This is my first post ever in this forum. I think that I have read all the relevant instructions on how to post. Still, if I am missing something let me know: I will gladly correct myself.

I need to study a system of polynomial equations as a certain parameter `\rho`

varies. I wrote the following and it works exactly as I want: result_block(0.78) gives me the solutions for the value 0.78 of the parameter and then the vector probabilities just keeps the ones I am interested in.

```
# Equations for the blocking parameter
using HomotopyContinuation # load the package into the current Julia session
@var x y z; # declare the variables x and y and z
f_block(ρ) = System([x - ρ * z*(z + 2*y*(1-z)),
y - ρ * (x^2 + 2*x*(1-x)*(y+z) + y*z*(1-4*x+3*x^2)),
z - ρ * (z^2 + 2*z*(1-z)*(y+x) + y*x*(1-4*z+3*z^2)) ]) # construct system f
result_block(ρ) = real_solutions(solve(f_block(ρ))) # solve f considering only real solutions
B = result_block(0.78)
probabilities = [B[i] for i=1:length(B) if -0.1<B[i][1]<1.1 && -0.1<B[i][2]<1.1 && -0.1<B[i][3]<1.1 && (B[i]!=[0,0,0])]
```

Now I would like to study what happens as `\rho`

varies. To do so, I want to plot a graph that is 0 when the probabilities is empty and 1 when probabilities contains some value. I want to use `\rho`

on the x-axis and y on the y-axis, where y is defined as described above. To implement such a definition of y I wrote the following:

```
y = [1.2]
pop!(y)
for ρ in range(0.6, 0.8, step = 0.01)
B = result_block(ρ)
probabilities = [B[i] for i=1:length(B) if -0.1<B[i][1]<1.1 && -0.1<B[i][2]<1.1 && -0.1<B[i][3]<1.1 && (B[i]!=[0,0,0])]
if probabilities != Any[]
push!(y,1)
else
push!(y,0)
end
end
```

which does not work and returns the following error:

```
MethodError: no method matching +(::Variable, ::Vector{Expression})
For element-wise addition, use broadcasting with dot syntax: scalar .+ array
Closest candidates are:
+(::Any, ::Any, ::Any, ::Any...) at C:\Users\Damiano\AppData\Local\Programs\Julia-1.7.1\share\julia\base\operators.jl:655
+(::Union{HomotopyContinuation.ModelKit.ExpressionRef, Expression, Variable}) at C:\Users\Damiano\.julia\packages\HomotopyContinuation\UFWkw\src\model_kit\symengine.jl:302
+(::Union{HomotopyContinuation.ModelKit.ExpressionRef, Expression, Variable}, ::Union{HomotopyContinuation.ModelKit.ExpressionRef, Expression, Variable}) at C:\Users\Damiano\.julia\packages\HomotopyContinuation\UFWkw\src\model_kit\symengine.jl:267
...
Stacktrace:
[1] f_block(ρ::Float64)
@ Main .\In[1]:4
[2] result_block(ρ::Float64)
@ Main .\In[1]:7
[3] top-level scope
@ In[3]:4
[4] eval
@ .\boot.jl:373 [inlined]
[5] include_string(mapexpr::typeof(REPL.softscope), mod::Module, code::String, filename::String)
@ Base .\loading.jl:1196
```

One additional piece of information: if I comment out the line `B = result_block(ρ)`

I get no error, so I assume that the problem lies there somehow. But to me this line looks so innocent to me!

I have already spent a few hours trying to solve this issue and I have also tried to google the error and stuff like this.

If you would be able to help me I would be really grateful!

Again, I am new to Julia, so I hope that I am not bothering you with something extremely stupid.