Regex ultima ratio puns on the phrase ultima ratio regum (literally, "the final argument of kings" - that is, war). Louis XIV apparently liked that phrase so much he had it put on French cannons. It also inspired a wonderful series of jokes in Neal Stephenson's Snowcrash involving a weapon named Ratio. (The joke manages to combine this Latin phrase with "I'll make him an offer he don't refuse..." from The Godfather movies.)

The second is apparently a reference to the motto (or mottos - see below) of the Royal Regiment of Canadian Artillery: Ubique quo fas et gloria ducunt, which is literally, "Everywhere (where) right and glory lead." I'm assuming that the idea is this (imagine the soldier speaking): "I'll follow everywhere that right and glory lead."

According to Wikipedia, the Ubique was separate from the rest, and you really have two mottos here: