LaTeX to XML Math Delimiters

Vim is amazing when used to edit MediaWiki text, but typing " . . . " can be tiresome and frustrating if formulas are used often. LaTeX delimiters are so concise and even come in two flavors: "\( . . . \)" for inline math and "\[ . . . \]" for centered formulas. The goal is to perform the following conversions: "\( . . . \)" becomes ". . ." "\[ . . . \]" becomes "
. . .
"

Input

Given two vectors \(\vec{x}\) and \(\vec{y}\) in \( \mathbb{R}^n \),
their '''dot product''' or '''inner product''' is defined as the following:

\[ \sum_{i=0}^{n} x_i \, y_i \]

----

Integration by parts is another way of writing the product rule of differentiation.
For two functions \(f(x)\) and \(g(x)\), the following are equivalent:

\[ \begin{align}
\frac{\mathrm{d}}{\mathrm{d}x} \left( f(x) \, g(x) \right) &= f'(x) \, g(x) + f(x) \, g'(x) \\
\int f(x) \, g'(x) \, \mathrm{d}x &= f(x) \, g(x) - \int f'(x) \, g(x) \, \mathrm{d}x
\end{align} \]

----

Matrix multiplication is not commutative

\(
\begin{align}
\begin{bmatrix}
    a_{11} & a_{12} \\
    a_{21} & a_{22}
\end{bmatrix} \,
\begin{bmatrix}
    b_{11} & b_{12} \\
    b_{21} & b_{22}
\end{bmatrix} &\ne
\begin{bmatrix}
    b_{11} & b_{12} \\
    b_{21} & b_{22}
\end{bmatrix} \,
\begin{bmatrix}
    a_{11} & a_{12} \\
    a_{21} & a_{22}
\end{bmatrix} \\

\begin{bmatrix}
    a_{11} \, b_{11} + a_{12} \, b_{21} & a_{11} \, b_{12} + a_{12} \, b_{22} \\
    a_{21} \, b_{11} + a_{22} \, b_{21} & a_{21} \, b_{12} + a_{22} \, b_{22}
\end{bmatrix} &\ne
\begin{bmatrix}
    a_{11} \, b_{11} + a_{21} \, b_{12} & a_{12} \, b_{11} + a_{22} \, b_{12} \\
    a_{11} \, b_{21} + a_{21} \, b_{22} & a_{12} \, b_{21} + a_{22} \, b_{22}
\end{bmatrix}
\begin{align}
\)

''Quod erat demonstrandum''.

Output

Given two vectors \vec{x} and \vec{y} in \mathbb{R}^n,
their '''dot product''' or '''inner product''' is defined as the following:


\sum_{i=0}^{n} x_i \, y_i


----

Integration by parts is another way of writing the product rule of differentiation.
For two functions f(x) and g(x), the following are equivalent:


\begin{align}
\frac{\mathrm{d}}{\mathrm{d}x} \left( f(x) \, g(x) \right) &= f'(x) \, g(x) + f(x) \, g'(x) \\
\int f(x) \, g'(x) \, \mathrm{d}x &= f(x) \, g(x) - \int f'(x) \, g(x) \, \mathrm{d}x
\end{align}


----

Matrix multiplication is not commutative


\begin{align}
\begin{bmatrix}
    a_{11} & a_{12} \\
    a_{21} & a_{22}
\end{bmatrix} \,
\begin{bmatrix}
    b_{11} & b_{12} \\
    b_{21} & b_{22}
\end{bmatrix} &\ne
\begin{bmatrix}
    b_{11} & b_{12} \\
    b_{21} & b_{22}
\end{bmatrix} \,
\begin{bmatrix}
    a_{11} & a_{12} \\
    a_{21} & a_{22}
\end{bmatrix} \\

\begin{bmatrix}
    a_{11} \, b_{11} + a_{12} \, b_{21} & a_{11} \, b_{12} + a_{12} \, b_{22} \\
    a_{21} \, b_{11} + a_{22} \, b_{21} & a_{21} \, b_{12} + a_{22} \, b_{22}
\end{bmatrix} &\ne
\begin{bmatrix}
    a_{11} \, b_{11} + a_{21} \, b_{12} & a_{12} \, b_{11} + a_{22} \, b_{12} \\
    a_{11} \, b_{21} + a_{21} \, b_{22} & a_{12} \, b_{21} + a_{22} \, b_{22}
\end{bmatrix}
\begin{align}


''Quod erat demonstrandum''.