Spotting LaTeX math common mistakes

Question

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.'':

Answer 1

There are quite a few but the one I would recommend is ChkTeX.

From the web page:

• Supports over 40 warnings. Warnings include:
  • Commands terminated with space. Ignores ``\tt\'', etc.
  • Space in front of references instead of ``~''.
  • Forgetting to group parenthesis characters when sub-/superscripting.
  • Italic correction (``/'') mistakes (double, missing, unnecessary).
  • Parenthesis and environment matching.
  • Ellipsis detection; also checks whether to use ``\dots'', ``\cdots'' or ``\ldots''.
  • Enforcement of normal space after abbreviation. Detects most abbreviations automagically.
  • Enforcement of end-of-sentence space when the last sentence ended with capital letter.
  • Math-mode on/off detection.
  • Quote checking, both wrong types (``"'') and wrong direction.
  • Recommends splitting three quotes in a row.
  • Searching for user patterns.
  • Displays comments.
  • Space in front of ``\label'' and similar commands.
  • Use of ``x'' instead of ``$\times$'' between numbers.
  • Multiple spaces in input which will be rendered as one space (or multiple spaces, where that is undesirable).
  • Warns about text which may be ignored.
  • Mathematical operators typeset as variables.
  • No space in front of/after parenthesis.
  • Demands a consistent quote style.
  • Punctuation inside inner math mode/outside display math mode.
  • Use of TeX primitives where LaTeX equivalents are available.
  • Space in front of footnotes.