How to record all the output (including error messages) of a mathematica script in a file?

Question

Is it possible to record all the output of a Mathematica script to a file? I am looking for the Mathematica equivalent of fortran ./a.out > out.dat which record all the output string to the file out.dat.

Using OpenWrite[] and WriteString[] can record only the part I can specify but not the error messages which also can appear during execution. For example consider the script test.m

Print@"Start";
x=1/0;
Print@x;
Quit[];

If you run math -script test.m it will produce a message about encountering 1/0 apart from the string "Start" and "ComplexInfinity" due to the Print. I want to record all these messages in a file. Is it possible?

Clarification

When you run a script in terminal it produces different messages, both user defined (with Print) or machine generated (like error messages). In a note book they are automatically recorded. But when running the script in background in a remote machine, it is not possible to keep track of all the messages. So I am looking for a way to record them in a file so that I can get an idea of the progress at any instance by looking at that file.

Answer 1

For this kind of "logging" in SubKernels for example I use the following code:

oldoutput = $Output; (* store $Output *)
oldmessages = $Messages; (* same for $Messages *)
CheckAbort[
  logstream = OpenWrite["yourlog.log"];
  $Output = {logstream}; (* redirect $Output *)
  AppendTo[$Messages, logstream]; (* add the logfile as an additional destination for $Messages *)
  (* your code *)
,
  AbortProtect[
    Close[logstream];
    $Output = oldoutput; (* restore $Output *)
    $Messages = oldmessages; (* restore $Messages *)
  ];
];
Close[logstream];
$Output = oldoutput; (* restore $Output *)
$Messages = oldmessages; (* restore $Messages *)

This code redirects the output (things that were Print[]ed for example) and the messages ("Division by zero" etc) to the file "yourlog.log" and restores the old output channels after completion of the calculation.

The construction with CheckAbort[] is used to restore output channels in case of an Abort[] - either by your code or by the user.

PS: Sorry about the obvious comments. There seems to be a bug in the SE syntax highlighting code that breaks indentation when there is an unmatched number of dollar signs on a line.