Alignments · Reflow TeX

Aligned systems and matrices

Multi-line derivations align on their relation symbols, and matrices are set by TEX:

( 𝑓 ∘ 𝑔 ) ′ ( 𝑥 ) = 𝑓 ′

(

𝑔 ( 𝑥 )

)

𝑔 ′ ( 𝑥 ) , 𝑑 𝑑 𝑥 R 𝑎 𝑥 𝑓 ( 𝑡 ) 𝑑 𝑡 = 𝑓 ( 𝑥 ) , ( 𝑎 𝑏 𝑐 𝑑 ) − 1 = 1 𝑎 𝑑 − 𝑏 𝑐 ( 𝑑 − 𝑏 − 𝑐 𝑎 ) .

A numbered alignment with several aligned columns, rows of unequal width, and equation numbers:

(1) 𝑎 = 𝑏 𝑐 𝑐 𝑐 𝑐 𝑐 𝑐 𝑐 7 = 𝑑 𝑒 = 𝑓 (2) 𝑔 = ℎ 𝑖 = 𝑗 𝑘 = long entry

A piecewise definition in a cases environment, with some colour that changes with the theme:

sgn ( 𝑥 ) = { + 1 if 𝑥 > 0 , + 0 if 𝑥 = 0 , − 1 if 𝑥 < 0 .

\section*{Aligned systems and matrices}
Multi-line derivations align on their relation symbols, and matrices are set
by \TeX:
\begin{align*}
  (f \circ g)'(x) &= f'\bigl(g(x)\bigr)\,g'(x), \\
  \frac{d}{dx} \int_{a}^{x} f(t)\,dt &= f(x), \\
  \begin{pmatrix} a & b \\ c & d \end{pmatrix}^{-1}
    &= \textcolor{blue}{\frac{1}{ad - bc}}\begin{pmatrix} d & -b \\ -c & a \end{pmatrix}.
\end{align*}
A numbered alignment with several aligned columns, rows of unequal width,
and equation numbers:
\begin{align}
  a&=b & ccccccc^7&=d & e&=f \\
  g&=h & i&=j & k&=\text{long entry}
\end{align}
A piecewise definition in a \texttt{cases} environment, with some colour that
changes with the theme:
\[
  \operatorname{sgn}(x) =
  \begin{cases}
    \textcolor{blue}{+1} & \text{if } x > 0, \\
    \phantom{+}0 & \text{if } x = 0, \\
    \textcolor{red}{-1} & \text{if } x < 0.
  \end{cases}
\]