cannot remove schema public

Hi,
while writing some tests for an application, I want to remove all tables
and all schemas before running tests.

For the schema public I want to remove it and create again. However that
doesn't work, I'm wondering if that's on purpose, or it's a kind of a bug.

I'm using user 'szymon' in my console.

Then I created a user:

create user test password 'test';

and database

create database test owner test;

I logged into the database as the user:

test=# \c test test
You are now connected to database "test" as user "test".

And the owner of the public schema is not test, however it's an owner of
the test database.

test=# \dn
List of schemas
Name | Owner
--------+--------
public | szymon
(1 row)

When I try to remove the public schema, then I get:

test=> drop schema public cascade;
ERROR: must be owner of schema public

regards,
Szymon