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make pdf file generation work

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2022-10-10 14:28:05 -04:00
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quarto/precalc/polynomial.qmd
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@@ -122,7 +122,11 @@ Thinking in terms of transformations, this looks like the function $f(x) = x$ (w
The indeterminate value `x` (or some other symbol) in a polynomial, is like a variable in a function and unlike a variable in `Julia`. Variables in `Julia` are identifiers, just a means to look up a specific, already determined, value. Rather, the symbol `x` is not yet determined, it is essentially a place holder for a future value. Although we have seen that `Julia` makes it very easy to work with mathematical functions, it is not the case that base `Julia` makes working with expressions of algebraic symbols easy. This makes sense, `Julia` is primarily designed for technical computing, where numeric approaches rule the day. However, symbolic math can be used from within `Julia` through add-on packages.
Symbolic math programs include well-known ones like the commercial programs Mathematica and Maple. Mathematica powers the popular [WolframAlpha](www.wolframalpha.com) website, which turns "natural" language into the specifics of a programming language. The open-source Sage project is an alternative to these two commercial giants. It includes a wide-range of open-source math projects available within its umbrella framework. (`Julia` can even be run from within the free service [cloud.sagemath.com](https://cloud.sagemath.com/projects).) A more focused project for symbolic math, is the [SymPy](www.sympy.org) Python library. SymPy is also used within Sage. However, SymPy provides a self-contained library that can be used standalone within a Python session. That is great for `Julia` users, as the `PyCall` and `PythonCall` packages glue `Julia` to Python in a seamless manner. This allows the `Julia` package `SymPy` to provide functionality from SymPy within `Julia`.
Symbolic math programs include well-known ones like the commercial programs Mathematica and Maple. Mathematica powers the popular [WolframAlpha](www.wolframalpha.com) website, which turns "natural" language into the specifics of a programming language. The open-source [Sage](https://www.sagemath.org/) project is an alternative to these two commercial giants. It includes a wide-range of open-source math projects available within its umbrella framework. (`Julia` can even be run from within the free service [cloud.sagemath.com](https://cloud.sagemath.com/projects).) A more focused project for symbolic math, is the [SymPy](www.sympy.org) Python library. SymPy is also used within Sage. However, SymPy provides a self-contained library that can be used standalone within a Python session.
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`.
:::{.callout-note}