daviddoji/CalculusWithJuliaNotes.jl
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Merge pull request #64 from fangliu-tju/main

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Update polynomial.qmd
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john verzani 2023-04-11 14:39:48 -04:00 committed by GitHub
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quarto/precalc/polynomial.qmd
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@ -126,7 +126,7 @@ Symbolic math programs include well-known ones like the commercial programs Math
The [Symbolics](https://github.com/JuliaSymbolics/Symbolics.jl) package for `Julia` provides a "fast and modern CAS for fast and modern language." It is described further in [Symbolics.jl](../alternatives/symbolics.qmd).
As `SymPy` has some features not yet implemented in `Symbolics`, we use that her. The `PyCall` and `PythonCall` packages are available to glue `Julia` to Python in a seamless manner. These allow the `Julia` package `SymPy` to provide functionality from SymPy within `Julia`.
As `SymPy` has some features not yet implemented in `Symbolics`, we use that here. The `PyCall` and `PythonCall` packages are available to glue `Julia` to Python in a seamless manner. These allow the `Julia` package `SymPy` to provide functionality from SymPy within `Julia`.
:::{.callout-note}
@ -453,10 +453,10 @@ The following graphic illustrates the $4$ basic *overall* shapes that can result
```{julia}
#| echo: false
plot(; layout=4)
plot!(x -> x^4, -3,3, legend=false, xticks=false, yticks=false, subplot=1, title="n > even, aₙ > 0")
plot!(x -> x^5, -3,3, legend=false, xticks=false, yticks=false, subplot=2, title="n > odd, aₙ > 0")
plot!(x -> -x^4, -3,3, legend=false, xticks=false, yticks=false, subplot=3, title="n > even, aₙ < 0")
plot!(x -> -x^5, -3,3, legend=false, xticks=false, yticks=false, subplot=4, title="n > odd, aₙ < 0")
plot!(x -> x^4, -3,3, legend=false, xticks=false, yticks=false, subplot=1, title="n = even, aₙ > 0")
plot!(x -> x^5, -3,3, legend=false, xticks=false, yticks=false, subplot=2, title="n = odd, aₙ > 0")
plot!(x -> -x^4, -3,3, legend=false, xticks=false, yticks=false, subplot=3, title="n = even, aₙ < 0")
plot!(x -> -x^5, -3,3, legend=false, xticks=false, yticks=false, subplot=4, title="n = odd, aₙ < 0")
```
##### Example
@ -539,7 +539,7 @@ But will not factor things that are not hard to see:
```{julia}
x^2 - 2
factor(x^2 - 2)
```
The factoring $(x-\sqrt{2})\cdot(x + \sqrt{2})$ is not found, as $\sqrt{2}$ is not rational.