# Evaluating a list of multivariate equations at random values.

I have a list of multivariate equations, there are `o`

multivariate equations in the list where `o`

is an integer and `v = 2o`

, the variables that make up the equations are the generators of `P = PolynomialRing(K,'x',n)`

where `n = v + o`

so for example if `o = 2`

then `v = 4`

and `n = 6`

so the variables that make up the multivariate equations in the list would be `P.gens() = (x0, x1, x2, x3, x4, x5)`

. Now i need to substitute in random values from `GF(q)`

for the first `v`

variables in each of the multivariate equations in the list so in the example above where `v = 4`

random values from `GF(q)`

would be substituted in for the variables `x0, x1, x2, x3`

in each of the multivariate equations in the list, leaving equations in only two variables `x4 and x5`

. I have tried to implement this but i don't really know where to start as i know i am doing something wrong but what i have is the following. If the list of multivariate equations is called `eqn`

for example.

```
for i in range(v):
xi = var('x'+str(i))
eqnsub0 = eqn[i].subs({x[i]:GF(q).random_element()})
```

I already know this is very wrong as the indexing will already go out of bounds since `v > o`

but i don't really know where to start with this. Any help would be great, thanks.

see https://ask.sagemath.org/question/41655