Is it normal to use many Triggers?
The major problems with triggers are:

a) They are difficult to debug

b) Trigger cascades can be fatal to your database - take for example if you have an after update trigger in one table which updates another table, which also has an after update trigger, then you will run into lots of issues

A few questions:

a) How often are the "computed" summaries used within your application?

b) How often are the "computed" summaries required to be updated? 

c) Would you consider creating a "reporting" table which is refreshed on a regular basis with the major "computations" that you need?