Dear list,
I’d like to know the best approach to make this a bit more usable. I’m trying to typeset a table with sin/cos/tan values. I’d like to be able to convert the angles in degrees into radians (with math notation) and to compute the trigonometric function leading to sin(pi/4) = 1/2, or cos(pi/6) = sqrt(3)/2 and display it in math mode.
Here’s my current MWE, where I fail to convert the angles in radians and fail to display the result in symbolic form.
\starttext
\startluacode local angleList = {0, 30, 45, 60, 90, 120, 135, 150, 180, 210, 225, 240, 270, 300, 315, 330, 360}
context.bTABLE() context.bTR() context.bTD() context("$x$") context.eTD() context.bTD() context("$0$") context.eTD() for _, a in ipairs(angleList) do context.bTD() context("$\letterpercent.0f$",a) context.eTD() end context.eTR() context.bTR() context.bTD() context("$\cos(x)$") context.eTD() for _, a in ipairs(angleList) do context.bTD() context("$\letterpercent.3f$",math.cos(math.rad(a))) context.eTD() end context.eTR() context.bTR() context.bTD() context("$\sin(x)$") context.eTD() for _, a in ipairs(angleList) do context.bTD() context("$\letterpercent.3f$",math.sin(math.rad(a))) context.eTD() end context.eTR() context.bTR() context.bTD() context("$\tan(x)$") context.eTD() for _, a in ipairs(angleList) do if a == 90 or a == 270 then context.bTD() context("$-$") context.eTD() else context.bTD() context("$\letterpercent.3f$",math.tan(math.rad(a))) context.eTD() end end context.eTR() context.eTABLE() \stopluacode
\stoptext
\stoptext
One possible way would be to use Python and the t-filter module, like this
\usemodule[filter] %It depends on your OS. In mine it's python3 \defineexternalfilter [pythontyping] [filtercommand={python3 \externalfilterinputfile \space > \externalfilteroutputfile}, output={\externalfilterbasefile.tex}, cache=yes, readcommand=\typefile, spacebefore=medium, spaceafter=medium] %We copy settings to save typing \defineexternalfilter[pythonformula][pythontyping] %But instead of typing, we input a formula \setupexternalfilter[pythonformula] [readcommand=\samplefile] %\input should also work
\starttext
Convert angle to radians: $\startpythonformula from sympy import * print(latex(pi/180*60)) \stoppythonformula$
Compute trigonometric function: $\startpythonformula from sympy import * print(latex(cos(pi/3))) \stoppythonformula$
\stoptext
However, I haven’t managed so far to combine things (lua and Python) in an automatic way.
How should I proceed?
A. Christe
On 25 Oct 2023, at 16:45, Alexandre Christe aleks.christe@gmail.com wrote:
Dear list,
I’d like to know the best approach to make this a bit more usable. I’m trying to typeset a table with sin/cos/tan values. I’d like to be able to convert the angles in degrees into radians (with math notation) and to compute the trigonometric function leading to sin(pi/4) = 1/2, or cos(pi/6) = sqrt(3)/2 and display it in math mode.
You can use templates to subtitute values into a string and then send that out to be typeset. For example: if you want to turn "sin(pi/4) = 1/2" to
\startformula \sin{\frac{\pi}{4}} = \frac{1}{2} \stopformula
Then use this Lua code:
local myTrigTemplate = [[ \startformula %fname%{\frac{\pi}{%divisor%}} = \frac{%numerator%}{%denominator%} \stopformula ]]
context.templates[myTrigTemplate] { fname = "sin", divisor = 4, numerator = 1, denominator = 2 }
By combining them (using the result of a simple template as the parameter value into a larger template) you can create a function similar to Python's latex() that handles the trig functions you are using. That is the easy bit.
Converting the angle into radians and then getting the result as a fraction of pi requires you to implement a continued fraction algorithm to determine numerator and denominator.
Extending that to determine whether to use sqrt(3)/2 instead of some other fractional approximation is another significant step up in complexity.
I can send you some code that does that - but it's written in HP-71 BASIC so you'll have to adapt it. :-)
The real question is: do you really want to be able to generate an expression from *any* initial angle value or just those in your table? If it's just those in your table then I think it would be much, much less effort to extend 'angleList' with accompanying lists holding the values to substitute into the template. Or even just typeset the whole table by hand (prepare a list of the expressions and use editor macros to ConTeXtify them).
Regards, — Bruce Horrocks Hampshire, UK
On Wed, 25 Oct 2023, Alexandre Christe wrote:
Dear list,
I’d like to know the best approach to make this a bit more usable. I’m trying to typeset a table with sin/cos/tan values. I’d like to be able to convert the angles in degrees into radians (with math notation) and to compute the trigonometric function leading to sin(pi/4) = 1/2, or cos(pi/6) = sqrt(3)/2 and display it in math mode.
Here’s my current MWE, where I fail to convert the angles in radians
there is math.sind, cosd, etc. for computing sin for angle in degrees. The implementation is l-math.lua is:
local pipi = 2*math.pi/360
function math.sind(d) return sin(d*pipi) end function math.cosd(d) return cos(d*pipi) end function math.tand(d) return tan(d*pipi) end
and fail to display the result in symbolic form.
Context doesn't do symbolic math. You can try checking if one of the symbolic math libraries in lua provides all the features that you want.
One possible way would be to use Python and the t-filter module, like this
This can work as follows. Take the array of angles, and convert them to the desired format in python and write them to a temp file. Read that temp file in lua and typeset it as you want.
Another option is an old proof of concept by Luigi: https://github.com/bastibe/lunatic-python which allowed two-way communication between python and luatex. Not sure if it still works.
Aditya
Hi,
Thanks for your inputs Aditya and Bruce.
I’m still having some issues when trying to include the output of the filter module within lua.
MNWE:
\defineexternalfilter [sympy] [filtercommand={/Users/aleks/miniconda3/bin/python3 \externalfilterinputfile\space > \externalfilteroutputfile}, bufferbefore=init, output={\externalfilterbasefile.out}, readcommand=\typefile, read=no,]
\startbuffer[init] from sympy import * \stopbuffer
\starttext
\startluacode local deg2rad = [[ %\startsympy
print(latex(rad(%angleVal%))) %\stopsympy ]]
local calcTrigFunction = [[ \startsympy from sympy import *
print(latex(%fname%(rad(%angleVal%)))) \stopsympy ]]
local angleList = {0, 30, 45, 60, 90, 120, 135, 150, 180, 210, 225, 240, 270, 300, 315, 330, 360}
for _, a in ipairs(angleList) do context.templates[calcTrigFunction] { fname = "sin", angleVal = a } end
\stopluacode
\stoptext
In particular, it fails as soon as \startsympy and \stopsympy are part of the template. Should I protect these?
A. Christe Le 25 oct. 2023 à 21:56 +0200, Aditya Mahajan adityam@umich.edu, a écrit :
On Wed, 25 Oct 2023, Alexandre Christe wrote:
Dear list,
I’d like to know the best approach to make this a bit more usable. I’m trying to typeset a table with sin/cos/tan values. I’d like to be able to convert the angles in degrees into radians (with math notation) and to compute the trigonometric function leading to sin(pi/4) = 1/2, or cos(pi/6) = sqrt(3)/2 and display it in math mode.
Here’s my current MWE, where I fail to convert the angles in radians
there is math.sind, cosd, etc. for computing sin for angle in degrees. The implementation is l-math.lua is:
local pipi = 2*math.pi/360
function math.sind(d) return sin(d*pipi) end function math.cosd(d) return cos(d*pipi) end function math.tand(d) return tan(d*pipi) end
and fail to display the result in symbolic form.
Context doesn't do symbolic math. You can try checking if one of the symbolic math libraries in lua provides all the features that you want.
One possible way would be to use Python and the t-filter module, like this
This can work as follows. Take the array of angles, and convert them to the desired format in python and write them to a temp file. Read that temp file in lua and typeset it as you want.
Another option is an old proof of concept by Luigi: https://github.com/bastibe/lunatic-python which allowed two-way communication between python and luatex. Not sure if it still works.
Aditya
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