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Re: How to write a "proper" math document

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  • Subject: [mg120207] Re: How to write a "proper" math document
  • From: Andrzej Kozlowski <akoz at>
  • Date: Wed, 13 Jul 2011 03:10:51 -0400 (EDT)
  • References: <> <iuukk8$epi$> <15944200.6757.1309943765495.JavaMail.root@m06> <iv45b8$es8$> <> <ivh9dm$llg$> <>

My point was that you were (probably deliberately) confusing two 
different aspects of Mathematica (and thus confusing the "naive user" 
whose interests you so often claim to represent).

The first "aspect" is that of a computer algebra system. As you know 
perfectly well, all computer algebra systems employ certain standard or 
canonical forms for representing certain mathematical expression which 
arise from algorithmic considerations and sometimes result in output 
that differs from standard mathematical practice. One, rather trivial 
example, that was discussed recently is Mathematica's outputting 
Sqrt[2*n] as Sqrt[2]*Sqrt[n], which is not the normal thing to do in 
mathematics. There is, of course, a great deal more of this kind of 
thing. Of course one can uses various programming tricks to convert such 
output into "standard" mathematics but, as you have yourself pointed 
out, it is a a little like "trying to teach a pig to sing". It is easier 
to make the necessary changes by hand (enabling "drag and drop" of text 
in the Preferences makes it, for me anyway, even easier). Doing such 
editing in Mathematica is certainly easier than doing it in TeX, where 
you (usually) have to work with the "source".

But then there is the second aspect of Mathematica and that is one of 
the things that distinguishes it from all other CAS known to me. It is 
also a complete, high quality, WYSIWIG mathematical typesetting system, 
capable of producing professional or "near professional" quality 
technical publications. If you doubt it, get hold of a copy of William 
Shaw's "Complex Analysis with Mathematica", CUP 2006 and see if you can 
tell the difference between this and similar books written in TeX.

Actually, as I wrote in my post, I think there is a difference but it 
involves very subtle things, like precise spacing, the size of secondary 
indices, and some other things that most people don't pay much attention 
to. Also, I myself have never succeeded getting Mathematica to produce a 
result as nice as Shaw's book, which is why I don't think it is easy. 
But Mathematica, even when uses as a "static editor" has lots of 
advantages over TeX editors, like the ability to paste high resolution 
pictures and parts of pdf files directly into a notebook (at least on 
the Mac). When you then print to PDF you get a single pdf file in which 
the stuff originally written in Mathematica and the things that were 
pasted in are merged seamlessly together. Achieving anything like this 
with TeX takes a great deal more effort.

Actually, Shaw's book is also a fine example of how one should approach 
Mathematica's input and output in what is primarily a mathematics book. 
Shaw clearly distinguishes Mathematica's input and output on the one 
hand form "mathematical formula's", on the other and does not attempt to 
"tweak" Mathematica's output to make it look more like conventional 
mathematics.  On the very few occasions  where the output looks 
different from standard mathematics, Shaw still keeps the Mathematica 
form in the output but uses "ordinary" notation in the text. (One such 
case involves the spacing between the symbols in a product such as x y, 
which in Mathematica's output is too wide compared with the usual 
convention in mathematics).

In any case, the point is that Mathematica is a fully capable 
mathematics typesetting system and the fact that it is also a CAS does 
not in any essential way diminish these capabilities. Personally I find 
it still too hard to achieve results as good as with TeX, particularly 
for the kind of mathematics that I do (e.g. Mahematica is not very good 
and producing "commutative diagrams" etc), but there is no reason, in 
principle, why it should not become as good in the future. The fact that 
it is a CAS is no obstacle.

Andrzej Kozlowski

On 12 Jul 2011, at 16:08, Richard Fateman wrote:

> On 7/12/2011 3:59 AM, Andrzej Kozlowski wrote:
>> On 8 Jul 2011, at 10:52, Richard Fateman wrote:
>>> I find it far preferable to take stuff out of a computer algebra system
>>> as TeX and paste it into a static document.  This also provides an
>>> opportunity to fix the broken displays.  E.g. we really don't expect a
>>> display of f=ma   to  come out   f=am.   Or E=mc^2 to come out e=c^2m
>>> (note also that E=2.718... not energy). Mathematica thinks it knows
>>> better than Einstein and Newton.
>> This argument is entirely bogus.
> So you don't do what I do.
> If you really want to produce a "static
>> document" in Mathematica there is no need to evaluate anything. You
>> enter f=ma and it stays that way.
> No, I would take stuff I computed, (which might as, sub-expressions, include forms with particular mnemonic value such as f=ma...) and
> paste them into a static document.
> You can also write E=mc^2 or
>> whatever you like and it will stay this way too. This is so obvious it
>> is hard to believe anyone could fail to have noticed it.
> It is hard to believe that anyone could believe that I was interested in pasting a text or non-evaluable expression re-rendered in TeX from Mathematica into a TeX document.  Of course the intent would be to take stuff that you have computed in a computer algebra system and paste it in to a static document.  E.g.  "Here is the result of our algorithm as computed in Mathematica, with terms rearranged slightly for ease of comprehension :  .... insert TeX here .... "
>> Of course things are different when evaluated output is concerned but it
>> also obvious that it is much easier to "fix it" in Mathematica than to
>> copy and paste into TeX and then fix it there.
>> There are good reasons for using TeX instead of Mathematica for journal
>> articles (I almost always do so myself) but very few of them were given
>> in this thread (and none in the above passage). One of the main reasons
>> is that in fact it is often very hard and sometimes perhaps impossible
>> to produce in Mathematica mathematical documents of the kind of
>> professional quality that is expected by mathematics journals.
> So you do exactly what I do. Just wanted to argue, I suppose.
>> On the other hand I use Mathematica exclusively for such things as
>> writing homework or exam problems for my students and almost all
>> "informal" mathematical writing. The advantages of Mathematica for all
>> such purposes seem to me so obvious that I won't bother listing them
>> here.
>> Andrzej Kozlowski

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