Command to replace a variable inside angle bracket

Question

In my current document, I have a lot of angle brackets, which are computed via:

\langle a, b \rangle

Is there anyway I could create a new command, something in the look of:

\newcommand{\dotproduct{ab}}{\langle a, b \rangle}

so that I could replace the a and b by other variables? To be more specific, I would love for that command template to work also for:

\dotproduct{cd}, \dotproduct{Q,R}

Answer 1

The standard LaTeX syntax would be

\newcommand\dotproduct[2]{\langle#1,#2\rangle}

then

 \dotproduct{Q}{R}

Answer 2

I'd prefer the syntax suggested by @DavidCarlisle.

If you still want your syntax (which is imho unclean) this macro will test whether your argument contains a comma, if so it just uses it as is, if not it will put a comma after the first item of your input.

\documentclass[]{article}

\usepackage{xparse}

\ExplSyntaxOn
\NewDocumentCommand \dotproduct { m }
  {
    \langle
    \tl_if_in:nnTF { #1 } { , }
      { #1 }
      { \tl_head:n { #1 } , \tl_tail:n { #1 } }
    \rangle
  }
\ExplSyntaxOff

\begin{document}
$\dotproduct{a,b} \dotproduct{cd} \dotproduct{abc}$
\end{document}