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I ran across a small curiosity when working today; specifically that LaTeX defines \coth by default, but not \sech or \csch. I’d like to know why. I think of the three functions are being very similar, so I’m curious as to why one is defined by default, but the others aren’t.

I know that a lot of thought went into the original design of LaTeX, and that suggesting changes (however minor) to the core functionality is a bad idea. So I’m not trying to cast a value judgement on this, I just want to know why it’s done that way.

However, I can imagine that the designers of LaTeX probably aren't interested in explaining (relatively minor) design decisions like this, or that there might not be a single right answer to the question.

Is this an appropriate question to ask on TeX.se? More generally, are questions asking for explanations of why LaTeX behaves as it does appropriate, or should they be reserved to personal curiosities?

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    I am undecided on this however it is quite convenient to define a new operator and there are many questions on the main site too. But I don't know why they are left out. – percusse Jun 2 '13 at 18:22
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    I knew that I had seen something similar on main at one point, here it is why is lcm not defined by default – Scott H. Jun 3 '13 at 2:42
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    I share percusse's doubts: on the one hand, such questions can be useful to understand the internal mechanics of TeX; on the other hand, by allowing them on the site, you run the risk of seeing TeX gutted by a horde of curious (albeit well-meaning) enthusiasts. There must be some middle ground that is acceptable. – jub0bs Jun 3 '13 at 9:16
  • @Jubobs: do you imply that these questions would uncover an inconvenient truth that most TeX users are trying to hide (or at least to ignore)? ;) Or that allowing the questions (and answers) to be too technical could be discouraging to the more casual users? We do have quite a lot of heavily-technical questions and answers already, though. – T. Verron Jun 3 '13 at 11:47
  • @T.Verron: I read Jubobs’ comment to mean that the internal mechanics of TeX aren’t perfect (which is surely true of any programming language), and while it might be useful to understand major architectural features, turning the site into a series of questions criticising the design isn’t very helpful. Especially trivial questions like this, which don’t lend any insight into how TeX works, and are really just me scratching a curious itch. – alexwlchan Jun 3 '13 at 14:53
  • With that in mind, perhaps an answer would be something like: it’s acceptable to discuss major features in the design of TeX, but trivial questions (such as "Why is command \X not defined" and "Why does command \Y do Z") should be avoided. Then you need to establish what a “major” feature means. Does that sound reasonable? – alexwlchan Jun 3 '13 at 14:55
  • @T.Verron Any inconvenient truth should be uncovered :p I mean the second thing you wrote: a large number of questions dissecting every single detail of TeX (e.g. What purpose does \relax serve in the definition of \@ensuredmath?) is undesirable. I don't doubt the merits of such questions, but a large number of them would be detrimental to the site as they would drown "casual" users in "technical" noise. – jub0bs Jun 3 '13 at 16:18
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    The list of predefined operator in LaTeX is just the same as the list in Plain TeX, as Knuth wrote it. I believe that hyperbolic secant and cosecant are not that widely used, just like the trigonometric secant and cosecant, which are (mis)used in calculus courses and nowhere else in ”real” mathematics. – egreg Jun 3 '13 at 21:48
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A question such as “Why indentation is suppressed in minipage?” would certainly be a legitimate one. On the other hand, asking why some operator is missing from the list of predefined operators can't have an answer different from “because”.

The LaTeX kernel provides a bunch of features that Leslie Lamport and the LaTeX team thought useful for general needs of typesetting. They couldn't forecast each and every need of LaTeX users; additional packages are the answer: if something proves useful to several people, some package will appear providing it.

The question about the “hyperbolic secant” is easily answered: the list of predefined operators in LaTeX is the same as in Plain TeX; Knuth provided the hyperbolic sine, cosine, tangent and cotangent, probably deeming them of non marginal use. Some choice has to be made as the list of operators actually used in mathematics is huge; it's nearly impossible to know them all. It's curious that there's no “lowest common multiple” predefined operator: possibly Knuth doesn't like it.


About “hyperbolic secant and cosecant”, I really don't know any usage for them. Nowadays the “circular secant and cosecant” are used (I'd say misused) only in calculus exercise books or in specialized technical fields such as topography. Their hyperbolic counterparts are just the reciprocal of cosine and sine.

  • Seeing this your answer, I think the question would be legitimate on the main site, and this answer (after crossing out the first paragraph) would be a legitimate answer to it ;) – yo' Jun 3 '13 at 23:40
  • That seems a sensible distinction. As I was writing out my question, I did think that maybe the operator question was a bit trivial, but I wanted to know whether similar questions (such as your minipage example) would be acceptable. Thanks. – alexwlchan Jun 4 '13 at 7:27

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