LaTeX Macros: Paired Delimiters With Mathtools Spacing

Hey guys! Ever found yourself wrestling with spacing around parentheses in your LaTeX math mode? It can be a real headache, especially when you want consistent and visually pleasing results. The mathtools package comes to the rescue with its powerful \DeclarePairedDelimiter command. But what if you want to add a little extra flair – like an optional spacing argument? That's what we're diving into today! We'll explore how to define paired-delimiter macros, specifically focusing on adding that sweet, symmetrical, horizontal spacing argument. So, buckle up, and let's get mathy!

Understanding the Basics of \DeclarePairedDelimiter

Before we jump into the fancy footwork, let's quickly recap the basics of \DeclarePairedDelimiter. This command is your best friend when it comes to defining macros for paired delimiters like parentheses, brackets, braces, and even those cool norm symbols. It takes three main arguments:

1. The macro name you want to create (e.g., \parens).
2. The "outer" delimiter (e.g., ().
3. The "inner" delimiter (e.g., )).

The beauty of this command is that it automatically handles resizing the delimiters using \left and \right when you use the starred version of the macro (e.g., \parens*). This is super handy for expressions with varying heights.

For example, if you simply want to create a parenthesis macro, the basic code will look like this:

\DeclarePairedDelimiter{\parens}{(}{)}

Now, you can use \parens{x} to get simple parentheses around x, and \parens*[\frac{a}{b}] to get automatically sized parentheses around the fraction a/b. Pretty neat, huh?

But let’s say you want a bit more control over the spacing. This is where the optional argument comes into play. We want to define our \parens macro so that we can optionally add horizontal space around the content inside the parentheses. This can be particularly useful for improving readability in certain mathematical expressions.

Why Spacing Matters

In the world of typography and mathematical notation, spacing is everything. Proper spacing can significantly enhance the readability and clarity of your equations. Too little space, and your expression might look cramped and confusing. Too much space, and it might look disjointed. Finding that sweet spot is crucial.

Think about it – when you're writing an essay, you use spaces between words to make it easier to read. The same principle applies to mathematical notation. Just like a well-spaced paragraph is easier on the eyes, a well-spaced equation is easier to understand.

Consider scenarios where you have complex expressions inside parentheses, such as long fractions, integrals, or summations. Without proper spacing, these expressions can become visually overwhelming. By adding a bit of horizontal space, we can create a visual buffer that helps the reader's eye to better parse the equation.

Moreover, consistent spacing contributes to the overall aesthetic appeal of your document. When spacing is applied uniformly, your equations will have a polished and professional look. This is particularly important in academic papers, theses, and other formal documents where presentation matters.

So, our goal here isn't just about adding space for the sake of it; it's about making our mathematical expressions as clear, readable, and visually appealing as possible. And that's why mastering the art of spacing with mathtools is a valuable skill for any LaTeX user.

Adding the Optional Spacing Argument

Okay, let’s get to the heart of the matter: adding that optional spacing argument. This involves a bit of LaTeX wizardry, but don’t worry, we’ll break it down step by step. The key is to use the \NewDocumentCommand command, which provides a more flexible way to define macros with optional arguments compared to the older \newcommand. I really enjoy using the \NewDocumentCommand because it lets me make more complex macros with ease.

First, we need to understand the syntax of \NewDocumentCommand. It generally looks like this:

\NewDocumentCommand{\macroName}{number of arguments}{definition}

Where:

• \macroName is the name of the macro you're defining.
• number of arguments is a specification string that tells LaTeX how many arguments the macro takes and whether they are optional or mandatory.
• definition is the code that the macro executes.

For our case, we want a macro that takes one mandatory argument (the content inside the parentheses) and one optional argument (the spacing). The argument specification string will look something like this: O{} m. Let's break it down:

• O{} means an optional argument with a default value of empty (no extra space). This will be our spacing argument.
• m means a mandatory argument. This will be the content we want to enclose in parentheses.

Now, let's put it all together. We’ll define a new macro called \parensPlus (to distinguish it from the basic \parens we defined earlier) that incorporates this optional spacing. The code looks like this:

\NewDocumentCommand{\parensPlus}{O{} m}{\left(\mspace{#1mu} #2 \mspace{#1mu}\right)}

Let's dissect this code:

• \NewDocumentCommand{\parensPlus}{O{} m}: This defines the macro \parensPlus with one optional argument (defaulting to empty) and one mandatory argument.
• {\left(\mspace{#1mu} #2 \mspace{#1mu}\right)}: This is the macro definition. It does the following:
  • \left(: Opens a parenthesis that will be sized automatically.
  • \mspace{#1mu}: Inserts horizontal space. #1 refers to the first argument (the optional spacing). We use mu (math unit) as the unit of measurement. A common value for spacing is something like 3 or 5 mu, but you can adjust it as needed.
  • #2: Refers to the second argument (the mandatory content inside the parentheses).
  • \mspace{#1mu}: Inserts horizontal space again, ensuring symmetrical spacing.
  • \right): Closes the parenthesis, again with automatic sizing.

Now, you can use \parensPlus{x} for standard parentheses, and \parensPlus[5]{x} to add 5 mu of space around x. This gives you fine-grained control over the spacing within your parentheses!

Example Usage and Comparison

To really see the difference, let's look at some examples. Suppose we have the following expression:

\frac{1}{2} + (\frac{3}{4})

This might look a bit cramped, especially the parentheses around the fraction. Now, let's use our \parensPlus macro:

\frac{1}{2} + \parensPlus[5]{\frac{3}{4}}

The 5 mu of extra space makes the expression much more readable. You can experiment with different values to find what looks best for your particular expression. I typically find that a value between 3 and 7 mu works well for most cases.

Let's compare this to the basic \parens macro we defined earlier:

\DeclarePairedDelimiter{\parens}{(}{)}

Using \parens{\frac{3}{4}} will give you parentheses, but without the extra spacing. The \parensPlus macro gives you that additional level of control, allowing you to fine-tune the appearance of your equations.

Another scenario where \parensPlus shines is with more complex expressions, like integrals or summations:

(\int_a^b f(x) dx)

Versus:

\parensPlus[5]{\int_a^b f(x) dx}

The extra space makes a noticeable difference in clarity. It helps to visually separate the parentheses from the integral symbol and the integration limits.

Handling the Starred Version for Automatic Sizing

So, we've got the optional spacing down, but what about the starred version for automatic sizing? We need to modify our \parensPlus macro to handle the * modifier. This requires a slightly more advanced technique using the xparse package (which mathtools loads anyway!).

The idea is to define a new macro that checks for the * and then calls the appropriate internal macro with or without the \left and \right commands. Here’s how we can do it:

\NewDocumentCommand{\parensPlus}{s O{} m}{%
  \IfBooleanTF{#1}{%
    \left(\mspace{#2mu} #3 \mspace{#2mu}\right)%
  }{%
    (\mspace{#2mu} #3 \mspace{#2mu})%
  }%
}

Let's break this down:

• \NewDocumentCommand{\parensPlus}{s O{} m}: We've added an s to the argument specification. This tells LaTeX that the macro can have an optional star. #1 will be true if the macro is called with a star (e.g., \parensPlus*), and false otherwise.
• \IfBooleanTF{#1}{...}{...}: This is a conditional statement that checks if the star was used. If #1 is true (star present), the first block of code is executed; otherwise, the second block is executed.
• {\left(\mspace{#2mu} #3 \mspace{#2mu}\right)}: This is the code for the starred version. It includes \left and \right for automatic sizing.
• {(\mspace{#2mu} #3 \mspace{#2mu})}: This is the code for the unstarred version. It uses fixed-size parentheses.

Notice that #2 now refers to the optional spacing argument, and #3 refers to the mandatory content argument. This is because the s argument “consumes” the first argument number.

Now, you can use \parensPlus*{...} for automatically sized parentheses with spacing, and \parensPlus[...] {…} for fixed-size parentheses with custom spacing. This gives you the best of both worlds!

Putting It All Together: A Complete Example

To make sure we're all on the same page, let's put together a complete example that you can copy and paste into your LaTeX document:

\documentclass{article}
\usepackage{mathtools}

\NewDocumentCommand{\parensPlus}{s O{} m}{%
  \IfBooleanTF{#1}{%
    \left(\mspace{#2mu} #3 \mspace{#2mu}\right)%
  }{%
    (\mspace{#2mu} #3 \mspace{#2mu})%
  }%
}

\begin{document}

Here are some examples of \verb|\parensPlus|:

$\parensPlus{\frac{a}{b}}$

$\parensPlus[5]{\frac{a}{b}}$

$\parensPlus*{\frac{a}{b}}$

$\parensPlus*[5]{\frac{a}{b}}$


$\int_0^1 \parensPlus[3]{\frac{x^2}{2}} dx$

$\int_0^1 \parensPlus*{\frac{x^2}{2}} dx$

\end{document}

This example defines the \parensPlus macro and then demonstrates its usage in various scenarios. You can compile this code to see the results for yourself and experiment with different spacing values.

Conclusion: Mastering Spacing with Mathtools

So, there you have it! We've journeyed through the ins and outs of defining paired-delimiter macros with optional spacing using the mathtools package. We've covered the basics of \DeclarePairedDelimiter, delved into the power of \NewDocumentCommand, and even tackled the starred version for automatic sizing. You're now equipped to create beautifully spaced and visually appealing mathematical expressions in LaTeX.

Remember, the key to effective mathematical typography is consistency and attention to detail. By mastering techniques like this, you can elevate the quality of your documents and make your mathematical writing shine. Play around with different spacing values, experiment with various expressions, and find what works best for you. Happy TeXing, and I hope this helps you guys out with the spacing on your equations!