# sympy.

**sympy** is a system for symbolic maths in python. It doesn't just compute, it also differentiates, integrates
and automates common calculus steps. The documentation for it can be found here.

**Notes**

The goal is to have the variable `c`

represent the circumference of the fence. By having
this as a variable instead of a number we might be able to do more interesting things with it.
We could for example ask the question, what if the circumference was bigger, what would the
maximum area then be? Maths allows us to answer these sort of questions and sympy helps us
automate it with python.

The code is listed below.

```
import sympy as sp
l, w = sp.symbols("l, w")
area = l * w
circumference = 2 * l + 2 * w
# define variable for circumference
c = sp.symbol("c")
l_expr = sp.solve(sp.Eq(circumference, c), l)[0]
opt_w = sp.solve(sp.diff(area.subs(l, l_expr), w), w)[0]
opt_l = l_expr.subs(w, opt_w)
opt_area = opt_w * opt_l
sp.plot(opt_area);
```

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