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answered 2014-01-03 21:27:56 +0100
p=7 R=PolynomialRing(IntegerModRing(7),'x') x=R.gen()
I'm not sure if f exist
Maybe f=(q*h+r)//e
Or you want something like this? q=f//g r=f.mod(g)
As for the next question:
f=x^14 + 4*x^7 + 7
g=x^3+1
xgcd(f,g)