Suppose given polynomials e,q,h,r in R[x], p∈R (R a ring), how can I use Sage to find f in R[x] so fe=qh+r(mod p)?
Similarly, given f,g in R[x] with gcd(f,g)=1, what function can I use to compute s,t in R[x] so sf+gh=1(mod p) ?
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)
Thanks!
and is there a way to work around the use of the integermodring? I'm writing an algorithm in which I have to succesively compute different functions e.g.
s_j g_j + t_j h_j = 1 modulo p^2^j
s_j g_j + t_j h_j = 1 modulo p^2^(j+1)Would it be best to redefine
R=PolynomialRing(IntegerModRing(p^2^j),'x') every time?
Asked: 11 years ago
Seen: 1,520 times
Last updated: Jan 09 '14
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