I am looking for a program that can read a LaTeX file and give a warning (+ ideally a fix suggestion) for each common mistake it spots in math formulas. If possible, free and works with Windows 7 SP1 x64 Ultimate.
Examples of common mistake in LaTeX math mode:
1) Differentials: $\int_0^1 f(x) dx$ instead of $ \int_0^1 f(x) \, dx$ :
2) Multi-letter function names: $log e^x = x$ instead of $\log e^x = x$:
3) Wrong kinds of dots: "$x,...,y$" instead of $x, \ldots, y $.
It would be even greater if it could give warnings for all the LaTeX writing, not just the math mode, e.g. one common mistake is writing "Yes." instead of ``Yes.'':