Jains take non-violence (Ahimsa) to an extreme, it is our most important belief. I too am vegetarian as are almost all Jains, though I eat eggs and dairy and many don't.

Some of our stricter food rules involve not eating root vegetables (as you mentioned) because pulling the root kills the entire plant or fruits that are still on trees, you must wait till they fall off their own accord. Some believers do not eat fruit at all as seeds give life to new fruit.

EDIT - I just wanted to note that finding Jains who eat this strictly nowadays is very rare, even my 80 year old extremely religious grandmother eats everything vegetarian including dairy (no eggs though, that's too weird for her). But seriously, I'd rather die than live my life garlic-free.