rm WeaveSupport
This commit is contained in:
@@ -14,17 +14,6 @@ using LinearAlgebra
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using ForwardDiff
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```
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```{julia}
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#| echo: false
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#| results: "hidden"
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using CalculusWithJulia.WeaveSupport
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frontmatter = (
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title = "2D and 3D plots in Julia with Plots",
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description = "Calculus with Julia: 2D and 3D plots in Julia with Plots",
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tags = ["CalculusWithJulia", "differentiable_vector_calculus", "2d and 3d plots in julia with plots"],
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);
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nothing
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```
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---
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@@ -121,10 +110,10 @@ for t in ts
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end
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```
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```{julia}
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#| echo: false
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note("""Adding many arrows this way would be inefficient.""")
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```
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:::{.callout-note}
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## Note
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Adding many arrows this way would be inefficient.
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:::
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### Setting a viewing angle for 3D plots
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@@ -381,10 +370,10 @@ zs = [Z(1, theta, phi) for theta in thetas, phi in phis]
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surface(xs, ys, zs)
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```
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```{julia}
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#| echo: false
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note("The above may not work with all backends for `Plots`, even if those that support 3D graphics.")
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```
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:::{.callout-note}
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## Note
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The above may not work with all backends for `Plots`, even if those that support 3D graphics.
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:::
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For convenience, the `plot_parametric` function from `CalculusWithJulia` can produce these plots using interval notation, `a..b`, and a function:
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@@ -419,4 +408,3 @@ a,b = 1,3
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f(x,y,z) = (x^2+((1+b)*y)^2+z^2-1)^3-x^2*z^3-a*y^2*z^3
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CalculusWithJulia.plot_implicit_surface(f, xlim=-2..2, ylim=-1..1, zlim=-1..2)
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```
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@@ -14,21 +14,6 @@ using Roots
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using QuadGK
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```
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```{julia}
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#| echo: false
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#| results: "hidden"
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using CalculusWithJulia.WeaveSupport
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frontmatter = (
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title = "Polar Coordinates and Curves",
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description = "Calculus with Julia: Polar Coordinates and Curves",
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tags = ["CalculusWithJulia", "differentiable_vector_calculus", "polar coordinates and curves"],
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);
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using LaTeXStrings
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nothing
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```
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---
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@@ -785,4 +770,3 @@ r(theta) = sqrt(cos(2theta) * sec(theta)^4)
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val, _ = quadgk(t -> sqrt(D(r)(t)^2 + r(t)^2), -pi/4, pi/4)
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numericq(val)
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```
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@@ -26,15 +26,7 @@ import Contour: contours, levels, level, lines, coordinates
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```{julia}
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#| echo: false
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#| results: "hidden"
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using CalculusWithJulia.WeaveSupport
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using CSV, DataFrames
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const frontmatter = (
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title = "Scalar functions",
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description = "Calculus with Julia: Scalar functions",
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tags = ["CalculusWithJulia", "differentiable_vector_calculus", "scalar functions"],
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);
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nothing
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```
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@@ -2436,4 +2428,3 @@ What equation does the function $f(x,y) = \cos(x) + \sin(y)$ satisfy?
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answ = 5
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radioq(ode_choices, answ, keep_order=true)
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```
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@@ -20,19 +20,6 @@ And the following from the `Contour` package:
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import Contour: contours, levels, level, lines, coordinates
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```
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```{julia}
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#| echo: false
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#| results: "hidden"
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using CalculusWithJulia.WeaveSupport
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const frontmatter = (
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title = "Applications with scalar functions",
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description = "Calculus with Julia: Applications with scalar functions",
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tags = ["CalculusWithJulia", "differentiable_vector_calculus", "applications with scalar functions"],
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);
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nothing
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```
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This section presents different applications of scalar functions.
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@@ -2309,4 +2296,3 @@ ts = fzeros(fn, 0, 2pi)
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val = maximum((f∘r).(ts))
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numericq(val)
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```
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@@ -14,19 +14,6 @@ using ForwardDiff
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using LinearAlgebra
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```
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```{julia}
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#| echo: false
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#| results: "hidden"
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using CalculusWithJulia.WeaveSupport
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const frontmatter = (
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title = "Functions ``R^n \\rightarrow R^m``",
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description = "Calculus with Julia: Functions ``R^n \\rightarrow R^m``",
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tags = ["CalculusWithJulia", "differentiable_vector_calculus", "functions ``R^n \\rightarrow R^m``"],
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);
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nothing
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```
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For a scalar function $f: R^n \rightarrow R$, the gradient of $f$, $\nabla{f}$, is a function from $R^n \rightarrow R^n$. Specializing to $n=2$, a function that for each point, $(x,y)$, assigns a vector $\vec{v}$. This is an example of vector field. More generally, we could have a [function](https://en.wikipedia.org/wiki/Multivariable_calculus) $f: R^n \rightarrow R^m$, of which we have discussed many already:
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@@ -1123,5 +1110,3 @@ radioq(choices, answ)
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```
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(The latter is of interest, as only when the expression is $0$ will the vector field be the gradient of a scalar function.)
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@@ -23,18 +23,6 @@ import DifferentialEquations
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import DifferentialEquations: ODEProblem, Tsit5
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```
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```{julia}
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#| echo: false
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#| results: "hidden"
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using CalculusWithJulia.WeaveSupport
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frontmatter = (
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title = "Vector-valued functions, ``f:R \\rightarrow R^n``",
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description = "Calculus with Julia: Vector-valued functions, ``f:R \\rightarrow R^n``",
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tags = ["CalculusWithJulia", "differentiable_vector_calculus", "vector-valued functions, ``f:R \\rightarrow r^n``"],
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);
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nothing
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```
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---
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@@ -2795,4 +2783,3 @@ choices = [
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answ = 1
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radioq(choices, answ)
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```
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@@ -13,19 +13,6 @@ using LinearAlgebra
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using SymPy
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```
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```{julia}
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#| echo: false
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#| results: "hidden"
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using CalculusWithJulia.WeaveSupport
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const frontmatter = (
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title = "Vectors and matrices",
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description = "Calculus with Julia: Vectors and matrices",
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tags = ["CalculusWithJulia", "differentiable_vector_calculus", "vectors and matrices"],
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);
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nothing
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```
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---
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@@ -716,13 +703,10 @@ and
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```{julia}
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[𝓊'; 𝓋']
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```
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```{julia}
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#| echo: false
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note("""
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:::{.callout-note}
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## Note
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The adjoint is defined *recursively* in `Julia`. In the `CalculusWithJulia` package, we overload the `'` notation for *functions* to yield a univariate derivative found with automatic differentiation. This can lead to problems: if we have a matrix of functions, `M`, and took the transpose with `M'`, then the entries of `M'` would be the derivatives of the functions in `M` - not the original functions. This is very much likely to not be what is desired. The `CalculusWithJulia` package commits **type piracy** here *and* abuses the generic idea for `'` in Julia. In general type piracy is very much frowned upon, as it can change expected behaviour. It is defined in `CalculusWithJulia`, as that package is intended only to act as a means to ease users into the wider package ecosystem of `Julia`.
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""")
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```
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:::
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---
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@@ -768,12 +752,11 @@ $$
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\vec{u} \times \vec{v} = \| \vec{u} \| \| \vec{v} \| \sin(\theta) \hat{n}.
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$$
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```{julia}
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#| echo: false
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note("""
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:::{callout-note}
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## Note
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The right-hand rule is also useful to understand how standard household screws will behave when twisted with a screwdriver. If the right hand fingers curl in the direction of the twisting screwdriver, then the screw will go in or out following the direction pointed to by the thumb.
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""")
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```
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:::
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The right-hand rule depends on the order of consideration of the vectors. If they are reversed, the opposite direction is determined. A consequence is that the cross product is **anti**-commutative, unlike multiplication:
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@@ -1519,4 +1502,3 @@ choices = [
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answ = 1
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radioq(choices, answ)
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```
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