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Dmodules :: paramBpoly(RingElement,String)

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

Synopsis

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 9fabd10
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GC Warning: Finalization cycle involving 841e130
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GC Warning: Finalization cycle involving 9fabd10
GC Warning: Finalization cycle involving 9fabda8
GC Warning: Finalization cycle involving 9fabc78
GC Warning: Finalization cycle involving 9fabbe0
GC Warning: Finalization cycle involving 9fab8e8
GC Warning: Finalization cycle involving 841e130
GC Warning: Finalization cycle involving 9fabe40
GC Warning: Finalization cycle involving 9fabd10
GC Warning: Finalization cycle involving 9fabda8
GC Warning: Finalization cycle involving 9fabc78
GC Warning: Finalization cycle involving 9fabb48
GC Warning: Finalization cycle involving 9fabbe0
GC Warning: Finalization cycle involving 9faba18
GC Warning: Finalization cycle involving 9fabab0
GC Warning: Finalization cycle involving 9fab850
GC Warning: Finalization cycle involving 9fab8e8
GC Warning: Finalization cycle involving 9fab390
GC Warning: Finalization cycle involving 9fab260
GC Warning: Finalization cycle involving 9fab2f8
GC Warning: Finalization cycle involving 841e130
GC Warning: Finalization cycle involving 9fabe40
GC Warning: Finalization cycle involving 9fabd10
GC Warning: Finalization cycle involving 9fabda8
GC Warning: Finalization cycle involving 9fabc78
GC Warning: Finalization cycle involving 9fabb48
GC Warning: Finalization cycle involving 9fabbe0
GC Warning: Finalization cycle involving 9faba18
GC Warning: Finalization cycle involving 9fabab0
GC Warning: Finalization cycle involving 9fab980
GC Warning: Finalization cycle involving 9fab850
GC Warning: Finalization cycle involving 9fab8e8
GC Warning: Finalization cycle involving 9fab390
GC Warning: Finalization cycle involving 9fab260
GC Warning: Finalization cycle involving 9fab2f8
GC Warning: Finalization cycle involving 841e130
GC Warning: Finalization cycle involving 9fabe40
GC Warning: Finalization cycle involving 9fabd10
GC Warning: Finalization cycle involving 9fabda8
GC Warning: Finalization cycle involving 9fabc78
GC Warning: Finalization cycle involving 9fabb48
GC Warning: Finalization cycle involving 9fabbe0
GC Warning: Finalization cycle involving 9faba18
GC Warning: Finalization cycle involving 9fabab0
GC Warning: Finalization cycle involving 9fab980
GC Warning: Finalization cycle involving 9fab850
GC Warning: Finalization cycle involving 9fab8e8
GC Warning: Finalization cycle involving 9fab7b8
GC Warning: Finalization cycle involving 9fab390
GC Warning: Finalization cycle involving 9fab260
GC Warning: Finalization cycle involving 9fab2f8
GC Warning: Finalization cycle involving 9fab130
GC Warning: Finalization cycle involving 9fab1c8
GC Warning: Finalization cycle involving 9fab098
GC Warning: Finalization cycle involving 841e8e8
GC Warning: Finalization cycle involving 841e130
GC Warning: Finalization cycle involving 841e720
GC Warning: Finalization cycle involving 841e7b8
GC Warning: Finalization cycle involving 9fabe40
GC Warning: Finalization cycle involving 9fabd10
GC Warning: Finalization cycle involving 9fabda8
GC Warning: Finalization cycle involving 9fabc78
GC Warning: Finalization cycle involving 9fabb48
GC Warning: Finalization cycle involving 9fabbe0
GC Warning: Finalization cycle involving 9faba18
GC Warning: Finalization cycle involving 9fabab0
GC Warning: Finalization cycle involving 9fab980
GC Warning: Finalization cycle involving 9fab850
GC Warning: Finalization cycle involving 9fab8e8
GC Warning: Finalization cycle involving 9fab7b8
GC Warning: Finalization cycle involving 9fab558
GC Warning: Finalization cycle involving 9fab390
GC Warning: Finalization cycle involving 9fab260
GC Warning: Finalization cycle involving 9fab2f8
GC Warning: Finalization cycle involving 9fab130
GC Warning: Finalization cycle involving 9fab1c8
GC Warning: Finalization cycle involving 9fab098
GC Warning: Finalization cycle involving 841e8e8
GC Warning: Finalization cycle involving 841e130
GC Warning: Finalization cycle involving 841e720
GC Warning: Finalization cycle involving 841e7b8
GC Warning: Finalization cycle involving ad21a18
GC Warning: Finalization cycle involving ad21ab0
GC Warning: Finalization cycle involving ad21b48
GC Warning: Finalization cycle involving 9fabe40
GC Warning: Finalization cycle involving 9fabd10
GC Warning: Finalization cycle involving 9fabda8
GC Warning: Finalization cycle involving 9fabc78
GC Warning: Finalization cycle involving 9fabb48
GC Warning: Finalization cycle involving 9fabbe0
GC Warning: Finalization cycle involving 9faba18
GC Warning: Finalization cycle involving 9fabab0
GC Warning: Finalization cycle involving 9fab980
GC Warning: Finalization cycle involving 9fab850
GC Warning: Finalization cycle involving 9fab8e8
GC Warning: Finalization cycle involving 9fab7b8
GC Warning: Finalization cycle involving 9fab688
GC Warning: Finalization cycle involving 9fab558
GC Warning: Finalization cycle involving 9fab4c0
GC Warning: Finalization cycle involving 9fab390
GC Warning: Finalization cycle involving 9fab260
GC Warning: Finalization cycle involving 9fab2f8
GC Warning: Finalization cycle involving 9fab130
GC Warning: Finalization cycle involving 9fab1c8
GC Warning: Finalization cycle involving 9fab098
GC Warning: Finalization cycle involving 841e8e8
GC Warning: Finalization cycle involving 841e130
GC Warning: Finalization cycle involving 841e5f0
GC Warning: Finalization cycle involving 841e688
GC Warning: Finalization cycle involving 841e720
GC Warning: Finalization cycle involving 841e7b8
GC Warning: Finalization cycle involving ad21a18
GC Warning: Finalization cycle involving ad21ab0
GC Warning: Finalization cycle involving ad21b48
GC Warning: Finalization cycle involving 9fabe40
GC Warning: Finalization cycle involving 9fabd10
GC Warning: Finalization cycle involving 9fabda8
GC Warning: Finalization cycle involving 9fabc78
GC Warning: Finalization cycle involving 9fabb48
GC Warning: Finalization cycle involving 9fabbe0
GC Warning: Finalization cycle involving 9faba18
GC Warning: Finalization cycle involving 9fabab0
GC Warning: Finalization cycle involving 9fab980
GC Warning: Finalization cycle involving 9fab850
GC Warning: Finalization cycle involving 9fab8e8
GC Warning: Finalization cycle involving 9fab7b8
GC Warning: Finalization cycle involving 9fab688
GC Warning: Finalization cycle involving 9fab558
GC Warning: Finalization cycle involving 9fab4c0
GC Warning: Finalization cycle involving 9fab390
GC Warning: Finalization cycle involving 9fab260
GC Warning: Finalization cycle involving 9fab2f8
GC Warning: Finalization cycle involving 9fab130
GC Warning: Finalization cycle involving 9fab1c8
GC Warning: Finalization cycle involving 9fab098
GC Warning: Finalization cycle involving 841e8e8
GC Warning: Finalization cycle involving 841e130
GC Warning: Finalization cycle involving 841e5f0
GC Warning: Finalization cycle involving 841e688
GC Warning: Finalization cycle involving 841e720
GC Warning: Finalization cycle involving 841e7b8
GC Warning: Finalization cycle involving ad21a18
GC Warning: Finalization cycle involving ad21ab0
GC Warning: Finalization cycle involving ad21b48
GC Warning: Finalization cycle involving 9fabe40
GC Warning: Finalization cycle involving ad21850
GC Warning: Finalization cycle involving 9fabd10
GC Warning: Finalization cycle involving ad218e8
GC Warning: Finalization cycle involving 9fabda8
GC Warning: Finalization cycle involving 9fabc78
GC Warning: Finalization cycle involving ad21980
GC Warning: Finalization cycle involving 9fabb48
GC Warning: Finalization cycle involving 9fabbe0
GC Warning: Finalization cycle involving 9faba18
GC Warning: Finalization cycle involving 9fabab0
GC Warning: Finalization cycle involving 9fab980
GC Warning: Finalization cycle involving 9fab850
GC Warning: Finalization cycle involving 9fab8e8
GC Warning: Finalization cycle involving 9fab7b8
GC Warning: Finalization cycle involving 9fab688
GC Warning: Finalization cycle involving 9fab558
GC Warning: Finalization cycle involving ad21098
GC Warning: Finalization cycle involving ad21130
GC Warning: Finalization cycle involving ad211c8
GC Warning: Finalization cycle involving 9fab4c0
GC Warning: Finalization cycle involving 9fab390
GC Warning: Finalization cycle involving ad21688
GC Warning: Finalization cycle involving 9fab260
GC Warning: Finalization cycle involving ad21720
GC Warning: Finalization cycle involving 9fab2f8
GC Warning: Finalization cycle involving 9fab130
GC Warning: Finalization cycle involving 9fab1c8
GC Warning: Finalization cycle involving 9fab098
GC Warning: Finalization cycle involving 841e8e8
GC Warning: Finalization cycle involving 841e130
GC Warning: Finalization cycle involving 841e5f0
GC Warning: Finalization cycle involving 841e688
GC Warning: Finalization cycle involving 841e720
GC Warning: Finalization cycle involving 841e7b8
GC Warning: Finalization cycle involving ad21a18
GC Warning: Finalization cycle involving ad21ab0
GC Warning: Finalization cycle involving ad21b48
GC Warning: Finalization cycle involving 9fabe40
GC Warning: Finalization cycle involving ad21850
GC Warning: Finalization cycle involving 9fabd10
GC Warning: Finalization cycle involving ad218e8
GC Warning: Finalization cycle involving 9fabda8
GC Warning: Finalization cycle involving 9fabc78
GC Warning: Finalization cycle involving ad21980
GC Warning: Finalization cycle involving 9fabb48
GC Warning: Finalization cycle involving 9fabbe0
GC Warning: Finalization cycle involving 9faba18
GC Warning: Finalization cycle involving 9fabab0
GC Warning: Finalization cycle involving 9fab980
GC Warning: Finalization cycle involving 9fab850
GC Warning: Finalization cycle involving 9fab8e8
GC Warning: Finalization cycle involving 9fab7b8
GC Warning: Finalization cycle involving 9fab688
GC Warning: Finalization cycle involving 9fab558
GC Warning: Finalization cycle involving ad21098
GC Warning: Finalization cycle involving ad21130
GC Warning: Finalization cycle involving ad211c8
GC Warning: Finalization cycle involving 9fab4c0
GC Warning: Finalization cycle involving 9fab390
GC Warning: Finalization cycle involving ad21688
GC Warning: Finalization cycle involving 9fab260
GC Warning: Finalization cycle involving ad21720
GC Warning: Finalization cycle involving 9fab2f8
GC Warning: Finalization cycle involving 9fab130
GC Warning: Finalization cycle involving 9fab1c8
GC Warning: Finalization cycle involving 9fab098
GC Warning: Finalization cycle involving 841e8e8
GC Warning: Finalization cycle involving 841e130
GC Warning: Finalization cycle involving 841e5f0
GC Warning: Finalization cycle involving 841e688
GC Warning: Finalization cycle involving 841e720
GC Warning: Finalization cycle involving 841e7b8
GC Warning: Finalization cycle involving ad21a18
GC Warning: Finalization cycle involving ad21ab0
GC Warning: Finalization cycle involving ad21b48
GC Warning: Finalization cycle involving 9fabe40
GC Warning: Finalization cycle involving ad21850
GC Warning: Finalization cycle involving 9fabd10
GC Warning: Finalization cycle involving ad218e8
GC Warning: Finalization cycle involving 9fabda8
GC Warning: Finalization cycle involving 9fabc78
GC Warning: Finalization cycle involving ad21980
GC Warning: Finalization cycle involving ad21e40
GC Warning: Finalization cycle involving 9fabb48
GC Warning: Finalization cycle involving ad21ed8
GC Warning: Finalization cycle involving 9fabbe0
GC Warning: Finalization cycle involving 9faba18
GC Warning: Finalization cycle involving 9fabab0
GC Warning: Finalization cycle involving ad21c78
GC Warning: Finalization cycle involving 9fab980
GC Warning: Finalization cycle involving 9fab850
GC Warning: Finalization cycle involving ad21d10
GC Warning: Finalization cycle involving 9fab8e8
GC Warning: Finalization cycle involving ad21260
GC Warning: Finalization cycle involving ad212f8
GC Warning: Finalization cycle involving 9fab7b8
GC Warning: Finalization cycle involving 9fab688
GC Warning: Finalization cycle involving 9fab558
GC Warning: Finalization cycle involving ad21000
GC Warning: Finalization cycle involving ad21098
GC Warning: Finalization cycle involving ad21130
GC Warning: Finalization cycle involving ad211c8
GC Warning: Finalization cycle involving 9fab4c0
GC Warning: Finalization cycle involving 9fab390
GC Warning: Finalization cycle involving ad21688
GC Warning: Finalization cycle involving 9fab260
GC Warning: Finalization cycle involving ad21720
GC Warning: Finalization cycle involving 9fab2f8
GC Warning: Finalization cycle involving 9fab130
GC Warning: Finalization cycle involving 9fab1c8
GC Warning: Finalization cycle involving 9fab098
GC Warning: Finalization cycle involving 841e8e8
GC Warning: Finalization cycle involving 841e130
GC Warning: Finalization cycle involving 841e5f0
GC Warning: Finalization cycle involving 841e688
GC Warning: Finalization cycle involving 841e720
GC Warning: Finalization cycle involving 841e7b8
GC Warning: Finalization cycle involving ad21a18
GC Warning: Finalization cycle involving ad21ab0
GC Warning: Finalization cycle involving ad21b48
GC Warning: Finalization cycle involving 9fabe40
GC Warning: Finalization cycle involving ad21850
GC Warning: Finalization cycle involving 9fabd10
GC Warning: Finalization cycle involving ad218e8
GC Warning: Finalization cycle involving 9fabda8
GC Warning: Finalization cycle involving 9fabc78
GC Warning: Finalization cycle involving ad21980
GC Warning: Finalization cycle involving ad21e40
GC Warning: Finalization cycle involving 9fabb48
GC Warning: Finalization cycle involving ad21ed8
GC Warning: Finalization cycle involving 9fabbe0
GC Warning: Finalization cycle involving 9faba18
GC Warning: Finalization cycle involving 9fabab0
GC Warning: Finalization cycle involving ad21c78
GC Warning: Finalization cycle involving 9fab980
GC Warning: Finalization cycle involving 9fab850
GC Warning: Finalization cycle involving ad21d10
GC Warning: Finalization cycle involving 9fab8e8
GC Warning: Finalization cycle involving ad21260
GC Warning: Finalization cycle involving ad212f8
GC Warning: Finalization cycle involving 9fab7b8
GC Warning: Finalization cycle involving 9fab688
GC Warning: Finalization cycle involving 9fab558
GC Warning: Finalization cycle involving ad21000
GC Warning: Finalization cycle involving ad21098
GC Warning: Finalization cycle involving ad21130
GC Warning: Finalization cycle involving ad211c8
GC Warning: Finalization cycle involving 9fab4c0
GC Warning: Finalization cycle involving 9fab390
GC Warning: Finalization cycle involving ad21688
GC Warning: Finalization cycle involving 9fab260
GC Warning: Finalization cycle involving ad21720
GC Warning: Finalization cycle involving 9fab2f8
GC Warning: Finalization cycle involving 9fab130
GC Warning: Finalization cycle involving 9fab1c8
GC Warning: Finalization cycle involving 9fab098
GC Warning: Finalization cycle involving 841e8e8
GC Warning: Finalization cycle involving 841e130
GC Warning: Finalization cycle involving 841e5f0
GC Warning: Finalization cycle involving 841e688
GC Warning: Finalization cycle involving 841e720
GC Warning: Finalization cycle involving 841e7b8
GC Warning: Finalization cycle involving ad21a18
GC Warning: Finalization cycle involving ad21ab0
GC Warning: Finalization cycle involving ad21b48
GC Warning: Finalization cycle involving 9fabe40
GC Warning: Finalization cycle involving ad21850
GC Warning: Finalization cycle involving 9fabd10
GC Warning: Finalization cycle involving ad218e8
GC Warning: Finalization cycle involving 9fabda8
GC Warning: Finalization cycle involving 9fabc78
GC Warning: Finalization cycle involving ad21980
GC Warning: Finalization cycle involving ad21e40
GC Warning: Finalization cycle involving 9fabb48
GC Warning: Finalization cycle involving ad21ed8
GC Warning: Finalization cycle involving 9fabbe0
GC Warning: Finalization cycle involving 9faba18
GC Warning: Finalization cycle involving 9fabab0
GC Warning: Finalization cycle involving ad21c78
GC Warning: Finalization cycle involving 9fab980
GC Warning: Finalization cycle involving 9fab850
GC Warning: Finalization cycle involving ad21d10
GC Warning: Finalization cycle involving 9fab8e8
GC Warning: Finalization cycle involving ad21260
GC Warning: Finalization cycle involving ad212f8
GC Warning: Finalization cycle involving 9fab7b8
GC Warning: Finalization cycle involving 9fab688
GC Warning: Finalization cycle involving 9fab558
GC Warning: Finalization cycle involving ad21000
GC Warning: Finalization cycle involving ad21098
GC Warning: Finalization cycle involving ad21130
GC Warning: Finalization cycle involving ad211c8
GC Warning: Finalization cycle involving 9fab4c0
GC Warning: Finalization cycle involving 9fab390
GC Warning: Finalization cycle involving ad21688
GC Warning: Finalization cycle involving 9fab260
GC Warning: Finalization cycle involving ad21720
GC Warning: Finalization cycle involving 9fab2f8
GC Warning: Finalization cycle involving 9fab130
GC Warning: Finalization cycle involving ad214c0
GC Warning: Finalization cycle involving 9fab1c8
GC Warning: Finalization cycle involving 9fab098
GC Warning: Finalization cycle involving 841e8e8
GC Warning: Finalization cycle involving 841e130
GC Warning: Finalization cycle involving 841e5f0
GC Warning: Finalization cycle involving b18cd10
GC Warning: Finalization cycle involving 841e688
GC Warning: Finalization cycle involving 841e720
GC Warning: Finalization cycle involving b18cc78
GC Warning: Finalization cycle involving 841e7b8
GC Warning: Finalization cycle involving ad21a18
GC Warning: Finalization cycle involving ad21ab0
GC Warning: Finalization cycle involving ad21b48
GC Warning: Finalization cycle involving 9fabe40
GC Warning: Finalization cycle involving ad21be0
GC Warning: Finalization cycle involving ad21850
GC Warning: Finalization cycle involving 9fabd10
GC Warning: Finalization cycle involving ad218e8
GC Warning: Finalization cycle involving 9fabda8
GC Warning: Finalization cycle involving 9fabc78
GC Warning: Finalization cycle involving ad21980
GC Warning: Finalization cycle involving ad21e40
GC Warning: Finalization cycle involving 9fabb48
GC Warning: Finalization cycle involving ad21ed8
GC Warning: Finalization cycle involving 9fabbe0
GC Warning: Finalization cycle involving 9faba18
GC Warning: Finalization cycle involving 9fabab0
GC Warning: Finalization cycle involving ad21c78
GC Warning: Finalization cycle involving 9fab980
GC Warning: Finalization cycle involving 9fab850
GC Warning: Finalization cycle involving ad21d10
GC Warning: Finalization cycle involving 9fab8e8
GC Warning: Finalization cycle involving ad21260
GC Warning: Finalization cycle involving ad212f8
GC Warning: Finalization cycle involving 9fab7b8
GC Warning: Finalization cycle involving 9fab688
GC Warning: Finalization cycle involving 9fab558
GC Warning: Finalization cycle involving ad21000
GC Warning: Finalization cycle involving ad21098
GC Warning: Finalization cycle involving ad21130
GC Warning: Finalization cycle involving ad211c8
GC Warning: Finalization cycle involving 9fab4c0
GC Warning: Finalization cycle involving 9fab390
GC Warning: Finalization cycle involving ad21688
GC Warning: Finalization cycle involving 9fab260
GC Warning: Finalization cycle involving ad21720
GC Warning: Finalization cycle involving 9fab2f8
GC Warning: Finalization cycle involving ad217b8
GC Warning: Finalization cycle involving 9fab130
GC Warning: Finalization cycle involving ad21428
GC Warning: Finalization cycle involving ad214c0
GC Warning: Finalization cycle involving 9fab1c8
GC Warning: Finalization cycle involving ad215f0
GC Warning: Finalization cycle involving 9fab098
GC Warning: Finalization cycle involving b18c390
GC Warning: Finalization cycle involving 841e8e8
GC Warning: Finalization cycle involving b18c428
GC Warning: Finalization cycle involving b18cb48
GC Warning: Finalization cycle involving b18cbe0
GC Warning: Finalization cycle involving 841e130
GC Warning: Finalization cycle involving b18cab0
GC Warning: Finalization cycle involving b18c980
GC Warning: Finalization cycle involving b18c8e8
GC Warning: Finalization cycle involving 841e5f0
GC Warning: Finalization cycle involving b18cd10
GC Warning: Finalization cycle involving 841e688
GC Warning: Finalization cycle involving 841e720
GC Warning: Finalization cycle involving b18cc78
GC Warning: Finalization cycle involving 841e7b8

             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.

See also