle involving 373e880
GC Warning: Finalization cycle involving 40bc660
GC Warning: Finalization cycle involving 4248330
GC Warning: Finalization cycle involving 2ea9440
GC Warning: Finalization cycle involving 4228ee0
GC Warning: Finalization cycle involving 2ea9660
GC Warning: Finalization cycle involving 3d23110
GC Warning: Finalization cycle involving 373e220
GC Warning: Finalization cycle involving 3dff660
GC Warning: Finalization cycle involving 38ee110
GC Warning: Finalization cycle involving 4311770
GC Warning: Finalization cycle involving 405d110
GC Warning: Finalization cycle involving 2c48bb0
GC Warning: Finalization cycle involving 2c48cc0
GC Warning: Finalization cycle involving 2d08ee0
GC Warning: Finalization cycle involving 283caa0
GC Warning: Finalization cycle involving 3d76110
GC Warning: Finalization cycle involving 4075cc0
GC Warning: Finalization cycle involving 4311880
GC Warning: Finalization cycle involving 2c48660
GC Warning: Finalization cycle involving 4132770
GC Warning: Finalization cycle involving 277a900
GC Warning: Finalization cycle involving 40f6880
GC Warning: Finalization cycle involving 1f8d660
GC Warning: Finalization cycle involving 3210ee0
GC Warning: Finalization cycle involving 3024aa0
GC Warning: Finalization cycle involving 3024cc0
GC Warning: Finalization cycle involving 4132cc0
GC Warning: Finalization cycle involving 2553aa0
GC Warning: Finalization cycle involving 3dc4aa0
GC Warning: Finalization cycle involving 2553990
GC Warning: Finalization cycle involving 2da6880
GC Warning: Finalization cycle involving 32d5220
GC Warning: Finalization cycle involving 404f770
GC Warning: Finalization cycle involving 3d00220
GC Warning: Finalization cycle involving 404f990
GC Warning: Finalization cycle involving 2553110
GC Warning: Finalization cycle involving 404fdd0
GC Warning: Finalization cycle involving 43d3990
GC Warning: Finalization cycle involving 2da2440

             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