[Tex/LaTex] Combining two custom commands

Question

I came across a problem when typing my report. I do not know how to fix this. The problem is as follows:

I have two custom commands defined like this:

\newcommand{\slr}[1][n]{\ensuremath{{\bf SL}(#1,\mathbb{R})}}

\newcommand{\lie}[1][G]{\ensuremath{{\bf L}(#1)}}

So that the first command gives an output like ${\bf SL}(n,\mathbb{R})$ and the second command gives the output like ${\bf L}(G)$. Here $n$ and $G$ are respectively the default arguments.

Now when I use these two commands together, I hope to get

$${\bf L}({\bf SL}(2,\mathbb{R}))$$

However, for some reason what I am getting is

$$ {\bf L}({\bf SL}(2),\mathbb{R})$$

Any ideas of what is going on here?

Answer 1

The problem in \lie[\slr[2]] is that the optional argument to \lie is taken to be \slr[2. You can solve the issue with xparse:

\documentclass{article}
\usepackage{amsmath,amssymb,xparse}

\DeclareMathOperator{\slrop}{\mathbf{SL}}
\DeclareMathOperator{\lieop}{\mathbf{L}}

\NewDocumentCommand{\slr}{O{n}}{\slrop(#1,\mathbb{R})}
\NewDocumentCommand{\lie}{O{G}}{\lieop(#1)}

\begin{document}
Here it is: $\lie[\slr]$

With optional argument: $\lie[\slr[2]]$
\end{document}

I removed \ensuremath as I believe that you gain nothing from using \lie in text rather than $\lie$; to the contrary, I firmly believe that the latter form is much better, because math is always treated as math.