Postgresql: generate default volume value to integer rank - sql

Question

Let's say I have the (fictional) table below to store messages in a discussion board, organised by topic, themselves identified by an integer:
CREATE TABLE MESSAGE(
message_global_id SERIAL PRIMARY KEY,
topic_id INTEGER DEFAULT 0,
message_nb_in_topic INTEGER,
text TEXT
);
I want to set the column message_nb_in_topic to the equivalent of a sequence, but that resets for each topic number.
For example,
I post for topic 0 -> the message has message_nb_in_topic = 0
I post for topic 0 -> the message has message_nb_in_topic = 1
I post for topic 1 -> the message has message_nb_in_topic = 0
I post for topic 0 -> the message has message_nb_in_topic = 2
I post for topic 1 -> the message has message_nb_in_topic = 1
I post for topic 2 -> the message has message_nb_in_topic = 0
Is it possible to generate such sequence in postgresql ? I was thinking of some CREATE FUNCTION, but I am not very familiar with their usages.
Any hint would be greatly appreciated.
EDIT
Gordon's solution is the cleanest, however I forgot to mention I was behind some middleware that does not allow me to carry out any complex update.
Yet I ended up with the trigger bellow:
CREATE FUNCTION set_message_nb()
RETURNS trigger AS '
DECLARE
max_for_topic int;
BEGIN
max_for_topic := (SELECT max(message_nb_in_topic) FROM MESSAGE WHERE topic_id=NEW.topic_id);
IF max_for_topic IS NULL THEN
NEW.message_nb_in_topic := 1;
ELSE
NEW.message_nb_in_topic := 1 + max_for_topic;
END IF;
RETURN NEW;
END' LANGUAGE 'plpgsql';
CREATE TRIGGER add_messagenb_at_insert
BEFORE INSERT ON MESSAGE
FOR EACH ROW
EXECUTE PROCEDURE set_message_nb();

Answer 1

You don't need your own function; row_number() does this for you:
select m.*,
row_number() over (partition by topic order by message_global_id) as seqnum
from messages m;
I missed that you want an update:
update messages m
set message_nb_in_topic = mm.seqnum
from (select m.*,
row_number() over (partition by topic order by message_global_id) as seqnum
from messages m
) mm
where m.message_global_id = mm.message_global_id;