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The standard font used for \mathcal does not include any lowercase characters. The Comprehensive LaTeX Symbols List suggests redefining \mathcal to use Zapf Chancery. However I do not particularly like that font. For example the uppercase "I" is very hard do distinguish from the non-mathcal "I". Are there any good alternatives?

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Why do you want lowercase calligraphic letters in mathematics? –  Jonathan Fine Aug 11 '10 at 20:45
    
@Jonathan: see my answer to your "solution" below. –  Caramdir Aug 11 '10 at 20:52
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I'm looking for lower case calligraphy because it's used to denote lines in Birkhoff, George David (1932) \href{jstor.org/stable/1968336}{ ``A Set of Postulates for Plane Geometry (Based on Scale and Protractors),''} {\it Annals of Mathematics}, Second Series, (Apr., 1932), pp. 329-345. –  user10834 Jan 16 '12 at 5:26
    
@EricRasmusen Welcome to TeX.sx! I converted the non-answer to a comment to the question, because the area below is for actual answers. –  Stefan Kottwitz Jan 16 '12 at 8:23
    
@user10834 : The article of Birkhoff your referring to uses lower case italics to denote lines, not lowercase calligraphy. –  Frédéric Grosshans Oct 29 at 16:51

5 Answers 5

up vote 9 down vote accepted

I'm a bit surprised that Will Robertson hasn't dropped by and mentioned the STIX fonts as these have the lowercase calligraphic (and lowercase blackboard bold) glyphs.

There doesn't yet seem to be a simple LaTeX package available mapping all the glyphs to particular commands, though. The stix package on CTAN at present seems to be just a copy of the fonts themselves (reorganised into correct texmf tree layout) but no style files as yet. I recall reading on the STIX website that LaTeX-related stuff was intended, but given how long it took the fonts to be released, I'm not holding my breath!

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No, I deleted my incorrect answer to look at mathrsfs. They don't have lowercase when I thought they did. 8-bit LaTeX for the STIX fonts is indeed intended for their 1.2 release (1.1 is OpenType math, which will then supersede — mostly — the XITS Math font). And you can use the XITS Math font with unicode-math right now, but that requires a relatively radical change to how you might compile your document. So no good answer from me right now :) –  Will Robertson Jul 30 '10 at 16:37
    
I accepted this solution because that is what I will try for the notes I'm currently typing. (Note that \mathscr needs to be used instead of \mathcal to produce lowercase letters.) –  Caramdir Aug 2 '10 at 18:18
    
From the STIX website: “Development is currently underway for the next release of the STIX fonts which will include support for LaTeX. We expect the release date to be no later than July 2012.” –  Caramdir May 26 '12 at 21:50
    
@Andrew: I just realized that unicode-math is not mentioned in the answer, but only a comment. Do you want to edit it in, or should I do it (or add a separate answer)? –  Caramdir May 26 '12 at 21:52
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@PeterLeFanuLumsdaine: \usepackage{unicode-math}\setmathfont{xits-math.otf} and compile with lualatex or xelatex. –  Caramdir Oct 3 '12 at 0:20

A lowercase L can be done with \ell. But this seems to be the only lowercase letter that is included without loading any packages.

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The 'calligraphic' lowercase L is an ordinary lowercase L written in a way that reduces confusion with the number 1. Typographically it is calligraphic but mathematically it is not. –  Jonathan Fine Aug 11 '10 at 20:44
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@Jonathan Fine This solves the mystery of this sole lowercase letter. Thanks. –  h0b0 Aug 12 '10 at 15:04

symbols suggests using the calligra package as an alternative to Zapf Chancery. Put

\DeclareMathAlphabet{\mathcalligra}{T1}{calligra}{m}{n}

in the document’s preamble to use \mathcalligra for calligraphic symbols in the Calligra font.

/EDIT: To be honest, I’m not thrilled by the result, and I expect you won’t be either. Still, I’ll leave this here. Perhaps someone can profit from it.

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When scaled correctly it is not bad, but quite a bit more "curly" than the default \mathcal. –  Caramdir Aug 2 '10 at 18:15

Think about meaning. Mathematical symbols are symbols used by mathematicians to carry a particular meaning (which may depend on the subject area). Unicode takes that point of view (more-or-less) by giving each distinct mathematical symbol its own code point.

Typographically, a calligraphic F is an 'F' in a particular font, but mathematically it is mathematical symbol with its own meaning. Ordinarily Unicode does not care about the font, but for math symbols it does.

In my experience, mathematicians don't use lower-case calligraphic symbols, and as far as I know there are no Unicode code points for them. Put another way, Knuth did not create lower-case mathematical calligraphic letters because mathematicians don't use them.

As a mathematician, I don't see a sufficiently good reason to start using them.

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Algebraic geometers are usually using curly letters to denote sheaves. And there is a definition of Hom(F,G) of sheaves of homomorphisms between sheaves. So "Hom" should be curly to distinguish it from the ordinary Hom-set in the category of sheaves. Similarly e.g. for curly "Ext". –  Caramdir Aug 11 '10 at 20:48
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Also I have seen people using curly lower case letters to denote ideals (handwritten; in print fraktur is common but few people actually write fraktur). –  Caramdir Aug 11 '10 at 20:50
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@Caramdir: Harthorne's Algebraic Geometry (p 67) uses "Hom" with a calligraphic "H" and italic "om" for this concept. The recent Bull. AMS. survey on Perverse Sheaves (de Cataldo and Migliorini) uses uppercase math italic letters for sheaves. –  Jonathan Fine Aug 12 '10 at 5:20
    
@Caramdir: Handwritten calligraphic 'g' indeed corresponds to typeset fraktur 'g'. This, I think, supports my opinion. –  Jonathan Fine Aug 12 '10 at 5:23
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@Jonathan: I know what Hartshorne (and other people) use. But this is a chicken-and-egg problem: As long as there are no lowercase calligraphic letters available nobody will use them. (And in my opinion calligraphic "H" with italic "om" looks terrible.) –  Caramdir Aug 12 '10 at 8:57

The font package boondoxo has both lowercase and uppercase calligraphic math symbols, as well as their bold versions. You may load it by \usepackage[cal=boondoxo]{mathalfa}, and see whether you like it.

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