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factorBFunction(RingElement) -- factorization of a b-function

Synopsis

Description

Fact. 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

Caveat

f should be an output of one of the b-function routines

See also