# How to Return the Roots from IntervalRootFinding.jl in pi terms?
**URL:** https://discourse.julialang.org/t/how-to-return-the-roots-from-intervalrootfinding-jl-in-pi-terms/95566
**Category:** General Usage
**Created:** [March 5, 2023, 5:52am UTC](https://discourse.julialang.org/t/how-to-return-the-roots-from-intervalrootfinding-jl-in-pi-terms/95566 "2023-03-05T05:52:23Z")
**Posts on this page:** 5
**Page:** 1
### Author:  [@Freya\_the\_Goddess](https://discourse.julialang.org/u/Freya_the_Goddess)
#### Post date: [March 5, 2023, 5:52am UTC](https://discourse.julialang.org/t/how-to-return-the-roots-from-intervalrootfinding-jl-in-pi-terms/95566/1 "2023-03-05T05:52:24Z")
Hi all,
I want to know how to make the roots computed by IntervalRootFinding returned in \pi terms instead of decimals / float value / numeric term ?
```julia
using SymPy, IntervalArithmetic, IntervalRootFinding
@syms x
v1(x) = log(1.5 + sin(x))
v2(x) = cos(x)/(1.5 + sin(x))
vd = diff((v1(x)), (x))
vdd = simplify(diff((vd), (x)))
V1 = IntervalRootFinding.roots(v2, -5..5)
println("Computing with Julia")
println("f'(x) = ", vd)
println("f''(x) = ", vdd)
println("a. absolute extreme points: ")
V1
```
---
### Author:  [@Sevi](https://discourse.julialang.org/u/Sevi)
#### Post date: [March 5, 2023, 10:39am UTC](https://discourse.julialang.org/t/how-to-return-the-roots-from-intervalrootfinding-jl-in-pi-terms/95566/2 "2023-03-05T10:39:18Z")
This might be related to the difference between symbolic expressions and `Float64` numbers. Floating point numbers are just an approximation to most “real” values that we might be interested in. That’s usually fine, because the approximation is very good, but if we want the “true” mathematical value, like in your case, the distinction is important.
It looks like `IntervalRootFinding` just finds the roots of normal Julia functions using floats. So even if the result is actually \pi/2 we just get the closest float that it could find and we can’t really tell that the solution is \pi / 2.
However, symbolic libraries like SymPy are exactly made for this kind of scenario and provides some tools to find roots (it’s usually just called `solve` since we want to _solve_ an equation f(x) = 0.
In this example:
```julia
julia> f1(x) = cos(x)/(1.5 + sin(x));
julia> solve(f1(x), x) # solving the equation f1(x) == 0 for x
2-element Vector{Sym}:
1.57079632679490
4.71238898038469
```
Hmm, it seems like it still didn’t work. The result are now symbolic numbers (`Vector{Sym}` not `Vector{Float64}`), but that has a different, slightly subtle reason: The `1.5` is a Julia floating point number and will be converted to a SymPy symbol when calling the function.
```julia
julia> Sym(1.5)
1.50000000000000
```
Although it is the right value, SymPy has some difficulty realizing that it is actually 3/2. I’m not exactly sure why this matters here (because the numerator `cos(x)` is zero regardless of the denominator), but the following would work:
```julia
julia> f2(x) = cos(x)/(Sym(3) / Sym(2) + sin(x)); # Define the fraction explicitly as symbolic value 3 / 2
julia> solve(f2(x), x)
2-element Vector{Sym}:
pi/2
3*pi/2
```
Note that `IntervalRootFinding` doesn’t work now anymore, since it doesn’t know how to use `Sym` values.
Hope that helps!
---
### Author:  [@j\_verzani](https://discourse.julialang.org/u/j_verzani)
#### Post date: [March 5, 2023, 12:47pm UTC](https://discourse.julialang.org/t/how-to-return-the-roots-from-intervalrootfinding-jl-in-pi-terms/95566/3 "2023-03-05T12:47:45Z")
Just to add to this excellent answer, using a rational (3//2) instead of the float (1.5 or 3/2) should be enough, as rationals promote to symbolic equivalents.
---
### Author:  [@Sevi](https://discourse.julialang.org/u/Sevi)
#### Post date: [March 5, 2023, 3:42pm UTC](https://discourse.julialang.org/t/how-to-return-the-roots-from-intervalrootfinding-jl-in-pi-terms/95566/4 "2023-03-05T15:42:11Z")
Very convenient, thanks for the hint!
---
### Author:  [@Freya\_the\_Goddess](https://discourse.julialang.org/u/Freya_the_Goddess)
#### Post date: [March 6, 2023, 5:00am UTC](https://discourse.julialang.org/t/how-to-return-the-roots-from-intervalrootfinding-jl-in-pi-terms/95566/5 "2023-03-06T05:00:40Z")
It helps a lot thanks for this amazing guidance.