The roots of any b-function are rational.
i1 : R = QQ[x, dx, WeylAlgebra => {x=>dx}]
o1 = R
o1 : PolynomialRing
|
i2 : f = x^10
10
o2 = x
o2 : R
|
i3 : b = globalBFunction f
10 9 8 7 6
o3 = 12500000s + 68750000s + 165000000s + 226875000s + 197216250s +
------------------------------------------------------------------------
5 4 3 2
112756875s + 42711625s + 10511875s + 1594197s + 132858s + 4536
o3 : QQ [s]
|
i4 : factorBFunction b
1 1 2 3 4 1 3 7
o4 = (s + 1)(s + -)(s + -)(s + -)(s + -)(s + -)(s + --)(s + --)(s + --)(s +
2 5 5 5 5 10 10 10
------------------------------------------------------------------------
9
--)
10
o4 : Expression of class Product
|