Ask Your Question

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

asked 2018-05-03 16:04:36 +0200

anonymous user


updated 2018-05-05 23:36:04 +0200

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!

edit retag flag offensive close merge delete


Could you please provide the explicit construction of p, m, F, f, h, k, d ? Then we have something to start with.

tmonteil gravatar imagetmonteil ( 2018-05-05 12:21:32 +0200 )edit

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

Necoroyals gravatar imageNecoroyals ( 2018-05-05 12:56:36 +0200 )edit

1 Answer

Sort by ยป oldest newest most voted

answered 2018-05-05 22:38:38 +0200

tmonteil gravatar image

updated 2018-05-05 22:42:30 +0200

What is wrong is the following argument ?

The degree of $\phi-\phi'$ is d, which is smaller than the degree of h since $d<h$ <="" p="">

Hence, $\phi-\phi' = 0 \mod h$ is equivalent to $\phi-\phi' = 0$. Hence $\phi = 0$ is the only solution to the equation.

edit flag offensive delete link more


Sorry i checked again and it should be phi * ksi = phi' mod h, where ksi is a fixed polynomial with degree h-1, terribly sorry about the confusion....

Necoroyals gravatar imageNecoroyals ( 2018-05-05 23:35:30 +0200 )edit

Your Answer

Please start posting anonymously - your entry will be published after you log in or create a new account.

Add Answer

Question Tools

1 follower


Asked: 2018-05-03 16:04:36 +0200

Seen: 199 times

Last updated: May 05 '18