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Apart question

• To: mathgroup at smc.vnet.net
• Subject: [mg73030] Apart question
• From: "dimitris" <dimmechan at yahoo.com>
• Date: Tue, 30 Jan 2007 06:40:15 -0500 (EST)

Dear All,

In[317]:=
f[x_]:=(x^2+2*x+4)/(x^4-7*x^2+2*x+17)

In[323]:=
Apart[f[x]]

Out[323]=
(4 + 2*x + x^2)/(17 + 2*x - 7*x^2 + x^4)

In[320]:=
Times@@Apply[#1[[1]] - #1[[2]] & , Solve[Denominator[f[x]] == 0, x], 
1]
Apart[(4 + 2*x + x^2)/%]
Map[FullSimplify, %, 1]

Out[320]=
(I/2 - (1/2)*Sqrt[15 - 4*I] + x)*(-(I/2) - (1/2)*Sqrt[15 + 4*I] + 
x)*((1/2)*(I + Sqrt[15 - 4*I]) + x)*
  ((1/2)*(-I + Sqrt[15 + 4*I]) + x)

Out[321]=
(4*I*((4 + 15*I) + (1 + 2*I)*Sqrt[15 - 4*I]))/(Sqrt[15 - 4*I]*(-2*I + 
Sqrt[15 - 4*I] - Sqrt[15 + 4*I])*
    (-2*I + Sqrt[15 - 4*I] + Sqrt[15 + 4*I])*(-I + Sqrt[15 - 4*I] - 
2*x)) - (4*I*((-4 - 15*I) + (1 + 2*I)*Sqrt[15 - 4*I]))/
   (Sqrt[15 - 4*I]*(2*I + Sqrt[15 - 4*I] - Sqrt[15 + 4*I])*(2*I + 
Sqrt[15 - 4*I] + Sqrt[15 + 4*I])*(I + Sqrt[15 - 4*I] + 2*x)) -
  (4*((15 + 4*I) + (2 + I)*Sqrt[15 + 4*I]))/(Sqrt[15 + 4*I]*(-2*I + 
Sqrt[15 - 4*I] - Sqrt[15 + 4*I])*
    (2*I + Sqrt[15 - 4*I] + Sqrt[15 + 4*I])*(-I - Sqrt[15 + 4*I] + 
2*x)) + (4*((-15 - 4*I) + (2 + I)*Sqrt[15 + 4*I]))/
   (Sqrt[15 + 4*I]*(-2*I - Sqrt[15 - 4*I] + Sqrt[15 + 4*I])*(-2*I + 
Sqrt[15 - 4*I] + Sqrt[15 + 4*I])*(-I + Sqrt[15 + 4*I] + 2*x))

Out[322]=
1/(1 + Sqrt[-15 + 4*I] - 2*I*x) + 1/(1 - Sqrt[-15 - 4*I] + 2*I*x) + 1/
(1 + Sqrt[-15 - 4*I] + 2*I*x) -
  1/(-1 + Sqrt[-15 + 4*I] + 2*I*x)

In[323]:=
Options[Apart]

Out[323]=
{Modulus -> 0, Trig -> False}

Why Apart cannot provide straightly the output Out[322]?

• Follow-Ups:
  • Re: Apart question
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>