What are some rules of thumb to construct adjectives from proper names? E.g.
Lagrange => Description lagrangienne.
Newton => Mécanique newtonienne.
Euler, Hamilton => eulérien et hamiltonien.
and so on. But,
Cauchy => ?
Although it is probably not popular, I would use cauchyssois as an analogy with Vichy - vichyssois.
I just found a single occurrence of it:
There is no specific rule for creating such adjectives. They are built the same way than gentilés for which there are no rules either, although there are trends.