Jupyter theorem environment - math

I am new to jupyter notebooks, and I am trying to use juptyter notebooks to create lecture notes. I can figure out how to do equation numbering, but I don't know how to enable a theorem-proof environment like in latex. I looked online, but they all describe latex commands or at best equation numbering. Any help will be appreciated.

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What is the best way to write down in-line math equations in a jupyter notebook to have best LaTeX results?

When I am writing math equations in a markdown cell of a jupyter notebook, I casually put all of that in $ ... $. Today, I converted an .ipynb file to .tex, and realized most of these equations are converted into messy stuff in the output pdf. For instance, I realized it is converting all '$'s into '$'s.
This is an example of what has happened:
Jupyter Notebook markdown:
$ \nabla ^{2} f(x) = \frac{-1}{(x+1)^{2}} $
Tex Output:
\$ \nabla \^{}\{2\} f(x) = \frac{-1}{(x+1)^{2}} \$
Does anyone have any ideas why this is happening? Is there a better way to write down in-line math equations so that it is more compatible with LaTeX?
If you are eventually going to LaTeX version, the traditional advice is spelled out in minrk's comment from November 8 of 2012:
"The best solution for that right now would be to use 'raw' cells instead of markdown, and just type LaTeX as you would. Then use nbconvert to turn the ipynb to TeX (code, figures and all), and run latex to render that to PDF, etc. You don't get live-rendered TeX in the browser like you do with MathJax / Markdown, but you do still have TeX / code in one document."
The step where you are converting now is probably using nbconvert under the hood even if you aren't directly. (You may be using it directly since you tagged with 'nbconvert`.)
Alternatively, if you are going to LaTeX ultimately, you may want to use a code cell and use the LaTeX magic cell line at the start of that cell. See here and here about %%latex cell magic. (You'll note it is also mentioned among the StackOverflow thread I referenced earlier.) In regards to the %%latex cell magic, I suggest actually consulting the link that leads use in an example notebook in this post because it seems it has to be full-blown LaTeX code and not just simple equations that work easily elsewhere with just dollar signs bracketing them, i.e., MathJax.
I tried that option with your equation and when I output the notebook as LaTeX, I didn't see additional backslashes added. (I didn't however actually try rendering the LaTeX, and so I cannot address if all the cruft/boilerplate that Jupyter is adding causes any issues for downstream useability.)

IDE with LaTeX and R support: Inline output in .Rmd notebooks and weaving LaTeX document with R code

I'm trying to improve my workflow when working with R and generating documentation. I've been going between TeXStudio, JupyterLab and RStudio for a while, and I'm trying to improve my workflow. TeXStudio has limited R support, and RStudio limited support for LaTeX.
VS Code has support for multiple languages, including R and LaTeX. The fact that it can run both Jupyter notebooks, R notebooks, and LaTeX, and has plugins for other languages as well, makes it seem desirable. However, I am unable to find documentation on how to configure it to work with R and LaTeX code in the same file. In addition, I am unable to configure R notebooks to allow inline code execution output.
However, I am unable to (a) set up code execution output under the code for .Rmd notebooks, and (b) I can't figure out how to weave .Rnw (R/LaTeX) documents with Sweave/knitr.
I'm trying to find an IDE that would include features like:
Markdown, code and code execution output in the same document
Auto R and LaTeX code completion
Automatic display of R function documentation
Spell check
Simple R console access
Compile .Rnw
Syntax highlighting for both R code and LaTeX code
I am, primarily, requesting ways to configure VS Code, or, secondly, way to configure another IDE that can meet my requirements. A tutorial on this would be much appreciated.
After a bit of digging around, I found that VS Code does nearly all the things I need.
Auto R and LaTeX code completion, Display of R function documentation in a tab in VS Code, Simple R console access, and Syntax highlighting for both R code and LaTeX code:
The R and LaTeX Workshop extensions, will provide highlighting and autocompletion of code in both languages. By installing R, you can easily open a session in a terminal window in VS Code, and from there open documentation inside VS Code.
Spell check
Code Spell Checker offers spell check for multiple languages. Install the extension and any desired dictionaries, and set the langauges you want to be included in the extension settings.
Compile .Rnw files
Turns out LaTeX Workshop can actually do this by default.
Markdown, code and code execution output in the same document
This is the only thing VS Code doesn't do as far as I can tell. It can compile .Rmd files, however, but the output can only be seen in the compiled PDF. I consider this less important, since I can use Jupyter notebooks instead.

Is there a way to write down chemical equations in jupyter notebook by using external packages for Mathjax?

I can't seem to figure out how to write down chemical equations in Jupyter notebook. How do we install mhchem for Mathjax to use inside Jupyter notebook?
Add the following code on top of your jupyter notebook:
$$\require{mhchem}$$
here you can find the detailed explanation on how to use and write chemical equations in jupyter notebook
https://notebooks.azure.com/OUsefulInfo/projects/gettingstarted/html/3.1.1%20Chemical%20Equations.ipynb
and without any extension's you can do as well
from IPython.display import display, Math, Latex
display(Math(r'F(k) = \int_{-\infty}^{\infty} f(x) e^{2\pi i k} dx'))
display(Math(r'\ce{H2O}'))
try these in jupyter

How to use inline code in markdown in Jupyter with R

How to use inline code in markdown in Jupyter with R?
CODE CELL
n <- 8
MARKDOWN CELL
The Number is {{n}}
What would be the correct syntax in Jupyter Markdown for R? Is it even possible?
In case you haven't done it already, you might want to give the python markdown extension a shot, that adds the markdown inline code functionality for Python to Jupyter notebooks. On their github they claim:
The Python Markdown extension allows displaying output produced by the current kernel in markdown cells. The extension is basically agnostic to the kernel language, however most testing has been done using Python.
Installation instructions are on the github page of the nbextensions. Make sure you'll enable the python markdown extension using a jupyter command or the extension configurator.
Calling variables then should work inside a markdown cell with the {{var-name}} syntax that you've already given (described in the readme of the corresponding github page (linked in the wiki)).
If this doesn't help, you might want to join the discussion of the corresponding issues in the issue trackers for ipython and jupyter.

Syntax highlight in R Sweave

I am fairly new to doing report with R Sweave and know the very basic applications of Latex. And I have been asked to produce some statistical reports. The R markdown is great and simple, and by default it has really nice syntax frame and grey background and syntax highlights, however, it is quite limited in terms of other type setting, not really optimal when you want to produce lengthy reports. Then I am switching to use R Sweave in R studio.
I basically want the same after-effect similar to R markdown in the Sweave. What are the easiest ways to do it? I have previously read the following post discussing:
Sweave syntax highlighting in output. And I have tried reading those package pdf, but have no clues what they are talking about, as they seem to assume readers have prior knowledges about the rendering process.
i have checked them out, but I seem to get stuck in making it to work. Can anyone tell me step by step on how to set it up (such as what to include in preamble), if possible can you kindly upload a simple Rnw file with a demonstration?
Thank!
If you use knitr rather than Sweave, you'll get syntax highlighting. It's probably possible to do it in Sweave, but knitr makes it easier.
Go to your Tools | Global Options | Sweave menu (or the similar one in Project Options) in RStudio, and choose to Weave Rnw files using knitr.
The two systems are very similar, but knitr is generally preferable these days.

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