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MathGroup Archive 2007

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Re: Apart question

  • To: mathgroup at smc.vnet.net
  • Subject: [mg73055] Re: Apart question
  • From: "dimitris" <dimmechan at yahoo.com>
  • Date: Wed, 31 Jan 2007 00:32:47 -0500 (EST)
  • References: <epn9uv$cn3$1@smc.vnet.net>

Thanks a lot Andrzej for your reply!

It is exactly the Option Extension of the Factor command that make me 
think that it should be more normal a similar setting of Apart command 
through a possible Option.

So my question should have been stated "why there is not an Option 
like this?"

Regards
Dimitris


Andrzej Kozlowski <akoz at mimuw.edu.pl> wrote:

I am not sure if this answer will satisfy you but one way to put it
is: for exactly the same reason why Factor requires you to specify
the extension manually. In fact, if you use Apart with Factor and
specify the correct extension you will get output equivalent to your
Out[322]. If, in addition, you FullSimplify the individual terms you
will get exactly Out[322].

In[50]:=
FullSimplify /@ Apart[Factor[(x^2 + 2*x + 4)/(x^4 - 7*x^2 + 2*x + 17),
Extension -> {Sqrt[-15 - 4*I], Sqrt[-15 + 4*I]}]]

Out[50]=
1/(2*I*x - Sqrt[-15 - 4*I] + 1) + 1/(2*I*x + Sqrt[-15 - 4*I] + 1) -
1/(2*I*x + Sqrt[-15 + 4*I] - 1) + 1/(-2*I*x + Sqrt[-15 + 4*I] + 1)

Andrzej Kozlowski

Ï/Ç dimitris Ýãñáøå:
> 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]?


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