chandra
December 10, 2023, 3:12am
1
“However, despite integration being an algorithmic procedure, integration is not.”

at

https://docs.juliahub.com/CalculusWithJulia/AZHbv/0.0.5/integrals/partial_fractions.html#

probably should read

However, despite differentiation being an algorithmic procedure, integration is not.

Where do I report possible corrections like this?

mkitti
December 10, 2023, 3:25am
2
Well first of all you’re looking at an older version. The newest version of the docs on the JuliaHub website are here at version 0.1.2 rather than 0.0.5.

https://docs.juliahub.com/CalculusWithJulia/AZHbv/0.1.2/

I’m also thinking you want to edit the notes rather than the package which are now in separate repository by @j_verzani .:

```
```
using CalculusWithJulia
using SymPy
```
---
Integration is facilitated when an antiderivative for $f$ can be found, as then definite integrals can be evaluated through the fundamental theorem of calculus.
However, despite integration being an algorithmic procedure, integration is not. There are "tricks" to try, such as substitution and integration by parts. These work in some cases. However, there are classes of functions for which algorithms exist. For example, the `SymPy` `integrate` function mostly implements an algorithm that decides if an elementary function has an antiderivative. The [elementary](http://en.wikipedia.org/wiki/Elementary_function) functions include exponentials, their inverses (logarithms), trigonometric functions, their inverses, and powers, including $n$th roots. Not every elementary function will have an antiderivative comprised of (finite) combinations of elementary functions. The typical example is $e^{x^2}$, which has no simple antiderivative, despite its ubiquitousness.
There are classes of functions where an (elementary) antiderivative can always be found. Polynomials provide a case. More surprisingly, so do their ratios, *rational functions*.
## Partial fraction decomposition
Let $f(x) = p(x)/q(x)$, where $p$ and $q$ are polynomial functions with real coefficients. Further, we assume without comment that $p$ and $q$ have no common factors. (If they did, we can divide them out, an act which has no effect on the integrability of $f(x)$.

I would submit a Github pull request or issue to that repository.

chandra
December 10, 2023, 6:07am
3
`jverzani:main`

← `kleinbottle:main`

opened 06:06AM - 10 Dec 23 UTC

@jverzani : I have changed the word 'integration' to 'differentiation' because I… think that was what was intended. The present sentence is not logical otherwise.

Pull request made. Thanks.

6 Likes

Just to answer such questions in general:

You file an issue in the repository the document came from. In this case, the document says it came from CalculusWithJulia.jl , so that is where you would file an issue.

If you have the time and knowledge, it is even better to submit a pull request with a correction. You can use github’s online editor to do that directly from your web browser.

In documentation made with Documenter.jl, there is often an “Edit on github” link at the top of each page of the documentation, that you can click to edit the page and submit a pull request, as @chandra did above. (See, for example, this page in the Julia manual.)

chandra:

Pull request made.

Thanks!

3 Likes