% 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