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I want to reduce system of symbolyc equations by modulo.

I create field and polynomical ring

F = GF(31)
R.<x, y, z> = PolynomialRing(F)

And try to create system:

system = [
    x == 3 * y,
    z = 2 * x
]

To use solve(system, [x, y, z]) (here I expected solution x = 3 * y, z = 6 * y). But all of equations evaluate to False.

How to create correct equatiations?

I want to reduce system of symbolyc equations by modulo.

I create field and polynomical ring

F = GF(31)
R.<x, y, z> = PolynomialRing(F)

And try to create system:

system = [
    x == 3 * y,
    z = 2 * x
]

To use solve(system, [x, y, z]) (here I expected solution x = 3 * y, z = 6 * y). But all of equations evaluate to False.

How to create correct equatiations?

I want to reduce system of symbolyc equations by modulo.

I create field and polynomical ring

F = GF(31)
R.<x, y, z> = PolynomialRing(F)

And try to create system:

system = [
    x == 3 * y,
    z = == 2 * x
]

To use solve(system, [x, y, z]) (here I expected solution x = 3 * y, z = 6 * y). But all of equations evaluate to False.

How to create correct equatiations?

I want to reduce system of symbolyc equations by modulo.

I create field and polynomical ring

F = GF(31)
R.<x, y, z> = PolynomialRing(F)

And try to create system:

system = [
    x == 3 * y,
    z == 2 * x
]

To use solve(system, [x, y, z]) (here I expected solution x = 3 * y, z = 6 * y). But all of equations evaluate to False.

How to create correct equatiations?