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