Avoiding dependent types wasn't due to a problem in Julia. Proper dependent types are essentially not something you want to mix with Jit compilation due to undecidability, at least not if you want to use bignums in your dependent values.

Of course you could emulate them some other way in Julia, but they are deliberately not baked into the language.

In the end we used the model that some computer algebra systems, like Sage and Magma use, of having parent objects for the rings in which the element objects live. I'll leave it up to the experts to figure out if this is dependent typing or not. It obviously works very well either way.