# \#implicit-equation

**URL:** https://discourse.julialang.org/tag/implicit-equation/717.md

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## [Testing and tolerances for implicitly calculated functions and their AD](https://discourse.julialang.org/t/testing-and-tolerances-for-implicitly-calculated-functions-and-their-ad/133575)

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**Author:** [@Tamas\_Papp](https://discourse.julialang.org/u/Tamas_Papp)\
**Replies:** 3\
**Last updated:** [December 2, 2025, 12:49pm UTC](https://discourse.julialang.org/t/testing-and-tolerances-for-implicitly-calculated-functions-and-their-ad/133575 "2025-12-02T12:49:17Z")

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To fix ideas, suppose we have a function x = g(p) defined by f(x(p), p) = 0, both arguments are scalars. The numerical implementation involves finding an x such that | f(x, p)| \\le \\mathrm{tol}, either by Newton’s metho…

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## [Implicit differentiation of rootfinding problem (w/ numerical issues)](https://discourse.julialang.org/t/implicit-differentiation-of-rootfinding-problem-w-numerical-issues/126293)

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**Author:** [@Tamas\_Papp](https://discourse.julialang.org/u/Tamas_Papp)\
**Replies:** 13\
**Last updated:** [February 26, 2025, 3:01pm UTC](https://discourse.julialang.org/t/implicit-differentiation-of-rootfinding-problem-w-numerical-issues/126293 "2025-02-26T15:01:40Z")

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I have written an algorithm that solves x = \\log\\left( \\sum\_i \\exp(a\_i + z\_i y) \\right) for y given x, a\_i, z\_i. It uses Newton’s method, which is the trivial part, the difficulty was getting a cheap but reasonable in…

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## [Mismatched ForwardDiff and FiniteDifference gradients with ImplicitDifferentiation](https://discourse.julialang.org/t/mismatched-forwarddiff-and-finitedifference-gradients-with-implicitdifferentiation/119756)

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**Author:** [@benjaminfaber](https://discourse.julialang.org/u/benjaminfaber)\
**Replies:** 12\
**Last updated:** [September 25, 2024, 7:31pm UTC](https://discourse.julialang.org/t/mismatched-forwarddiff-and-finitedifference-gradients-with-implicitdifferentiation/119756 "2024-09-25T19:31:05Z")

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@gdalle I am attempting to use ImplicitDifferentiation with ForwardDiff to compute the gradient of an optimization problem. I’ve tried to figure out how to reduce the problem to a minimum working example, but I have not…

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## [Implicit plot with plots](https://discourse.julialang.org/t/implicit-plot-with-plots/6585)

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**Author:** [@harven](https://discourse.julialang.org/u/harven)\
**Replies:** 17\
**Last updated:** [December 20, 2023, 4:29pm UTC](https://discourse.julialang.org/t/implicit-plot-with-plots/6585 "2023-12-20T16:29:28Z")

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How do I make an implicit plot with the plots package? pyplot has a contour function which admits a fourth argument to plot a single level line. But it does not seem to be implemented in plots.

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## [Diophantine equations 3-d plots](https://discourse.julialang.org/t/diophantine-equations-3-d-plots/85727)

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**Author:** [@Freya\_the\_Goddess](https://discourse.julialang.org/u/Freya_the_Goddess)\
**Replies:** 2\
**Last updated:** [August 14, 2022, 3:53pm UTC](https://discourse.julialang.org/t/diophantine-equations-3-d-plots/85727 "2022-08-14T15:53:36Z")

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Hi all, I see this equation and I want to plot it, but could not be able to do it: z^{3} - z = (x^{3} - x) + (y^{3} - y) This is my code: using Plots pyplot() x=range(-2,stop=2,length=100) y=range(sqrt(2),stop=2,le…

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## [Surface plot](https://discourse.julialang.org/t/surface-plot/82544)

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**Author:** [@SDA](https://discourse.julialang.org/u/SDA)\
**Replies:** 10\
**Last updated:** [June 15, 2022, 12:59am UTC](https://discourse.julialang.org/t/surface-plot/82544 "2022-06-15T00:59:49Z")

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There is no doubt a very simple answer to this that I’ve overlooked. How would one plot a surface x=y, where z is any real number?

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## [ContourPlot3D (surface) in Julia](https://discourse.julialang.org/t/contourplot3d-surface-in-julia/62923)

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**Author:** [@maoc](https://discourse.julialang.org/u/maoc)\
**Replies:** 2\
**Last updated:** [June 15, 2021, 12:52pm UTC](https://discourse.julialang.org/t/contourplot3d-surface-in-julia/62923 "2021-06-15T12:52:28Z")

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I am trying to plot the 3D surface given by the zero of a function. I have a complicated function given by function mcl(Y,w) BLAH BLAH end Where Y is a 2-element Array{Int64,1} and w is a real number. For example mcl(…