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. Consider the following example: inline $e^{\int _{0}^{1}1\,dx}=e$ and displayed

$e^{\int _{0}^{1}1\,dx}=e.$

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 $\iint g(x,y)\,\mathrm {dx} \,\mathrm {dy}$

Punctation

The punctuation marks that follow <math> environment should be put inside the environment -- otherwise the mark might appear at the beginning of the next line, depending on the position of the text in browser's window.

Issues for display <math> environments

Indentation

Policy: Use a single colon outside the <math> tag 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.

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

It was suggested that global resizing of PNG-renderd formulas is possible. This would eliminate the need for \scriptstyle (or leave it for its proper use). The only question would be to determine the "right" size, as the dispayed formulas will be affected too.

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.