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Test for Irreducibility of certain polynomials with

  • To: mathgroup at smc.vnet.net
  • Subject: [mg85443] Test for Irreducibility of certain polynomials with
  • From: "Guillermo Pineda Villavicencio" <g.pinedavillavicencio at ballarat.edu.au>
  • Date: Mon, 11 Feb 2008 06:02:15 -0500 (EST)

Hi there,

 I want to test the irreducibility of the following polynomials of
degree r with Mathematica. 

H[x_,d_] := Sum[(-d + 1)^(j)*Binomial[r - j, j]*x^(r - 2*j), {j, 0, (r -
1)/2}]

 I use the Mathematica function

 
IrreducibleQ[p_?PolynomialQ,Modulus->m_]:=Module[{f=FactorList[p,Modulus->m]},
    Total[Last/@DeleteCases[f,{_Integer,_Integer}]]==1
  ]

 But I want Mathematica to consider H[x,d] as a function in x (not in x
and d). Is it possible???

 Best regards,
Guillermo


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