# How to solve two symbolic nonlinear equations in Julia?

**URL:** <https://discourse.julialang.org/t/how-to-solve-two-symbolic-nonlinear-equations-in-julia/11916>\
**Category:** Optimization (Mathematical)\
**Created:** [June 24, 2018, 10:58pm UTC](https://discourse.julialang.org/t/how-to-solve-two-symbolic-nonlinear-equations-in-julia/11916 "2018-06-24T22:58:51Z")\
**Posts on this page:** 8\
**Page:** 2

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**Author:** ![dpsanders](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dpsanders/32/3573_2.png) [@dpsanders](https://discourse.julialang.org/u/dpsanders)\
**Post date:** [June 26, 2018, 3:05pm UTC](https://discourse.julialang.org/t/how-to-solve-two-symbolic-nonlinear-equations-in-julia/11916/21 "2018-06-26T15:05:36Z")

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Just a note that on the `master` branch you can do the following to check that all roots are reported as unique:

```julia
all(isunique, rts)

```

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**Author:** ![BLI](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/bli/32/37206_2.png) [@BLI](https://discourse.julialang.org/u/BLI)\
**Post date:** [June 27, 2018, 5:45am UTC](https://discourse.julialang.org/t/how-to-solve-two-symbolic-nonlinear-equations-in-julia/11916/22 "2018-06-27T05:45:16Z")

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I’m no expert on git, so I ended up uninstalling Julia, deleting c:\Users\username.julia, and re-installing it. Now it seems to be ok.

Directory c:\Users\username.julia had some 200 000 files and took some 5 GB of the disk. After the re-install, there are some 135 000 files and 4.6 GB on the disk.

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**Author:** ![BLI](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/bli/32/37206_2.png) [@BLI](https://discourse.julialang.org/u/BLI)\
**Post date:** [June 27, 2018, 6:01am UTC](https://discourse.julialang.org/t/how-to-solve-two-symbolic-nonlinear-equations-in-julia/11916/23 "2018-06-27T06:01:15Z")

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Thanks: I tested your code, and got the following warning:

```julia
julia> using IntervalArithmetic, IntervalConstraintProgramming, StaticArrays

WARNING: using IntervalArithmetic.sup in module Main conflicts with an existing identifier.

```

Running the rest of the code, I got the following error message:

```julia
UndefVarError: paving not defined

```

Is the problem due to first `using ImplicitEquations` in the same session? (There seems to be something like `paving` defined in `ImplicitEquations`, too…)

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<div class="post-metadata">

**Author:** ![dpsanders](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dpsanders/32/3573_2.png) [@dpsanders](https://discourse.julialang.org/u/dpsanders)\
**Post date:** [June 27, 2018, 6:08am UTC](https://discourse.julialang.org/t/how-to-solve-two-symbolic-nonlinear-equations-in-julia/11916/24 "2018-06-27T06:08:42Z")

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Sorry, paving.boundary should be paving1.boundary

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<div class="post-metadata">

**Author:** ![BLI](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/bli/32/37206_2.png) [@BLI](https://discourse.julialang.org/u/BLI)\
**Post date:** [June 27, 2018, 6:16am UTC](https://discourse.julialang.org/t/how-to-solve-two-symbolic-nonlinear-equations-in-julia/11916/25 "2018-06-27T06:16:38Z")

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OK… I found the problem… there is a typo in your code listing, I think:

```julia
plot!(paving.boundary, lw=1, lc=:blue, alpha=1, label="")

```

should probably be:

```julia
plot!(paving1.boundary, lw=1, lc=:blue, alpha=1, label="")

```

I don’t see black dots at all the solutions in my plot, as you seem to get. I’ll study the plot in more detail. Thanks, again.

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<div class="post-metadata">

**Author:** ![BLI](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/bli/32/37206_2.png) [@BLI](https://discourse.julialang.org/u/BLI)\
**Post date:** [June 27, 2018, 6:24am UTC](https://discourse.julialang.org/t/how-to-solve-two-symbolic-nonlinear-equations-in-julia/11916/26 "2018-06-27T06:24:10Z")

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Ah – you’re online, too… Thanks! It seems to work, now. Very nice!

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<div class="post-metadata">

**Author:** ![BLI](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/bli/32/37206_2.png) [@BLI](https://discourse.julialang.org/u/BLI)\
**Post date:** [June 27, 2018, 9:47am UTC](https://discourse.julialang.org/t/how-to-solve-two-symbolic-nonlinear-equations-in-julia/11916/27 "2018-06-27T09:47:34Z")

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I’ve looked at your package IntervalConstraintProgramming – really nice! A quick question… In the code, you use statement:

```julia
IntervalBox(-20..20,2)

```

Is this short hand notation for

```julia
IntervalBox(-20..20,-20..20)

```

In other words, with set `S=-20..20`, would `IntervalBox(S,n)` be equal to `S^n` – the Cartesian product `SxS...xS`, `n` times?

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<div class="post-metadata">

**Author:** ![dpsanders](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dpsanders/32/3573_2.png) [@dpsanders](https://discourse.julialang.org/u/dpsanders)\
**Post date:** [June 27, 2018, 11:54am UTC](https://discourse.julialang.org/t/how-to-solve-two-symbolic-nonlinear-equations-in-julia/11916/28 "2018-06-27T11:54:22Z")

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Yes, exactly.  
IntervalBox(X, n) gives the n-fold cartesian product.

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