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+% Sample file: multline.tpl
+% multiline math formula template file
+
+
+% Section 5.2 Gathering formulas
+
+\begin{gather}
+ x_{1} x_{2} + x_{1}^{2} x_{2}^{2} + x_{3}, \label{E:mm1.1}\\
+ x_{1} x_{3} + x_{1}^{2} x_{3}^{2} + x_{2}, \label{E:mm1.2}\\
+ x_{1} x_{2} x_{3}. \label{E:mm1.3}
+\end{gather}
+
+% 5.3 Splitting a long formula
+
+\begin{multline}\label{E:mm2}
+ (x_{1} x_{2} x_{3} x_{4} x_{5} x_{6})^{2}\\
+ + (y_{1} y_{2} y_{3} y_{4} y_{5} +y_{1} y_{3} y_{4} y_{5} y_{6}
+ + y_{1} y_{2} y_{4} y_{5} y_{6}
+ + y_{1} y_{2} y_{3} y_{5} y_{6})^{2}\\
+ + (z_{1} z_{2} z_{3} z_{4} z_{5} +z_{1} z_{3} z_{4} z_{5} z_{6}
+ + z_{1} z_{2} z_{4} z_{5} z_{6}
+ + z_{1} z_{2} z_{3} z_{5} z_{6})^{2}\\
+ + (u_{1} u_{2} u_{3} u_{4} + u_{1} u_{2} u_{3} u_{5} +
+ u_{1} u_{2} u_{4} u_{5} + u_{1} u_{3} u_{4} u_{5})^{2}
+\end{multline}
+
+\begin{multline*}
+ (x_{1} x_{2} x_{3} x_{4} x_{5} x_{6})^{2}\\
+ + (x_{1} x_{2} x_{3} x_{4} x_{5}
+ + x_{1} x_{3} x_{4} x_{5} x_{6}
+ + x_{1} x_{2} x_{4} x_{5} x_{6}
+ + x_{1} x_{2} x_{3} x_{5} x_{6})^{2}\\
+ + (x_{1} x_{2} x_{3} x_{4} + x_{1} x_{2} x_{3} x_{5}
+ + x_{1} x_{2} x_{4} x_{5} + x_{1} x_{3} x_{4} x_{5})^{2}
+\end{multline*}
+\begin{setlength}{\multlinegap}{0pt}
+ \begin{multline*}
+ (x_{1} x_{2} x_{3} x_{4} x_{5} x_{6})^{2}\\
+ + (x_{1} x_{2} x_{3} x_{4} x_{5}
+ + x_{1} x_{3} x_{4} x_{5} x_{6}
+ + x_{1} x_{2} x_{4} x_{5} x_{6}
+ + x_{1} x_{2} x_{3} x_{5} x_{6})^{2}\\
+ + (x_{1} x_{2} x_{3} x_{4} + x_{1} x_{2} x_{3} x_{5}
+ + x_{1} x_{2} x_{4} x_{5} + x_{1} x_{3} x_{4} x_{5})^{2}
+ \end{multline*}
+\end{setlength}
+
+\begin{multline*}
+ (x_{1} x_{2} x_{3} x_{4} x_{5} x_{6})^{2}\\
+ \shoveleft{+ (x_{1} x_{2} x_{3} x_{4} x_{5}
+ + x_{1} x_{3} x_{4} x_{5} x_{6}
+ + x_{1} x_{2} x_{4} x_{5} x_{6}
+ + x_{1} x_{2} x_{3} x_{5} x_{6})^{2}}\\
+ + (x_{1} x_{2} x_{3} x_{4} + x_{1} x_{2} x_{3} x_{5}
+ + x_{1} x_{2} x_{4} x_{5} + x_{1} x_{3} x_{4} x_{5})^{2}
+\end{multline*}
+
+% 5.4.3 Group numbering
+
+\begin{gather}
+ x_{1} x_{2} + x_{1}^{2} x_{2}^{2} + x_{3},\label{E:mm1} \\
+ x_{1} x_{3} + x_{1}^{2} x_{3}^{2} + x_{2},\tag{\ref{E:mm1}a}\\
+ x_{1} x_{2} x_{3};\tag{\ref{E:mm1}b}
+\end{gather}
+
+\begin{subequations}\label{E:gp}
+ \begin{gather}
+ x_{1} x_{2} + x_{1}^{2} x_{2}^{2} + x_{3},\label{E:gp1}\\
+ x_{1} x_{3} + x_{1}^{2} x_{3}^{2} + x_{2},\label{E:gp2}\\
+ x_{1} x_{2} x_{3},\label{E:gp3}
+ \end{gather}
+\end{subequations}
+
+ % 5.5 Aligned columns
+
+\begin{align}\label{E:mm3}
+ f(x) &= x + yz & g(x) &= x + y + z\\
+ h(x) &= xy + xz + yz & k(x) &= (x + y)(x + z)(y + z)
+ \notag
+\end{align}
+
+% 5.5.1 An align variant
+
+\begin{flalign}\label{E:mm3fl}
+ f(x) &= x + yz & g(x) &= x + y + z\\
+ h(x) &= xy + xz + yz & k(x) &= (x + y)(x + z)(y + z)
+ \notag
+\end{flalign}
+
+% 5.5.2 eqnarray, the ancestor of align
+
+\begin{eqnarray}
+ x & = & 17y \\
+ y & > & a + b + c
+\end{eqnarray}
+
+\begin{align}
+ x & = 17y \\
+ y & > a + b + c
+\end{align}
+
+% 5.5.3 The subformula rule revisited
+
+\begin{align}
+ x_{1} + y_{1} + \left( \sum_{i < 5} \binom{5}{i}
+ &+ a^{2} \right)^{2}\\
+ \left( \sum_{i < 5} \binom{5}{i} + \alpha^{2} \right)^{2}
+\end{align}
+
+\begin{align*}
+ &x_{1} + y_{1} + \left( \sum_{i < 5} \binom{5}{i}
+ + a^{2} \right)^{2}\\
+ &\phantom{x_{1} + y_{1} + {}}
+ \left( \sum_{i < 5} \binom{5}{i} + \alpha^{2} \right)^{2}
+\end{align*}
+
+% 5.5.4 The alignat environment
+
+\begin{alignat}{2}\label{E:mm3A}
+ f(x) &= x + yz & g(x) &= x + y + z\\
+ h(x) &= xy + xz + yz & k(x) &= (x + y)(x + z)(y + z)
+ \notag
+\end{alignat}
+
+\begin{alignat}{2}\label{E:mm3B}
+ f(x) &= x + yz & g(x) &= x + y + z\\
+ h(x) &= xy + xz + yz \qquad & k(x) &= (x + y)(x + z)(y + z)
+ \notag
+
+\begin{alignat}{2}\label{E:mm4}
+ x &= x \wedge (y \vee z) & &\quad\text{(by distributivity)}\\
+ &= (x \wedge y) \vee (x \wedge z) & &
+ \quad\text{(by condition (M))}\notag\\
+ &= y \vee z \notag
+\end{alignat}
+
+\begin{alignat}{2}
+ (A + B C)x &+{} &C &y = 0,\\
+ Ex &+{} &(F + G)&y = 23.
+\end{alignat}
+
+\begin{alignat}{4}
+ a_{11}x_1 &+ a_{12}x_2 &&+ a_{13}x_3 && &&= y_1,\\
+ a_{21}x_1 &+ a_{22}x_2 && &&+ a_{24}x_4 &&= y_2,\\
+ a_{31}x_1 & &&+ a_{33}x_3 &&+ a_{34}x_4 &&= y_3.
+\end{alignat}
+
+% 5.5.5 Intertext
+
+\begin{align}\label{E:mm5}
+ h(x) &= \int \left(
+ \frac{ f(x) + g(x) }
+ {1 + f^{2}(x)} +
+ \frac{1 + f(x)g(x)}
+ { \sqrt{1 - \sin x} }
+ \right) \, dx\\
+ \intertext{The reader may find the following form easier to
+ read:}
+ &= \int \frac{1 + f(x)}
+ {1 + g(x)}
+ \, dx - 2 \arctan(x - 2) \notag
+\end{align}
+
+\begin{align*}
+ f(x) &= x + yz & \qquad g(x) &= x + y + z \\
+ \intertext{The reader also may find the following
+ polynomials useful:}
+ h(x) &= xy + xz + yz
+ & \qquad k(x) &= (x + y)(x + z)(y + z)
+\end{align*}
+
+% 5.6 Aligned subsidiary math environments
+
+% 5.6.1 Subsidiary variants of aligned math environments
+
+\[
+ \begin{aligned}
+ x &= 3 + \mathbf{p} + \alpha \\
+ y &= 4 + \mathbf{q}\\
+ z &= 5 + \mathbf{r} \\
+ u &=6 + \mathbf{s}
+ \end{aligned}
+ \text{\qquad using\qquad}
+ \begin{gathered}
+ \mathbf{p} = 5 + a + \alpha \\
+ \mathbf{q} = 12 \\
+ \mathbf{r} = 13 \\
+ \mathbf{s} = 11 + d
+ \end{gathered}
+\]
+
+\begin{align}\label{E:mm5}
+ h(x) &= \int \left(
+ \frac{ f(x) + g(x) }
+ {1 + f^{2}(x)} +
+ \frac{1 + f(x)g(x)}
+ { \sqrt{1 - \sin x} }
+ \right) \, dx\\
+ \intertext{The reader may find the following form easier to
+ read:}
+ &= \int \frac{1 + f(x)}
+ {1 + g(x)}
+ \, dx - 2 \arctan(x - 2) \notag
+\end{align}
+
+\begin{equation}\label{E:mm6}
+ \begin{aligned}
+ h(x) &= \int \left(
+ \frac{ f(x) + g(x) }
+ { 1 + f^{2}(x) } +
+ \frac{ 1 + f(x)g(x) }
+ { \sqrt{1 - \sin x} }
+ \right) \, dx\\
+ &= \int \frac{ 1 + f(x) }
+ { 1 + g(x) } \, dx - 2 \arctan (x - 2)
+ \end{aligned}
+\end{equation}
+
+\[
+ \begin{aligned}[b]
+ x &= 3 + \mathbf{p} + \alpha \\
+ y &= 4 + \mathbf{q}\\
+ z &= 5 + \mathbf{r} \\
+ u &=6 + \mathbf{s}
+ \end{aligned}
+ \text{\qquad using\qquad}
+ \begin{gathered}[b]
+ \mathbf{p} = 5 + a + \alpha \\
+ \mathbf{q} = 12 \\
+ \mathbf{r} = 13 \\
+ \mathbf{s} = 11 + d
+ \end{gathered}
+\]
+
+% 5.6.2 Split
+
+\begin{equation}\label{E:mm7}
+ \begin{split}
+ (x_{1}x_{2}&x_{3}x_{4}x_{5}x_{6})^{2}\\
+ &+ (x_{1}x_{2}x_{3}x_{4}x_{5}
+ + x_{1}x_{3}x_{4}x_{5}x_{6}
+ + x_{1}x_{2}x_{4}x_{5}x_{6}
+ + x_{1}x_{2}x_{3}x_{5}x_{6})^{2}
+ \end{split}
+\end{equation}
+
+\begin{align}\label{E:mm8}
+ \begin{split}
+ f &= (x_{1} x_{2} x_{3} x_{4} x_{5} x_{6})^{2}\\
+ &= (x_{1} x_{2} x_{3} x_{4} x_{5}
+ + x_{1} x_{3} x_{4} x_{5} x_{6}
+ + x_{1} x_{2} x_{4} x_{5} x_{6}
+ + x_{1} x_{2} x_{3} x_{5} x_{6})^{2},
+ \end{split}\\
+ g &= y_{1} y_{2} y_{3}.\label{E:mm9}
+\end{align}
+
+\begin{gather}\label{E:mm10}
+ \begin{split}
+ f &= (x_{1} x_{2} x_{3} x_{4} x_{5} x_{6})^{2}\\
+ &= (x_{1} x_{2} x_{3} x_{4} x_{5}
+ + x_{1} x_{3} x_{4} x_{5} x_{6}
+ + x_{1} x_{2} x_{4} x_{5} x_{6}
+ + x_{1} x_{2} x_{3} x_{5} x_{6})^{2}\\
+ &= (x_{1} x_{2} x_{3} x_{4}
+ + x_{1} x_{2} x_{3} x_{5}
+ + x_{1} x_{2} x_{4} x_{5}
+ + x_{1} x_{3} x_{4} x_{5})^{2}
+ \end{split}\\
+ \begin{align*}
+ g &= y_{1} y_{2} y_{3}\\
+ h &= z_{1}^{2} z_{2}^{2} z_{3}^{2} z_{4}^{2}
+ \end{align*}
+\end{gather}
+
+% 5.7 Adjusted columns
+
+\begin{equation*}
+ \left(
+ \begin{matrix}
+ a + b + c & uv & x - y & 27\\
+ a + b & u + v & z & 1340
+ \end{matrix}
+ \right) =
+ \left(
+ \begin{matrix}
+ 1 & 100 & 115 & 27\\
+ 201 & 0 & 1 & 1340
+ \end{matrix}
+ \right)
+\end{equation*}
+
+\begin{equation*}
+ \left(
+ \begin{array}{cccr}
+ a + b + c & uv & x - y & 27\\
+ a + b & u + v & z & 1340
+ \end{array}
+ \right) =
+ \left(
+ \begin{array}{rrrr}
+ 1 & 100 & 115 & 27\\
+ 201 & 0 & 1 & 1340
+ \end{array}
+ \right)
+\end{equation*}
+
+\begin{equation}\label{E:mm11}
+ f(x) =
+ \begin{cases}
+ -x^{2}, &\text{\CMR if $x < 0$;} \\
+ \alpha + x, &\text{\CMR if $ 0 \leq x \leq 1$;}\\
+ x^{2}, &\text{\CMR otherwise.}
+ \end{cases}
+\end{equation}
+
+% 5.7.1 Matrices
+
+\begin{equation*}
+ \left(
+ \begin{matrix}
+ a + b + c & uv & x - y & 27 \\
+ a + b & u + v & z & 1340
+ \end{matrix}
+ \right) =
+ \left(
+ \begin{matrix}
+ 1 & 100 & 115 & 27 \\
+ 201 & 0 & 1 & 1340
+ \end{matrix}
+ \right)
+\end{equation*}
+
+\begin{matrix}
+ a + b + c & uv & x - y & 27 \\
+ a + b & u + v & z & 134
+\end{matrix}
+
+\begin{equation}\label{E:mm12}
+ \setcounter{MaxMatrixCols}{12}
+ \begin{matrix}
+ 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12\\
+ 1 & 2 & 3 & \hdotsfor{7} & 11 & 12
+ \end{matrix}
+\end{equation}
+
+\begin{equation}\label{E:mm12dupl}
+ \setcounter{MaxMatrixCols}{12}
+ \begin{matrix}
+ 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12\\
+ 1 & 2 & 3 & \hdotsfor[3]{7} & 11 & 12
+ \end{matrix}
+\end{equation}
+
+% Matrix variants
+
+\begin{alignat*}{3}
+ &\
+ \begin{matrix}
+ a + b + c & uv\\
+ a + b & c + d
+ \end{matrix}
+ \qquad
+ & &
+ \begin{pmatrix}
+ a + b + c & uv\\
+ a + b & c + d
+ \end{pmatrix}
+ \qquad
+ & &
+ \begin{bmatrix}
+ a + b + c & uv\\
+ a + b & c + d
+ \end{bmatrix}
+ \\
+ &
+ \begin{vmatrix}
+ a + b + c & uv\\
+ a + b & c + d
+ \end{vmatrix}
+ \qquad
+ & &
+ \begin{Vmatrix}
+ a + b + c & uv\\
+ a + b & c + d
+ \end{Vmatrix}
+ \qquad
+ & &
+ \begin{Bmatrix}
+ a + b + c & uv\\
+ a + b & c + d
+ \end{Bmatrix}
+\end{alignat*}
+
+\begin{equation*}
+ \left(
+ \begin{matrix}
+ 1 & 0 & \dots & 0 \\
+ 0 & 1 & \dots & 0 \\
+ \vdots & \vdots & \ddots & \vdots\\
+ 0 & 0 & \dots & 1
+ \end{matrix}
+ \right]
+\end{equation*}
+\end{verbatim}
+which produces
+\begin{equation*}
+ \left(
+ \begin{matrix}
+ 1 & 0 & \dots & 0 \\
+ 0 & 1 & \dots & 0 \\
+ \vdots & \vdots & \ddots & \vdots\\
+ 0 & 0 & \dots & 1
+ \end{matrix}
+ \right]
+\end{equation*}
+
+% Small matrix
+
+$\begin{pmatrix}
+ a + b + c & uv\\
+ a + b & c + d
+\end{pmatrix}$
+
+$\left(
+\begin{smallmatrix}
+ a + b + c & uv \\
+ a + b & c + d
+\end{smallmatrix}
+\right)$
+
+% 5.7.2 Arrays
+
+\begin{equation*}
+ \left(
+ \begin{array}{cccc}
+ a + b + c & uv & x - y & 27 \\
+ a + b & u + v & z & 134
+ \end{array}
+ \right)
+\end{equation*}
+
+% 5.7.3 Cases
+
+\begin{equation}
+ f(x)=
+ \begin{cases}
+ -x^{2}, &\text{if $x < 0$;}\\
+ \alpha + x, &\text{if $0 \leq x \leq 1$;}\\
+ x^{2}, &\text{otherwise.}
+ \end{cases}
+\end{equation}
+
+% 5.8 Commutative diagrams
+
+\[
+ \begin{CD}
+ A @>>> B \\
+ @VVV @VVV\\
+ C @= D
+ \end{CD}
+\]
+
+\[
+ \begin{CD}
+ \mathbb{C} @>H_{1}>> \mathbb{C} @>H_{2}>> \mathbb{C} \\
+ @VP_{c,3}VV @VP_{\bar{c},3}VV @VVP_{-c,3}V \\
+ \mathbb{C} @>H_{1}>> \mathbb{C} @>H_{2}>> \mathbb{C}
+ \end{CD}
+\]
+
+\[
+ \begin{CD}
+ A @>\log>> B @>>\text{bottom}> C
+ @= D @<<< E
+ @<<< F\\
+ @V\text{one-one}VV @. @AA\text{onto}A @|\\
+ X @= Y @>>> Z
+ @>>> U\\
+ @A\beta AA @AA\gamma A @VVV @VVV\\
+ D @>\alpha>> E @>>> H
+ @. I\\
+ \end{CD}
+\]
+
+% 5.9 Pagebreak
+
+{\allowdisplaybreaks
+\begin{align}\label{E:mm13}
+ a &= b + c,\\
+ d &= e + f,\\
+ x &= y + z,\\
+ u &= v + w.
+\end{align}
+}% end of \allowdisplaybreaks