Merge pull request #7378 from debugger22/expr_coeff_fix

Fix a bug in coeff for Mul
Remove UTF related comment at top of file
Merge pull request #7355 from bjodah/fix_coeff_for_Indexed

Fix coeff for indexed

Fixes #5758.
Moved finite_diff from core to series. Extended doc of finite_diff.
Updated Derivative.as_finite_diff() doc, tests and default step-size.
Adds test extra test for latex of IndexedBase
Merge remote-tracking branch 'upstream/master' into finite_difference
Fixed/updated docstrings with new master
Merge branch 'master' into clear-atoms(Symbol)
merging master with newly updated files
polyroots: always refine all roots

Previously if the given root was already converged, it wasn't refined. But this
seems to increase the number of iterations needed to converge considerably.
polyroots: Raise error if convergence not achieved
polyroots: chop small numbers in "cleanup" mode

Previously only small real or imaginary parts were chopped. But if abs(x) is
close to zero, we want to chop this case as well.
polyroots: use `extraprec` argument

Previously this argument was not used at all by a mistake and instead the
default value 10 was assigned directly.
polyroots: fix tolerance calculation

We now set the tolerance `tol` directly equal to `ctx.eps`. This is the right
way to do it, since if more working precision is needed, the user needs to
assign the `extraprec` argument.
Refactor nroots() to make it more robust

The following changes were made:

* The polynomial coefficients are always converted to integers. Previously, a
  floating point number was used instead, which loses accuracy, and then for
  higher order polynomials (e.g. Legendre of order 64) one has to use large
  working precision just to represent polynomial coefficients accurately
  enough (otherwise one gets inaccurate roots, for example complex roots
  solution instead of real ones). Now this problem is completely avoided.

* We set extra precision in polyroots() based on the polynomial order.
  "10*order" seem to work well. This formula can be adjusted. This takes care
  of the problem that higher order polynomials suffer from numerical
  cancellation.

* We remove the `error` argument. Now the error is always either lower than `n`
  digits, or an exception is raised.

* The roots are now ordered by mpmath, which returns the correct ordering (real
  roots first, then complex ones).
Add tests for nroots()

We test roots of Legendre polynomial of order 64, as well as some smaller
polynomials. Besides accuracy, these tests also ensure the proper ordering of
the roots.
polyroots: use NoConvergence instead of Exception

A test written as well.
Add a note to tests about the roots order
Merge branch 'master' of git://github.com/sympy/sympy