# Revision history [back]

### How to solve a differential equation in polynomial ring (modulo polynomial)

I'm working in an arbitrary field F=GF(p^m,'a',modulus=f) where f is a irreducible polynomial of degree m in F_p. I then took an irreducible polynomial h of degree k in PolynomialRing(F). Now i am trying to solve the differential equation for phi with degree(phi)= d with d < k fixed

phi= phi' mod h

I tried solving this the regular way by defining phi as a function and using desolve(), but i don't see how to implement the mod h part and how to demand phi to have degree d.

Any help would be greatly appreciated!

### How to solve a differential equation in polynomial ring (modulo polynomial)

I'm working in an arbitrary field F=GF(p^m,'a',modulus=f) where f is a irreducible polynomial of degree m in F_p. I then took an irreducible polynomial h of degree k in PolynomialRing(F). Now i am trying to solve the differential equation for phi with degree(phi)= d with d < k fixed

phi= phi * ksi = phi' mod hh, where ksi is a fixed polynomial with degree h-1

I tried solving this the regular way by defining phi as a function and using desolve(), but i don't see how to implement the mod h part and how to demand phi to have degree d.

Any help would be greatly appreciated!