RFC: Proposals for enhanced MathML support in ConTEXt: Localisation and subject dependend typesetting

DRAFT as of 2001-03-10

1 Localisation

1.1 String localisation

There are only a few strings in the Math Meta Language, but there are.

α) <otherwise/> is according to the MathML recommondation 2.0 from February 2001 typed as “otherwise”. This needs to be localised.

− German: “Sonst” − …: “… ”

β) “true” and “false” are used either in English or in the translation (or simply ⇐ 1 = 1 which is equivalent to ⇐ true or = true)

− German: “wahr”, “falsch” − …: “… ”

γ) Some “function”/operator names are translated, some of them always (in one languare) other only occasional.

1. German, always: <curl/> is typeset “rot” (Rotation) instead of “curl”.

2. German, rarely: <image/> is sometimes typeset as “Bild” instead of “Image”.

Subject and culture depended typesetting

This can be divided in two parts: The first is the subject/content/audience depended typesetting (this contains mainly variants of typesetting, especially for the differences between “mathematician’s” and “physicist’s” typesetting). The second is about the way something is printed in different countries; the MathML recommondation lists some examples, which I have included here. Since this cannot directly mapped to a language, I haven’t included it into the localisation part.

Subject and style depend typesetting

Some of those style issues are already supported in ConTEXt, I won’t list those.

1. <conjugate/> There are two main ways to show the conjugation of a complex number: Overlining (\overline{z}) and staring (ψ^{∗}). The former seems to be prefered by mathematicians, the latter by physicists (but I won’t draw a strict line!).

2. The nabla calculation (or <curl/>, <div/> and <grad/>). The standard representaton is simply “curl”, “div”, “grad”. There is also the vector-must-be-bold fraction which type it bold: “curl”, “div”, “grad” (the divergence is no vector!). And the wider fraction which likes to use the nabla (∇) symbol: “∇×”, “∇·”, “∇”. There is even a sub-fraction which likes the vector arrow: ∇×, “∇·”, “∇”. (Yet another possibility would be to use vector arrows instead of bold in the second case.) The most importanted are the first and the third.

3. The Laplacian should be either typeset as ∇^{2} (current behaviour) or as Δ.

4. Vector representation (<ci type="vector">): I know tree repesentations: Vector arrow (“a⃗”), boldening (“a”) and underlining (“\underline{a}”). (The latter seems to be almost only used on blackboards.)

5. The <determinat/> has two representations: The bar (| · |) and the det-form (det ·). Presently ConTEXt uses the first alternative. I think both should be supported, but also a third which is a combination and should be the default:

det I = | \begin{matrix}1 & 0 \\ 0 & 1 \end{matrix} | = 1

6. The exponential function: This can be represented in two ways exp(iEt/ℏ) and e^{iEt/ℏ}. ConTEXt uses the second notation, but sometimes the first looks better (as always a matter of taste).

7. Cardinality of a set: I know three different representations: |ℕ| = #ℕ = card ℕ = ℵ.

8. Sets: The present notation for natural number etc is ℕℤℚℝℂℙ but some say this is only for blackboards and use NZQRCP or even NZQRCP.

9. The exponetial “e” and the image “i” can be also shown as outline (a lowercase 𝔼𝕀 but the only free font which includes these letters [and of which I know] is Taco’s outline font [this can also be used to represent the I matrix as a outlined one]).

1.2 Cultural differences

Those differences should be set as default (as those in section 1) when a language is choosen, but this should be general switches since this can also depend on the style of the typesetter.

1. At least in Germany the imaginary and real part of a compley number z is usually “Im z” and “Re z” instead of “ℑz” and “ℜz”, respectively.

2. (5.4.1 in MathML 2.0) tan x vs. tg x

3. (5.4.1 in MathML 2.0) ( \begin{matrix}n \\ k \end{matrix} ) vs. _{n}C^{k} vs. C_{k}^{n} (French) vs. C_{n}^{k} (Russian)