CZ:Formatting mathematics

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This page contains CZ policy (either established by consensus or under debate) for how to format mathematics in CZ articles.

This page does not explain how to type mathematical formula in the software that we are using here. For that, you are referred to Help:Displaying mathematical formulas.

Issues for all <math> environments

Use <math> environments instead of HTML markup

Note: this policy is at odds with one formatting section below. When consensus is reached, this item and that one should be coordinated.

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

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.

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

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

Punctuation

The punctuation marks that follow a <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, or be ridiculously too high or too low.

Fractions

Writing

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

looks good when "displayed", but when "inline", $3/4$ is 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

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

Issues for display <math> environments

Indentation

Policy: Use a single colon outside the <math> tag to indent a displayed equation.

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.

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 obvious 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.

Proper non-TeX mathematical notation

Note: using non-TeX mathematical notation at all is at odds with one proposed policy above. When consensus is reached, this item and that one should be coordinated.

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

(a² + b²) = c²

\frac versus \cfrac

Compare and contrast:

$4\int _{0}^{\infty }{\frac {xe^{-x{\sqrt {5}}}}{\cosh x}}\,dx={1 \over 1+{1^{2} \over {1+{1^{2} \over {1+{2^{2} \over 1+{2^{2} \over {1+{3^{2} \over {1+{3^{2} \over {1+\cdots \quad }}}}}}}}}}}}.$

$4\int _{0}^{\infty }{\frac {xe^{-x{\sqrt {5}}}}{\cosh x}}\,dx={\cfrac {1}{{}\quad 1+{\cfrac {1^{2}}{1+{\cfrac {1^{2}}{1+{\cfrac {2^{2}}{1+{\cfrac {2^{2}}{1+{\cfrac {3^{2}}{1+{\cfrac {3^{2}}{1+\cdots \qquad \qquad {}}}}}}}}}}}}}\quad {}}}$

Michael Hardy 17:47, 13 August 2007 (CDT)

PS: The identity is (of course) due to Ramanujan. Michael Hardy 17:49, 13 August 2007 (CDT)