----- Original message (slightly reformatted) ----
I want to find the value of h0, h1, h2, h3, h4 such that
(x - a1)*(x - a2)*(x - a3)*(h0 + h1*x^1 + h2*x^2 + h3*x^3 + h4*x^4 +
x^5)
is equal to
(x + b)*g2 + (a*x + d)
for some a, b, d, in GF(p).
Below is my code which is unable to solve it
a, b, d, a1, a2, a3, h0, h1, h2, h3, h4 = var('a b d a1 a2 a3 h0 h1 h2
h3 h4')
RHS = (x - a1)*(x - a2)*(x - a3)*(h0 + h1*x^1 + h2*x^2 + h3*x^3 +
h4*x^4 + x^5)
g2 = x^7 + 74604*x^6 + 351974*x^5 + 18952*x^4 + 148817*x^3 + 256076*x^2
+ 168356*x + 278165
LHS = (x + b)*g2 + (a*x + d)
Coeff = RHS.coefficients(x, sparse=False)
print(solve(RHS == LHS, h0, h1, h2, h3, h4))
-----
- What is the value of p that you want to work with?
Or is p also an unknown?
- Why do you define "Coeff"? You don't seem to use it.
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