daviddoji/CalculusWithJuliaNotes.jl
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2025-01-24 11:04:54 -05:00
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quarto/precalc/polynomial.qmd
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# Polynomials
Now that basic properties of functions have been discussed, we move to various types of related functions beginning with polynomial functions.
{{< include ../_common_code.qmd >}}
In this section we use the following add-on packages:
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---
Polynomials are a particular class of expressions that are simple enough to have many properties that can be analyzed. In particular, the key concepts of calculus: limits, continuity, derivatives, and integrals are all relatively trivial for polynomial functions. However, polynomials are flexible enough that they can be used to approximate a wide variety of functions. Indeed, though we don't pursue this, we mention that `Julia`'s `ApproxFun` package exploits this to great advantage.
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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 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`.
As `SymPy` has some features not yet implemented in `Symbolics`, we use `SymPy` in these notes. The `PyCall` and `PythonCall` packages are available to glue `Julia` to Python in a seamless manner. These allow the `Julia` package `SymPy` (or `SymPyPythonCall`) to provide functionality from SymPy within `Julia`.
:::{.callout-note}