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 * ksi = phi' mod h, 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!
Could you please provide the explicit construction of
p, m, F, f, h, k, d? Then we have something to start with.f=x^13+x^4+x^3+x+1, p=2, m=13, F=GF(p^m, name="a", modulus=f), h is a random irreducible polynomial of degree 8 in the polynomial ring of GF, d is the degree of phi, it should be less than or equal to 4