writting an expression
- To: mathgroup at smc.vnet.net
- Subject: [mg75291] writting an expression
- From: dimitris <dimmechan at yahoo.com>
- Date: Tue, 24 Apr 2007 03:22:45 -0400 (EDT)
Hello.
I have the expression
In[193]:=
ee = 1/(1 + o^4);
and I want to write in the form
Out[194]=
(-Sqrt[2] + o)/(2*Sqrt[2]*(-1 + Sqrt[2]*o - o^2)) + (Sqrt[2] + o)/
(2*Sqrt[2]*(1 + Sqrt[2]*o + o^2))
Currently I can think something like
In[237]:=
1 + o^4 == (a + b*o + o^2)*(c + d*o + o^2) + O[o]^5
LogicalExpand[%]
({ToRules[#1]} & )[(Reduce[#1, {a, b, c, d}] & )[Reduce[% && a < b,
Reals]]]
Apart[1/((a + b*o + o^2)*(c + d*o + o^2) /. %[[1]])]
Out[237]=
1 + o^4 == SeriesData[o, 0, {a*c, b*c + a*d, a + c + b*d, b + d, 1},
0, 5, 1]
Out[238]=
-1 + a*c == 0 && b + d == 0 && b*c + a*d == 0 && a + c + b*d == 0
Out[239]=
{{a -> 1, b -> Sqrt[2], c -> 1, d -> -Sqrt[2]}}
Out[240]=
(-Sqrt[2] + o)/(2*Sqrt[2]*(-1 + Sqrt[2]*o - o^2)) + (Sqrt[2] + o)/
(2*Sqrt[2]*(1 + Sqrt[2]*o + o^2))
Any other ideas?
Thanks.
Dimitris
- Follow-Ups:
- Re: writting an expression
- From: Daniel Lichtblau <danl@wolfram.com>
- Re: writting an expression