As you can see from the text of the file as used in Moodle 1.9 (http://cvs.moodle.org/moodle/filter/algebra/algebradebug.php?revision=1.19.2.3&view=markup), login is required.....
I don't know what you have done vis-a-vis installing a new algebradebug.php file and I suppose it is possible that you are where you are because you have downloaded an inapporpriate version.
Now, if you invoke the debugger as it is supposed to be invoked (logged in) after having turned on the Tex filter and having debugged the tex filter (as the algebra filter requires the tex filter as the algebra filter simply parses "algebra" text expressions and and then converts to Tex and passes the Tex expressions to the Tex filter) what does your system tell you?