Re: Apart question
- To: mathgroup at smc.vnet.net
- Subject: [mg73046] Re: Apart question
- From: Paul Abbott <paul at physics.uwa.edu.au>
- Date: Tue, 30 Jan 2007 23:56:39 -0500 (EST)
- Organization: The University of Western Australia
- References: <epn9uv$cn3$1@smc.vnet.net>
In article <epn9uv$cn3$1 at smc.vnet.net>, "dimitris" <dimmechan at yahoo.com> wrote: > 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]? Why does Factor not factor the denominator into linear factors? With the appropriate extension (Extension -> Automatic does not work), one can factor the denominator Factor[(x^2 + 2*x + 4)/(x^4 - 7*x^2 + 2*x + 17), Extension -> {Sqrt[-15 + 4*I], Sqrt[-15 - 4*I]}] and then obtain the desired result using Apart and FullSimplify. FullSimplify /@ Apart[%] Cheers, Paul _______________________________________________________________________ Paul Abbott Phone: 61 8 6488 2734 School of Physics, M013 Fax: +61 8 6488 1014 The University of Western Australia (CRICOS Provider No 00126G) AUSTRALIA http://physics.uwa.edu.au/~paul