As Volker said, the transaction log records which rows were inserted, updated and deleted and in what order. It doesn't specifically record which triggers were executed, however.

There is no trigger trace feature built in to SQL Anywhere. You can build one using a CREATE TABLE to hold one row per trigger execution (current timestamp, table name, trigger name, triggering operation), and a CREATE EVENT to INSERT a row to record the trigger execution.

Add a TRIGGER EVENT statement to the trigger logic and pass the timestamp, etc, as EVENT_PARAMETER values. An event must be used because it needs to do a COMMIT and you can't code a COMMIT in a trigger; an event runs as a separate connection.

You can also turn the trace on and off by setting a CREATE VARIABLE Y/N in the application and checking the value in the trigger... a separate connection level variable value will exist for each application connection and it will be visible in all the procedures and triggers executing on the application connection.

The CREATE EVENT and TRIGGER EVENT statements provide a powerful tool for launching parallel processes in SQL Anywhere.

The following code shows (and hopefully clears up) some of the confusion surrounding the scope of EVENT_PARAMETER variables...

CREATE EVENT eee
HANDLER BEGIN
   DECLARE @p VARCHAR ( 128 );
   SET @p = COALESCE ( EVENT_PARAMETER ( '@p' ), 'NULL' );
   MESSAGE STRING ( '@p passed to event: ', @p ) TO CONSOLE;
   MESSAGE STRING ( CONNECTION_PROPERTY ( 'Name' ) ) TO CONSOLE;
END;

-- Testing...

BEGIN
   DECLARE @p VARCHAR ( 128 );
   DECLARE @v VARCHAR ( 254 );
   SET @p = 'hello';
   SET @v = 'world';
   MESSAGE STRING ( '@p before event: ', @p );
   TRIGGER EVENT eee ( @p = @v );
   MESSAGE STRING ( '@p after event: ', @p );
END;

@p before event: hello
@p after event: hello
@p passed to event: world
eee

Just to add: In case you want to log the context in which the triggers were invoked (from a batch, procedure or the like), see that question and the sa_stack_trace() system procedure.