# Revision history [back]

### How to solve system of equations in polynomial ring over GF with a different variables

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?

### How to solve system of equations in polynomial ring over GF with a different variables

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?

 3 None Max Alekseyev 5828 ●7 ●38 ●125

### How to solve system of equations in polynomial ring over GF with a different variables

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?

 4 retagged FrédéricC 5141 ●3 ●43 ●112

### How to solve system of equations in polynomial ring over GF with a different variables

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?