Mathematical typesetting requirements

Question

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): $$ A {\cal A} {\boldcal A} {\frak A} {\boldfrak A} {\bb A} {\bbb A} {\sf A} {\sfb A} etc. $$

Answer 1

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.

Answer 2

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.

Answer 3

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.

• Knuth, Larrabee and Roberts, Mathematical Writing
• Vivaldi, Mathematical Writing an Undergraduate Course

Answer 4

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.