lineno and amsmath compatibility

UPDATE 2 (READ THIS!): As Ulrich Diez points out, this can be made more compact. Here's the result (place this in the preamble, probably anywhere):

\newcommand*\patchAmsMathEnvironmentForLineno[1]{%
  \expandafter\let\csname old#1\expandafter\endcsname\csname #1\endcsname
  \expandafter\let\csname oldend#1\expandafter\endcsname\csname end#1\endcsname
  \renewenvironment{#1}%
     {\linenomath\csname old#1\endcsname}%
     {\csname oldend#1\endcsname\endlinenomath}}% 
\newcommand*\patchBothAmsMathEnvironmentsForLineno[1]{%
  \patchAmsMathEnvironmentForLineno{#1}%
  \patchAmsMathEnvironmentForLineno{#1*}}%
\AtBeginDocument{%
\patchBothAmsMathEnvironmentsForLineno{equation}%
\patchBothAmsMathEnvironmentsForLineno{align}%
\patchBothAmsMathEnvironmentsForLineno{flalign}%
\patchBothAmsMathEnvironmentsForLineno{alignat}%
\patchBothAmsMathEnvironmentsForLineno{gather}%
\patchBothAmsMathEnvironmentsForLineno{multline}%
}

This is all that is needed for the standard AMS math environments. However, if you want to add environment BLAH, you can add

\patchAmsMathEnvironmentForLineno{BLAH}

before the closing curly brace. If you want to add environments BLAH and BLAH*, you can add

\patchBothAmsMathEnvironmentsForLineno{BLAH}

before the closing curly brace.

UPDATE 1: If you use the mathlines lineno option, you may notice that amsmath environments like align may create strange double numbers at the end of the environment. I haven't looked into why this is the case. If you really need mathlines loaded, you may want to consider ways of using equation or equation* exclusively. Keep in mind that you will still need to load at least the equation and equation* lines:

\AtBeginDocument{%
%
\let\oldequation\equation%
\let\endoldequation\endequation%
\renewenvironment{equation}%
  {\linenomath\oldequation}{\endoldequation\endlinenomath}%
%
\expandafter\let\expandafter\oldequationstar\csname equation*\endcsname%
\expandafter\let\expandafter\endoldequationstar\csname endequation*\endcsname%
\renewenvironment{equation*}%
  {\linenomath\oldequationstar}{\endoldequationstar\endlinenomath}%
}

You may think that the displaymath option of lineno will do this for you, but loading amsmath seems to prevent that. I haven't looked into why.

A comp.text.tex post gives some history behind this fix.

It's well-known that lineno and amsmath don't play well together. After loading amsmath, the paragraph that precedes an equation, equation*, align, align*, or any of the other amsmath environments will cease to get line numbers. The ugly fix to this is to wrap every math environment with a linenomath environment. That's pretty annoying. Here's a fix that redefines the equation environment and the amsmath environments so that they'll work with noalign. Yes, it even handles the starred versions of these.

% To deal with amsmath, must redefine math environments later
\AtBeginDocument{%
%
\let\oldequation\equation%
\let\endoldequation\endequation%
\renewenvironment{equation}%
  {\linenomath\oldequation}{\endoldequation\endlinenomath}%
%
\expandafter\let\expandafter\oldequationstar\csname equation*\endcsname%
\expandafter\let\expandafter\endoldequationstar\csname endequation*\endcsname%
\renewenvironment{equation*}%
  {\linenomath\oldequationstar}{\endoldequationstar\endlinenomath}%
%
\let\oldalign\align%
\let\endoldalign\endalign%
\renewenvironment{align}%
  {\linenomath\oldalign}{\endoldalign\endlinenomath}%
%
\expandafter\let\expandafter\oldalignstar\csname align*\endcsname%
\expandafter\let\expandafter\endoldalignstar\csname endalign*\endcsname%
\renewenvironment{align*}%
  {\linenomath\oldalignstar}{\endoldalignstar\endlinenomath}%
%
\let\oldflalign\flalign%
\let\endoldflalign\endflalign%
\renewenvironment{flalign}%
  {\linenomath\oldflalign}{\endoldflalign\endlinenomath}%
%
\expandafter\let\expandafter\oldflalignstar\csname flalign*\endcsname%
\expandafter\let\expandafter\endoldflalignstar\csname endflalign*\endcsname%
\renewenvironment{flalign*}%
  {\linenomath\oldflalignstar}{\endoldflalignstar\endlinenomath}%
%
\let\oldalignat\alignat%
\let\endoldalignat\endalignat%
\renewenvironment{alignat}%
  {\linenomath\oldalignat}{\endoldalignat\endlinenomath}%
%
\expandafter\let\expandafter\oldalignatstar\csname alignat*\endcsname%
\expandafter\let\expandafter\endoldalignatstar\csname endalignat*\endcsname%
\renewenvironment{alignat*}%
  {\linenomath\oldalignatstar}{\endoldalignatstar\endlinenomath}%
%
\let\oldgather\gather%
\let\endoldgather\endgather%
\renewenvironment{gather}%
  {\linenomath\oldgather}{\endoldgather\endlinenomath}%
%
\expandafter\let\expandafter\oldgatherstar\csname gather*\endcsname%
\expandafter\let\expandafter\endoldgatherstar\csname endgather*\endcsname%
\renewenvironment{gather*}%
  {\linenomath\oldgatherstar}{\endoldgatherstar\endlinenomath}%
%
\let\oldmultline\multline%
\let\endoldmultline\endmultline%
\renewenvironment{multline}%
  {\linenomath\oldmultline}{\endoldmultline\endlinenomath}%
%
\expandafter\let\expandafter\oldmultlinestar\csname multline*\endcsname%
\expandafter\let\expandafter\endoldmultlinestar\csname endmultline*\endcsname%
\renewenvironment{multline*}%
  {\linenomath\oldmultlinestar}{\endoldmultlinestar\endlinenomath}%
%
}

The pattern is pretty clear. You can use it along with any of your own environments. For example, add this at the end (before the closing curly brace) to fix your BLAH environment:

\let\oldBLAH\BLAH%
\let\endoldBLAH\endBLAH%
\renewenvironment{BLAH}%
  {\linenomath\oldBLAH}{\endoldBLAH\endlinenomath}%

and drop this at the end (before the closing curly brace) to fix your BLAH* environment:

\expandafter\let\expandafter\oldBLAHstar\csname BLAH*\endcsname%
\expandafter\let\expandafter\endoldBLAHstar\csname endBLAH*\endcsname%
\renewenvironment{BLAH*}%
  {\linenomath\oldBLAHstar}{\endoldBLAHstar\endlinenomath}%

I hope that's useful for someone.