Solving a system to equations in a specified form

[Madhurima Mukhopadhyay]

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)=(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))


Please provide me suggestions

[slelievre]

----- 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.

[Madhurima Mukhopadhyay]

p=534601 is known
Defining coefficients is redundant , it is to be omitted.

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--
Madhurima Mukopadhyay
Senior Research Fellow
Applied Statistics Unit
ISI, Kolkata