CZ:Formatting mathematics

this page: CZ policy (either established by consensus or under debate) for how to format mathematics in CZ articles

Issues for all <math> environments

Use <math> environments instead of HTML markup

Proposed policy: Always use a <math> environment when typesetting mathematics (for example, whenever a $ environment would be used in TeX), rather than using by-hand italics or HTML markup. (discuss this)

Inline or display?

Consider using display style for complex expressions (particulary if they include integrals, sums, products, matrices, etc.) rather than inline expressions. Sometimes, there will be compelling reasons for not doing this, but a useful strategy to difficulties with awkward inline expressions is avoidance.

The $dx$ in integrals

Proposed policy: Insert a "thin space" \, before any $dx$-type object in an integral or differential; let the <math> environment typeset it in normal math font, rather than altering it. (discuss this)

Proposed good examples: $d{\bar {f}}=u\,dx-iv\,dy$ and $\iint g(x,y)\,dx\,dy$

Proposed bad examples: $d{\bar {f}}=udx-ivdy$ and $\iint g(x,y)\,\mathrm {dx} \,\mathrm {dy}$

Issues for display <math> environments

Indentation

Policy: Use a single colon to indent a displayed equation. (discuss this)

Good example:

$\zeta (s)=\sum _{n=1}^{\infty }{\frac {1}{n^{s}}}$

Bad example:

$\zeta (s)=\sum _{n=1}^{\infty }{\frac {1}{n^{s}}}$

Issues for inline <math> environments

Use of \scriptstyle

To determine: Whether to use \scriptstyle to reduce the size of PNG-rendered inline math formulas. (discuss this)

Example with \scriptstyle: The identity $\scriptstyle e^{2\pi i}=\int _{0}^{\infty }e^{-x}\,dx$ is cool.

Example without \scriptstyle: The identity $e^{2\pi i}=\int _{0}^{\infty }e^{-x}\,dx$ is cool.

Example in which alignment is bad when scriptstyle is not used: $e^{\int _{0}^{1}1\,dx}$.

The base, e, should be aligned with the surrounding text; the superscript should be higher.

Size problems: The letters in $A+B=C\,$ look comically gigantic on some browsers.

Fractions

Writing

${\frac {3}{4}}$

looks good when "displayed", but when "inline", 3/4 may be better.

In superscripts

$e^{-x^{2}/2}\,$

looks better than

$e^{-{\frac {x^{2}}{2}}}.$

In fractions-within-fractions, a similar issue is raised:

${\frac {{\overline {x}}-\mu }{s/{\sqrt {n}}}}$

versus

${\frac {{\overline {x}}-\mu }{\frac {s}{\sqrt {n}}}}.$

Proper non-TeX mathematical notation

Italicizing variables bot not digits and not punctuation matches TeX style. Spacing before and after "+" or "=" or the like matches TeX style.

(a² + b²) = c²

Issues for the text

Capitalizing theorem names

Proposed policy: Do not capitalize names of theorems for that reason alone, either when referring to them in prose or when creating new CZ articles. Normally capitalized words within theorem names should still be capitalized. (discuss this)

Proposed good example: The fundamental theorem of covering spaces should never be called Martin's theorem, because Martin isn't a topologist.

Proposed bad example: The Fundamental Theorem of Covering Spaces should never be called Martin's Theorem, because Martin isn't a topologist.

Using phrases like "it is clear that", "obviously"

This is tricky. Spelling out every detail of an argument can be awkward, pedantic, or boring, and it can disrupt the narrative. On the other hand, what might be ovious to one reader might not be obvious to another. Some suggestions:

• Pay attention to the level of mathematical sophistication expected of the reader in the surrounding text.

• Consider using endnotes or hyperlinks to point readers to more detailed explantions, or to articles providing necessary background and context.