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Thank you from the bottom of my heart!!

I noticed that Step 1 was not done either. How do I specify the order of the coefficient t to be d (d=10, etc.)?

Hello, I consider a multivariate polynomial ring F_p[t][x,y] with a univariate polynomial ring F_p[t] over a finite field F_p as a coefficient ring (p is prime number).

I want to generate polynomials as follows.

1. the degree of each coefficient of t is d
2. the terms of x and y are random except for the constant term
3. the constant term should have a specific value (e.g., the value obtained by substituting x=t, y=t^2 for the terms other than the constant term). I want to replace constant coefficient to them.

I have done so far. As follows,

p = 31
P.<t> = PolynomialRing(GF(p))
Q.<x,y> = PolynomialRing(P)
X = Q.random_element(degree = 2,terms = 6,choose_degree = True)
while len(list(X)) <= 5:
    X = Q.random_element(degree = 2,terms = 6,choose_degree = True)
print(X)

But I can't make step 3. What should I do??

I appreciate it ! Thank you so much!

Replace coefficient to specific value on multivariate polynomial Hello, I consider a multivariate polynomial ring F_p[t