When writing in math, do you use a comma or colon preceding an equation?

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This is a general question about mathematical writing especially for writing research papers and the like.

Question: Do you precede an equation with a comma or colon?

Example A:

  1. The following equation is the Yosida-Hawking-Penrose-Dantzig function
    \begin{equation}
    f(x) = \frac{1}{2} D_\alpha(x,y)
    \end{equation}
  2. The following equation is the Yosida-Hawking-Penrose-Dantzig function,
    \begin{equation}
    f(x) = \frac{1}{2} D_\alpha(x,y)
    \end{equation}
  3. The following equation is the Yosida-Hawking-Penrose-Dantzig function:
    \begin{equation}
    f(x) = \frac{1}{2} D_\alpha(x,y)
    \end{equation}

Example B:

  1. In fact, we can express the earlier function using a much simpler expression
    \begin{equation}
    f(x) = \varphi(x,y)
    \end{equation}
    where \varphi(x,y) is the Demiane functional
  2. In fact, we can express the earlier function using a much simpler expression,
    \begin{equation}
    f(x) = \varphi(x,y)
    \end{equation}
    where \varphi(x,y) is the Demiane functional
  3. In fact, we can express the earlier function using a much simpler expression:
    \begin{equation}
    f(x) = \varphi(x,y)
    \end{equation}
    where \varphi(x,y) is the Demiane functional

Can anyone comment on which one is the best practice?

Answer

Generally, I would treat the equation as if it were any ordinary noun phrase, and use the usual rules for comma, colon, or no punctuation.

A colon is used if the equation is an elaboration, or an item. So, just as you might write

Lips are characterized by the following properties: fleshy, paired, red.

you would write

An ellipse is characterized by the following equation:

\frac{x^2}{a^2}+\frac{y^2}{b^2} = 1

A comma precedes a non-restrictive clause (one that describes rather than identifies the noun phrase), so by analogy with

The line can be assigned to a simpler character, Polonius.

we might write

A line can be described with a simpler equation,

y = mx+b

In comparison, with a restrictive clause, we use no comma, so just as we would write

From this, the oiler obtained the formula CH_3C_6H_4C_2H_5.

we would also write

From this, Euler obtained the formula

e^{i\pi}+1 = 0

I suspect there aren’t any hard and fast rules for this, however. Whatever you choose to do, be consistent and reasonable.

ETA: You’ll notice that I have no periods at the ends of these equations. The papers I have generally (though not universally) observe this pattern. However, in other fields, equations may have ending punctuation depending on how they occur within a sentence. It may be useful for a writer to consult the publication’s style guide, if applicable, or at least examine previous articles within the same publication or outlet.

Attribution
Source : Link , Question Author : Shamisen Expert , Answer Author : Brian Tung

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