# Strange behaviour in simplifying a function

I am developping a long notebook to master Sage. But each time I fall on a problem. This time

```
p, D, w_0, x, I = var('p, D, w_0, x, I')
β = var('beta')
π = var('pi')
w00=8
D1=6
p1=0.5
A = matrix(SR, 2, 2, [[w_0, 1],[w_0-π,1]])
y = vector([w_0-D, w_0-D-π+I])
sol=A.solve_right(y)
sola=sol[0].full_simplify().function(D, π, w_0)
solb=sol[1].full_simplify().function(D, π, I, w_0)
f=(sola*x + solb).function(x, D, π, I, w_0)
g=f(x, D, β*I*(1-p), I, w_0).factor().collect(x).simplify().function(x, D, β, p, w_0)
h(x, D, p, w0)=g(x, D, 1, p, I, w_0).collect(D).collect(x).simplify()
show(f)
show(g)
show(h)
```

1) this is the main question : You can observe that `g`

is independanr of `I`

. But `h`

is `g`

with $\beta = 1$. So why `I`

does reappear in h ?

2) How could we explain **SM** to write the slope of the 3 curves as I would write them in a sheet of paper ?

`g`

is a function of 5 arguments, but you are passing 6, including the parameter`I`

.Thanks some time I would like to put aways my stupid questions.