I have the irreducible fraction: $$\frac{t^2}{t^4+1}$$ When I use the function "apart" in mathematica the output is $\frac{t^2}{t^4+1}$, which means that it was not able to find a way to factor the denominator, instead when I use "apart" in wolfram alpha, I get $$-\frac{t}{2\sqrt2(-t^2+\sqrt2t-1)}-\frac{t}{2\sqrt2(t^2+\sqrt2t+1)}$$ which is correct. Does anyone know how or why the "apart" function gives different results in mathematica and wolfra alpha (i am strictly talking about irreducible fractions)
$\begingroup$
$\endgroup$
2
-
1$\begingroup$ Hi user372003 It is not my intention to criticize but please do not accept the answer I provided for a period of 24 hours. This gives others the chance and impetus to answer. I have never taken back an accepted answer so I do not even know if it is possible but if you can I will not be offended. $\endgroup$– bobbymFeb 12, 2017 at 10:31
-
$\begingroup$ @bobbym I'll keep in mind for next time! However, the answer you gave me, was the on I was looking for $\endgroup$– user372003Feb 14, 2017 at 7:40
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
3
Maybe Alpha is calling additional commands behind the scene.
Factor[t^2/(t^4 + 1), Extension -> Sqrt[2]]
will break it apart but not exactly as you have.
To do better
Factor[t^2/(t^4 + 1), Extension -> Sqrt[2]]//Apart
as Bob Hanlon points out below.
-
$\begingroup$ Thank you! That might have been the problem $\endgroup$ Feb 12, 2017 at 8:54
-
$\begingroup$ Let us wait for more users to answer and then we will see. $\endgroup$– bobbymFeb 12, 2017 at 8:54
-
3$\begingroup$
Factor[t^2/(t^4 + 1), Extension -> Sqrt[2]] // Apart$\endgroup$ Feb 12, 2017 at 14:06