fractionsmatrices
The fractions in my column vector look too large:
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\[
\begin{bmatrix} -4 \\ - \frac{5}{2} \\ \frac{9}{2} \end{bmatrix}
\]
\end{document}
The denominator "2" from "-5/2" actually creeps slightly over the numerator "9" from "9/2". Is this correct behaviour? It looks bad.
Note that you have extra space around your vector. You should probably using something like (pmatrix is part of the amsmath package)
\begin{pmatrix}a\\b\end{pmatrix}
The standard LaTeX \newcommand provides a way to have a single optional argument.
\newcommand*\colvec[3][]{
\begin{pmatrix}\ifx\relax#1\relax\else#1\\\fi#2\\#3\end{pmatrix}
}
Note that you have to use \colvec[a]{b}{c} if you want three elements or \colvec{a}{b} if you want two.
Update
As per your request in the comments, here's one that takes any number of elements based on the number passed in the first argument.
\newcount\colveccount
\newcommand*\colvec[1]{
\global\colveccount#1
\begin{pmatrix}
\colvecnext
}
\def\colvecnext#1{
#1
\global\advance\colveccount-1
\ifnum\colveccount>0
\\
\expandafter\colvecnext
\else
\end{pmatrix}
\fi
}
You use it exactly as you wanted, \colvec{5}{a}{b}{c}{d}{e}.
I'd just use the normal \frac or \tfrac. For display style maths they still look the best. I would use \nicefrac (or similar) only (if at all) in text maths.
\documentclass{article}
\usepackage{amsmath}
\def\frstfrac{\frac{2}{\sqrt{2y+1}\sqrt{2 \pi}}} % just a shortcut
\begin{document}
\begin{align*}
&= \frstfrac \exp \left( -y - \frac{1}{2}\right) && \forall y \in \left[- \frac{1}{2}, \infty\right) \\
&= \frstfrac \cdot e^{ -y - \frac{1}{2}} && \forall y \in \left[-\tfrac{1}{2}, \infty\right) \\
&= \frstfrac \cdot e^{ - \left(y + \frac{1}{2}\right)} && \forall y \in \left[-\tfrac{1}{2}, \infty\right) \\
&= \frstfrac \cdot e^{\textstyle -\!\left(y + \frac{1}{2}\right)} && \forall y \in \left[-\tfrac{1}{2}, \infty\right) \\
&= \frstfrac \exp \left( -y - 1/2 \right) && \forall y \in \left[- 1/ 2 , \infty\right)
\end{align*}
\end{document}
\smashAlso, consider using \sqrt{\smash[b]{2y+1}}\sqrt{\smash[b]{2 \pi}} in your denominator for better roots.
To quote from the amsmath documentation:
With the amsmath package
\smashhas optional argumentstandb, because occasionally it is advantageous to be able to “smash” only the top or only the bottom of something while retaining the natural depth or height.
Compare:
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation*}
\frac{2}{\sqrt{\smash[b]{2y+1}}\sqrt{\smash[b]{2 \pi}}} = \frac{2}{\sqrt{2y+1}\sqrt{2 \pi}}
\end{equation*}
\end{document}
The top bar of the root is aligned different and even the lower point is not on equal heights.
The LaTeX Companion has a very elaborated text about \smash and its uses. The first two examples (licensed under the LPPL) are shown here. Take a close look at the root's lower end and the top bar.
\documentclass{article}
\usepackage{amsmath}
\begin{document}
$ \sqrt{x} + \sqrt{y} + \sqrt{z} $ \par
$ \sqrt{x} + \sqrt{\mathstrut y} + \sqrt{z} $ \par
$ \sqrt{x} + \sqrt{\smash{y}} + \sqrt{z} $ \par
$ \sqrt{x} + \sqrt{\smash[b]{y}} + \sqrt{z} $
\[
\sqrt{ \frac{a+b}{ x_j } } \quad
\sqrt{ \frac{a+b}{ \smash{x_j }} } \quad
\sqrt{ \frac{a+b}{{}\smash{x_j }} } \quad
\sqrt{ \frac{a+b}{ \smash{x_j+b}} }
\]
\end{document}
Best Answer
A TABstack allows the inter-row baselineskip to be specified, while still keeping the baselineskip uniform, which I find important for vector/matrix notation.