I would like to use Python to generate my own algebra to pre-calculus worksheets to print and use. The purpose is to teach kids how to practice algebra. What is the best way generate the expressions?
Update:
I am planning to use Latex to generate nicely formatted equations.
The question I have is how to come up with a large number of the equations. One way of doing this is to define the list for each topics but this is tedious. I want to automate using some kind generator (e.g. Context Free Grammar)
If you want to generate nice looking typeset equations, you should probably output LaTeX code, which can then be compiled into pdf, dvi, postscript, or what have you. There are a few python libraries for this, but it's just text so generating it shouldn't be much of a problem once you know how it works. Alternatively, you can embed python code into a LaTeX document using something like this. In any case I haven't tried any of the python libraries for this so I can't really recommend any of them.
My approach to this problem would be to write a Python script to generate a LaTeX document which could then be compiled into a PDF document to be printed.
I assume that you want Python so that the sheets are different.
One way to do this would be to generalize the structure of an equation. The simplest ones are properly those that are of the form:
a*x+b*x+c=d*x+e*x+f
(any of the values can be 0, and they need not be distinct). Then I would suggest you simply constructed a method to return the latex code to typeset such an equation, which puts in random values for a, b, c, d, e and f.
You can then call that method as many times a you want different equations.
Related
The exams package is a really fantastic tool for generating exams from R.
I am interested in the possibilities of using it for (programming) assignments. The main difference from an exam is that besides solutions I'd also like hints to be included in the PDF / HTML output file.
Typically I put the hints for (sub)-questions in a separate section at the end of the PDF assignment (using a separate Latex section), but this requires manual labour. These are for students to consult if they need help getting started on any particular exercise, and it avoids having them look at the solutions directly for hints on how to start.
An assignment might look like:
Question 1
Question 2 ...
Question 10
Hints to all questions
I'd be open to changing the exact format as long it is possible to look up hints without looking up the answer, and it remains optional to read the hints.
So in fact I am looking for an intermediate "hints" section between the between the "question" and "solution" section, which is present for some questions but not for all.
My questions: Is this already possible? If not, how could this be implemented using the exams package?
R/exams does not have dedicated/native support for this kind of assignment so it isn't available out of the box. So if you want to get this kind of processing you have to ensure it yourself using LaTeX for PDF or CSS for HTML.
In LaTeX I think it should be possible to do what you want using the newfloat and endfloat packages in the LaTeX template that you pass to exams2pdf(). Any LaTeX template needs to provide {question} and {solution} environments, e.g., the plain.tex template shipped with the package has
\newenvironment{question}{\item \textbf{Problem}\newline}{}
\newenvironment{solution}{\textbf{Solution}\newline}{}
with the exercises embedded as
\begin{enumerate}
%% \exinput{exercises}
\end{enumerate}
Now instead of the \newenvironment{solution}... you could use
\usepackage{newfloat,endfloat}
\DeclareFloatingEnvironment{hint}
\DeclareDelayedFloat{hint}{Hint}
\DeclareFloatingEnvironment{solution}
\DeclareDelayedFloat{solution}{Solution}
This defines two new floating environments {hint} and {solution} which are then declared delayed floats. And then you would need to customize these environments regarding the text displayed within the questions at the beginning and the listing at the end. I'm not sure if this can get you exactly what you want, though, but hopefully it is a useful place to start from.
I am currently translating some MATLAB scripts to R for Multivariate Data Analysis. Currently I am trying to generate the same data as the Coeffs.Linear and Coeffs.Const part of the fitdiscr function in MATLAB.
The code being used is:
fitcdiscr(data, groups, 'DiscrimType', 'linear');
The data consists of 3 groups.
Unfortunately the R function seems to do the LDA only for two LDs and MATLAB seems to always compare all groups in all constellations. Does anybody have an idea how I could obtain that data?
I suspect you mean information on the implementation of various MATLAB function, which would be doc <functionname> (doc fitcdiscr would yield this documentation page on fitcdscr) to get the documentation, and edit <functionname> to get the implementation, if it is not obscured by The MathWorks. If those two do not give you enough information, I'm afraid you're out of luck, since not all TMW codes are available non-obscured.
fitcdiscr is non-obscured, although very brief; it's just a wrapper for some other functions. Keep doing edit <functionname> and doc <functionname> and see how deep the rabbit hole takes you.
NB: there's no built-in function called fitdiscr, but the syntax you describe is that of fitcdiscr (note the c), so I used that as examples. If the actual function being called is named fitdiscr, it's custom-made and you'll have to spit through its file by edit fitdiscr and hope for the best.
Forgive me if this may be already asked. I am kind of new to all this. I wondered if there is a simple facility to have Matlab or R import or convert from LaTeX documents? This would be no different than how you can create a MuPAD script document and convert into Matlab M code. This would be through the Matlab Math Symbol toolbox.
Thanks
No, converting general LaTeX equations into some sort of procedural programming language is most decidedly not possible.
LaTeX is a system for creating documents with structured text formatting and typesetting. It is not much different than writing individual letters and symbols onto a piece of paper yourself; there are no intrinsic semantics as to which symbols mean what. It doesn't know (or care) if the expression x = y is an assignment or a test for equality. Or if \cdot is a dot product or simple multiplication. All that really matters in the end is that the equations are readable and look good to a human eye. To convert this soup of symbols into a procedural programming language is quite impossible.
MuPAD, however, is a computer algebra system. You tell it what is a function and what are variables. It has this knowledge. As such, it is able to identify inputs and outputs and some sort of directional flow. It has a grammar to its equations: you must, for example, use := to denote assignment. When converting to an m-file, MuPAD uses this additional information to determine which variables are scalar or vector, what is an assignment and what is a boolean test, what is input and what is output, etc.
This difference is obvious in usage of MuPAD vs LaTeX: one can rearrange and simplify your equations for you, the other cannot.
I'm in the process of documenting some of my functions for an R package I'm making.
I'm using roxygen markup, though that is largely irrelevant to my question.
I have put equations into my documentation using \deqn{...}. My question is:
Is there a way to cross-reference this equation later on?
For example, in my Rd file:
\deqn{\label{test}
y = mx + b
}
Can I later do something like:
Referring to equation \ref{test}, ...
I've tried \eqref{test}, \ref{test} (which both get "unknown macro" and don't get linked ), and also \link{test} (which complains it can't find function test because it's really just for linking to other functions).
Otherwise I fear I may have to do something hacky and add in the -- (1) and Refer to equation (1) manually within the \deqn etc in the Rd file...
Update
General answer appears to be "no". (awww...)
However, I can write a vignette and use "normal" latex/packages there. In any case, I've just noticed that the matrix equations I spent ages putting into my roxygen/Rd file look awful in the ?myFunction version of the help (they show up as just-about literal latex source). Which is a shame, because they look beautiful in the pdf version of the help.
#Iterator has pointed out the existence of conditional text, so I'll do ASCII maths in the .Rd files, but Latex maths in the pdf manual/vignette.
I'm compiling my comments above into an answer, for the benefit of others.
First, I do not actually know whether or not .Rd supports tagging of equations. However, the .Rd format is such a strict subset of LaTeX, and produces very primitive text output, that shoehorning extensive equations into its format could be a painful undertaking without much benefit to the user.
The alternative is to use package vignettes, or even externally hosted documentation (as is done by Hadley Wickham, for some of his packages). This will allow you to use PDFs or other documentation, to your heart's content. In this way, you can include screenshots, plots, all of the funkiest LaTeX extensions that only you have, and, most significantly, the AMS extensions that we all know and love.
Nonetheless, one can specify different rendering of a given section of documentation (in .Rd) based on the interface, such as text for the console, nice characters for HTML, etc., and conditional text supports that kind of format variation.
It's a good question. I don't know the answer regarding feasibility, but I had similar questions about documenting functions and equations together, and this investigation into what's feasible with .Rd files has convinced me to use PDF vignettes rather than .Rd files.
Basically I have created two MATLAB functions which involve some basic signal processing and I need to describe how these functions work in a written report. It specifically requires me to describe the algorithms using mathematical notation.
Maths really isn't my strong point at all, in fact I'm quite surprised I've even been able to develop the functions in the first place. I'm quite worried about the situation at the moment, it's the last section of writing I need to complete but it is crucially important.
What I want to know is whether I'm going to have to grab a book and teach myself mathematical notation in a very short space of time or is there possibly an easier/quicker way to learn? (Yes I know reading a book should be simple enough, but maths + short time frame = major headache + stress)
I've searched through some threads on here already but I really don't know where to start!
Although your question is rather vague, and I have no idea what sorts of algorithms you have coded that you are trying to describe in equation form, here are a few pointers that may help:
Check the MATLAB documentation: If you are using built-in MATLAB functions, they will sometimes give an equation in the documentation that describes what they are doing internally. Some examples are the functions CONV, CORRCOEF, and FFT. If the function is rather complicated, it may not have an equation but instead have links to some papers describing the algorithm, which may themselves have equations for the algorithm. An example is the function HILBERT (which you can also find equations for on Wikipedia).
Find some lists of common mathematical symbols: Some standard symbols used to represent common mathematical operations can be found here.
Look at some sample pseudocode to see how it's done: For algorithms you yourself have coded up, you'll have to write them out in equation or pseudocode form. A paper that I've used often in my work is Templates for the Solution of Linear Systems, and it has some examples of pseudocode that may be helpful to you. I would suggest first looking at the list of symbols used in that paper (on page iv) to see some typical notations used to represent various mathematical operations. You can then look at some of the examples of pseudocode throughout the rest of the document, such as in the box on page 8.
I suggest that you learn a little bit of LaTeX and investigate Matlab's publish feature. You only need to learn enough LaTeX to write mathematical expressions. Then you have to write Matlab comments in your source file in LaTeX, but only for the bits you want to look like high-quality maths. Finally, open the Matlab editor on your .m file, and select File | Publish.
See Very Quick Intro to LaTeX and check your Matlab documentation for publish.
In addition to the answers already here, I would strongly advise using words in addition to forumlae in your report to describe the maths that you are presenting.
If I were marking a student's report and they explained the concepts of what they were doing correctly, but had poor or incorrect mathematical notation to back it up: this would lose them some marks, but would hopefully not impede my understanding of the hard work they've put in.
If they had poor/wrong maths, with no explanation of what they meant to say, this could jeapordise my understanding of their entire project and cost them a passing grade.
The reason you haven't found any useful threads is because most of the time, people are trying to turn maths into algorithms, not vice versa!
Starting from an arbitrary algorithm, sometimes pseudo-code, along with suitable comments, is the clearest (and possibly only) representation.