macro help with $\mathbb{Z}/p^{a}\mathbb{Z}$

Question

I am using \mathbb{Z}/p^{a}\mathbb{Z} many times in my work with variable a, I was thinking can I define a macro like \Z_p^{a} which will give the above result. I tried

\newcommand{\Z_p}[1]{\ensuremath{\mathbb{Z}/p^{#1}\mathbb{Z}}}

but LaTeX did not like it.

Answer 1

I'd go with

\newcommand{\Zp}[1]{\mathbb{Z}/p^{#1}\mathbb{Z}}

and $\Zp{a}$ will do what you want. It's not possible to have _ in the name of a macro (unless playing nasty and fragile tricks).

Maybe I'd do

\newcommand{\Zp}[2][p]{\mathbb{Z}/#1^{#2}\mathbb{Z}}

so, for the case where you want to use a different prime you can type

\Zp[q]{a}

Why not \ensuremath? Because it serves little purpose; I find it much better to segregate math in the proper way, that is, between $ symbols or inside \(...\).

If you already have

\newcommand{\Z}{\mathbb{Z}}

it's better doing

\newcommand{\Zp}[2][p]{\Z/#1^{#2}\Z}

so a change of formatting for the integers will automatically produce the same change in \Zp. Better yet, I usually advice to do something like

\newcommand{\numberset}[1]{\mathbb{#1}}
\newcommand{\Z}{\numberset{Z}}
\newcommand{\Q}{\numberset{Q}}
% ... other possible number sets ...

\newcommand{\Zp}[2][p]{\Z/#1^{#2}\Z}

so uniformity is ensured for all alike symbols.

Answer 2

With Plain TeX syntax you can do it:

\documentclass{article}
\usepackage{amsfonts}

\def\Z_p#1{\ensuremath{\mathbb{Z}/p^{#1}\mathbb{Z}}}

\begin{document}

\Z_p {137}% or Z_p{137}, it's all up to you

\end{document}

Notice that this overwrites a previous command \Z if it exists, but by default none exist. To be extra sure with other packages loaded, insert

\newcommand\Z{}

before the \def to give a chance to LaTeX to protest.