Mathematical typesetting requirements

I'm not really sure if this is the right place to ask this, but given the seemingly large concentration of mathematicians, and the tangentiality to TeX, I'll just ask here: what are the mathematical typesetting requirements regarding things like blackboard bold, bold calligraphic, and sans-serif; Are there situations where one would need all of the above in addition to their non-bold variants inside the same equation? Or is there only a requirement for the above so that the whole equation is then very bold/sans-serif?

Clarification: Are there situations where one would need all of the following inside the same equation (possibly non-existent mark-up, I hope you get the idea): $$A {\cal A} {\boldcal A} {\frak A} {\boldfrak A} {\bb A} {\bbb A} {\sf A} {\sfb A} etc.$$

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I am not sure I understand the question. Do you wish to know if there are mathematical texts which use all the different fonts? Can you please clarify? –  Yossi Gil Feb 12 '11 at 16:45
I took a course in measure theory once that had about four "M"s and a mu. That was hard enough. I also read a book that made heavy use of a "w" and an omega. Not easy to follow... –  Seamus Feb 12 '11 at 17:04
Are you writing a program that needs to display mathematics without running TeX? It's actually pretty rare to have an equation that is entirely bold. More often, you're writing expressions like x∈ℝ, mixing blackboard bold (etc.) with regular weight. –  Ross Churchley Feb 12 '11 at 17:07
“Double struck bold” is a strange idea: double struck developed as a substitute for bold... –  Caramdir Feb 12 '11 at 17:42
@morbusg: You're asking a yes/no question and the answer is almost certainly no. Is the issue that you're running out of mathematical fonts? I guess I don't really understand what you hope to get out of answers to this question. –  TH. Feb 17 '11 at 7:30

I have seen (and write) documents with four or more fonts in the same equation.

The idea behind is to visually differentiate the signification of symbol. for exemple : mathitalic for variable, sans-serif for matrix, fraktur for ideals and so on.

For example : $$\mathfrak p=\big(\mathsfup P\big)\coloneq\big((p)\big)$$ denotes a prime ideal in a matrix ring who's engendrate by a single element.

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I'll just ask here: what are the mathematical typesetting requirements regarding things like blackboard bold, bold calligraphic, and sans-serif;

Before you touch the fonts heed the advice of Halmos (of "halmos tombstone" fame). Choose your notation carefully. Bad notation can make good exposition bad and bad exposition worse;

It is highly unlikely that you can adhere to the above and have to use all of the above in one single equation or single paper, although you might encounter all of them, if you are the editor of a Mathematical Journal.

Personally, I managed to write a highly mathematical PhD thesis (in Mechanical Engineering), without any blackboard bold or bold calligraphic.

Edit

Now that the question is a bit more clearer to me, it was not hard to think of an example where all the font variants can be used albeit by ignoring good advice.

In general you have to try very hard to find examples with more than three variants together and almost impossible to find any with sans serif fonts in a Journal. Having all of them together is not impossible but highly improbable.

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I should probably point out that I'm not a mathematician. I don't write papers or anything like that. I am writing a set of definitions for Plain-format for use with XeTeX, trying to make available all the bells and whistles fonts like STIX/XITS/Asana has to offer. However, TeX's 16 family limit poses some challenges on what is a sane way to arrange them. Hence the question. –  morbusg Feb 12 '11 at 17:55
@morbusg How does unicode-math get around that limitation? –  Caramdir Feb 12 '11 at 18:08
@Caramdir: the question isn't about getting around the limitations. –  morbusg Feb 12 '11 at 18:22
@morsburg I am sorry, if I misunderstood your question, I posted before you clarified your question. –  Yiannis Lazarides Feb 12 '11 at 19:05
@Yniansn Zlaridaes: No problem! –  morbusg Feb 12 '11 at 19:39

I'm not entirely sure what this question is asking, or what sort of answer would deserve the bounty offered on it, but here's my take.

If you found yourself needing 3 or more of the above list of weights, slants, fonts and what have you, then I'd recommend you reconsider your naming of concepts.

I think it's a good idea to have a list of more or less semantic names for special symbols you use a lot. That way you can easily change all ocurrences of a particular symbol in one go if you need to. Here's an example for something I was writing recently:

\newcommand{\Bee}{\ensuremath{ \mathbf{B}}}
\newcommand{\Vee}{\ensuremath{ \mathbf{V}}}
\newcommand{\Veeplus}{\ensuremath{ \mathbf{V^+}}}
\newcommand{\Ell}{\ensuremath{ \mathbf{L}}}
\newcommand{\Arr}{\ensuremath{ \mathbf{R}}}
\newcommand{\CQ}{\ensuremath{ \mathbf{CQ}}}
\newcommand{\DS}{\ensuremath{\mathbf{DS}}}
\newcommand{\Wvee}{\ensuremath{\mathbf{W}}}
\newcommand{\Wveeplus}{\ensuremath{\mathbf{W^+}}}


These are all symbols with special meaning in that paper. They are all sets of functions, so it makes sense that they are all typeset in roughly the same way. Likewise, arbitrary members of these sets (specific functions in one or the other of the sets) are denoted by lowercase boldface letters. In addition to this I use \mathbb{R} for the real line which is pretty commonplace, so I don't feel like my two Rs will get confused. If I had, say a \mathcal{R} or a sans serif R as well, I'd begin to worry about readability.

I was reading something that used w and \omega for distinct things: this was difficult. Those two glyphs are too similar.

Here are some resources on mathematical writing that might offer more guidance.

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”If you found yourself needing 3 or more of the above list of weights, slants, fonts and what have you, then I'd recommend you reconsider your naming of concepts.” I strongly disagree with that sentence. I find texts that use different fonts for different types of objects much more readable. E.g., italic for normal variables, sans-serif for vectors (when seen as a finite collection of coordinates), upright for operators, fraktur for ideals or Lie algebras, script for sheaves, etc. –  Caramdir Feb 17 '11 at 17:48
@Caramdir What I meant was if you have italic, bold, fraktur and caligraphic versions of the same letter in an equation, then you should rename different ones by different letters. I agree that different fonts etc for different types of thing is a good thing, but different font faces with the same letter are hard to distinguish sometimes. That was the point I wanted to make. I'll edit this later. –  Seamus Feb 17 '11 at 17:58
That is something I agree with. –  Caramdir Feb 17 '11 at 17:59

I am giving a hypothetical answer here to myself in the hope of clarifying the question further. It is quite possibly filled with errors.

You wouldn't need sans-serif fonts in the same equation with serif-fonts ever. You would use sans-serif fonts document-wide in things like presentations and such.

Same goes for bold; you wouldn't mix the bold glyphs with their non-bold variants inside the same equation. You could use the bold variants (for everything) to emphasise a specific equation. Note that the "normal" bold glyphs of \bf et such are a different story; they only bolden the latin alphabet, greek uppercase, and digits. Those are used inside the same equation with their non-bold variants.

It could also be that the bold variants were added to STIX to be ready for situations where you'd run out of glyphs to represent things.

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People might use bold or (to a lesser extend) sans-serif versions of a symbol to denote a vector-valued version of an operator. –  Caramdir Feb 17 '11 at 16:11