sympy/sympy — pull request #1746 by prasoon2211 (2013-01-31 14:52:34+00:00)
Title: Solving solvable quintics: First implementation

Please see this:
http://code.google.com/p/sympy/issues/detail?id=3548

Also, see this:
https://groups.google.com/forum/?fromgroups=#!topic/sympy/xXyiOUWH0SU

According to the discussions on above links, this PR introduces solving quintics exactly (not numerically) when they are solvable.

There are a lot of constants involved. So, I created a new file and made a new class for quintics containing required constants.
Also note that solving quintics exactly takes( for x**5 + 15*x +12 =0 ) ~ 40 secs. The long time is attributed to solving five equations of the form x**5 - R =0 somewhere in the middle of the code.

Also, I have used simplify a few times. It seems that the code became almost 3 times as fast with using simplify, than without it.

There is an extra flag; quintics. When set to true, the new roots_quintic method is called and if the quintic is solvable, the solution is returned. I am attaching a screenshot :
![sympy](https://f.cloud.github.com/assets/2565248/114827/89eefb22-6bb5-11e2-8331-e668d8771320.png)

Here you can see the solution of x**5 + 15*x +12 = 0.

I have not added any tests.
@asmeurer Please look at the code. Let me know for changes required.