It is open-source and it might even use Python.
To find out what package installs Software Center:
$ apt-file find -F /usr/bin/software-center
software-center: /usr/bin/software-center
To download the source code:
$ mkdir software-center
$ cd software-center/
$ apt-get source software-center
Look for the word ‘search’ in the source code. utils/search_query.py seems relevant. It looks like it uses xapian module to do the actual work. It queries /var/lib/apt-xapian-index/index xapian database among others.
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solved How ubuntu software center make “search” operation? [closed]