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Question: residue class ring, how do I define the ring F_q[x]/(f), where f is an arbitrary Polynomial of degree >1, F_q finite field

Question:residue class ring, how do I define the ring F_q[x]/(f), where f is an arbitrary Polynomial of degree >1, F_q finite field

bellaqueame 15 Maple
polynomial residue finite-field
January 31 2019
1

Hello,

I do know how to define the finite field F_q=GF(p,k). But know I am looking at the residue class ring R:= \F_q[x]/(f) with f an arbitrary polynomial in F_q[x]  of degree(f)>1. And I need all the calculations over R. My f will be reducible, so R wont be a field. Can anyone help me how I tell Maple to do the arithmetic in R? With the right remainder calculation? And with [f]=[0], so that the sesidue class of f is the same as the residue class of 0?

Thank you very much for any help!!

 
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