Thursday, 27 December 2018

Latex, Physics Forums, Desmos, Symbolab, MathJax, GrindEQ

This is somewhat out of date for me. I have now purchased GrindEQ Word->Latex, which is highly idiosyncratic and have written Word macros to greatly improve it. See XXXXX.

Latex is a script used to display equations on websites by Physics Forums, Desmos the grapher,  Symbolab the equation solver and this Blogger blog with MathJax. Latex is described on Physics Forums here and more completely by Mark Gates here. I also have some Latex tips here (MS-Word). I started by using something from Codecogs but it was not good at displaying inline equations (##\mu=0##) or adjusting the font size of indexed variables ( ##{\partial }_{\mu }y^{\alpha }## ) .

GrindEQ can save a word document containing equations as a .tex plain text file. This contains some non-Latex (for the MS-Word text) and bits of delimited Latex. So it it fairly easy to copy and paste the Latex to other websites. The only difference is in the characters that delimit the Latex. These are summarise below.

Format
Delimiter for
Delimiter
PF (website)
New line
$$

In line
##
.tex  (file from GrindEQ)
New line
\[

In line
$
MathJax
New line
$$

In line
$
Symbolab

none
Desmos

none

Here's something I wrote and pasted the RHS into Desmos and Symbolab.
$$ x = \frac{t\left(\sin \left(l\right)-1\right)}{\cos \left(l\right)} $$
You can copy and paste the Latex of the RHS directly into Desmos and Symbolab equations. It is

\frac{t\left(\sin \left(l\right)-1\right)}{\cos \left(l\right)}

Then I created a test Word document pictured below
Image from MS-word
And here is the same thing produced by GrindEQ and then pasted out of the .tex file into this blog.

So the pullback operator is (##\mu## is row index, ##\alpha## is column)

$$  {\partial }_{\mu }y^{\alpha }=\left( \begin{array}{cc} {\mathrm{cos} \theta \ } & {\mathrm {sin} \theta \ } \\ -r{\mathrm{sin} \theta \ } & r{\mathrm{cos} \theta \ } \end{array} \right) $$

$${\partial }_{\mu }y^{\alpha }\equiv \frac{\partial y^{\alpha }}{\partial x^{\mu }} =\left( \begin{array}{cc} \frac{\partial x}{\partial r} & \frac{\partial y}{\partial r} \\  \  & \  \\  \frac{\partial x}{\partial \theta } & \frac{\partial y}{\partial \theta } \end{array} \right)=\left( \begin{array}{cc} {\mathrm{cos} \theta \ } & {\mathrm{sin} \theta \ } \\  -r{\mathrm{sin} \theta \ } & r{\mathrm{cos} \theta \ } \end{array} \right)$$

or on the final equation using \Large , \large and \small (\normal does not work)

##{\partial }_{\mu }y^{\alpha }  \equiv  \Large  \frac{\partial y^{\alpha }}{\partial x^{\mu }} \Large =   \left( \begin{array}{cc} \frac{\partial x}{\partial r} & \frac{\partial y}{\partial r} \\  \  & \  \\  \frac{\partial x}{\partial \theta } & \frac{\partial y}{\partial \theta } \end{array} \right) \small= \left( \begin{array}{cc} {\mathrm{cos} \theta \ } & {\mathrm{sin} \theta \ } \\  -r{\mathrm{sin} \theta \ } & r{\mathrm{cos} \theta \ } \end{array} \right)##

Sadly I only get ten free uses of GrindEQ nd then I have to pay 50€.

Installing the mathjax code to show equations in Blogger is simple and instructions are contained here. However the page freezes shortly after opening and the Blogger instructions are out of date, so the vital parts are worth repeating:

To enable MathJax, just drop in the following code snippet after the header (<head>) in the Blogger template (Theme →Edit HTML→Edit Template). The the £ sign should be replaced with the dollar currency sign. It is hard to get that in the text here! The unadulterated code snippet is also in this text file.

<!--Script to enable Latex from http://web.archive.org/web/20110412103745/http://mnnttl.blogspot.com/2011/02/latex-on-blogger.html -->
<script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js">
MathJax.Hub.Config({
 extensions: ["tex2jax.js","TeX/AMSmath.js","TeX/AMSsymbols.js"],
 jax: ["input/TeX", "output/HTML-CSS"],
 tex2jax: {
     inlineMath: [ ['£','£'], ["\\(","\\)"] ],
     displayMath: [ ['$$','$$'], ["\\[","\\]"] ],
 },
 "HTML-CSS": { availableFonts: ["TeX"] }
});
</script>

No doubt one could use different delimiters by changing the inlineMath and displayMath lines if one wanted.

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