# Latex and gitbook ## Quantum computing ### Brackets ``` \left\langle \frac{1}{2} \middle| 1 \right\rangle ``` $$\left\langle \frac{1}{2} \middle| 1 \right\rangle$$ ### Diagrams ``` \begin{matrix} && \Bbb Q(\sqrt{2},i) & \\ &\huge\diagup & \huge| & \huge\diagdown \\ \Bbb Q(\sqrt{2}) & & \Bbb Q(i\sqrt{2})& & \Bbb Q(i)\\ &\huge\diagdown & \huge| & \huge\diagup \\ &&\Bbb Q \end{matrix} ``` $$\begin{matrix} && \Bbb Q(\sqrt{2},i) & \ &\huge\diagup & \huge| & \huge\diagdown \ \Bbb Q(\sqrt{2}) & & \Bbb Q(i\sqrt{2})& & \Bbb Q(i)\ &\huge\diagdown & \huge| & \huge\diagup \ &&\Bbb Q \end{matrix}$$ ## Mathematics ### Fractions and brackets ``` \left( \begin{array}{cc} 2\tau & 7\phi-frac5{12} \\ 3\psi & \frac{\pi}8 \end{array} \right) \left( \begin{array}{c} x \\ y \end{array} \right) \mbox{~and~} \left[ \begin{array}{cc|r} 3 & 4 & 5 \\ 1 & 3 & 729 \end{array} \right] ``` $$\left( \begin{array}{cc} 2\tau & 7\phi-frac5{12} \ 3\psi & \frac{\pi}8 \end{array} \right) \left( \begin{array}{c} x \ y \end{array} \right) \mbox{~~and~~} \left\[ \begin{array}{cc|r} 3 & 4 & 5 \ 1 & 3 & 729 \end{array} \right]$$ ### Function definition ``` f(z) = \left\{ \begin{array}{rcl} \overline{\overline{z^2}+\cos z} & \mbox{for} & |z|<3 \\ 0 & \mbox{for} & 3\leq|z|\leq5 \\ \sin\overline{z} & \mbox{for} & |z|>5 \end{array}\right. ``` $$f(z) = \left{ \begin{array}{rcl} \overline{\overline{z^2}+\cos z} & \mbox{for} & |z|<3 \ 0 & \mbox{for} & 3\leq|z|\leq5 \ \sin\overline{z} & \mbox{for} & |z|>5 \end{array}\right.$$ ### Equations align ``` \eqalign{ (a+b)^2 &= (a+b)(a+b) \\ &= a^2 + ab + ba + b^2 \\ &= a^2 + 2ab + b^2 } ``` $$\eqalign{ (a+b)^2 &= (a+b)(a+b) \ &= a^2 + ab + ba + b^2 \ &= a^2 + 2ab + b^2 }$$ ### Hat ``` \hat\imath \hat\jmath \hat ab \hat{ab} ``` $$\hat\imath \ \hat\jmath \ \hat ab \ \hat{ab}$$ ### Matrices #### Type 1 ``` \begin{matrix} \hline x_{11} & x_{12} \\ x_{21} & x_{22} \strut \\ \hdashline x_{31} & x_{32} \strut \end{matrix} ``` $$\begin{matrix} \hline x\_{11} & x\_{12} \ x\_{21} & x\_{22} \strut \ \hdashline x\_{31} & x\_{32} \strut \end{matrix}$$ #### Type 2 ``` A = \pmatrix{ a_{11} & a_{12} & \ldots & a_{1n} \cr a_{21} & a_{22} & \ldots & a_{2n} \cr \vdots & \vdots & \ddots & \vdots \cr a_{m1} & a_{m2} & \ldots & a_{mn} \cr } ``` $$A = \pmatrix{ a\_{11} & a\_{12} & \ldots & a\_{1n} \cr a\_{21} & a\_{22} & \ldots & a\_{2n} \cr \vdots & \vdots & \ddots & \vdots \cr a\_{m1} & a\_{m2} & \ldots & a\_{mn} \cr }$$ ### Limits ``` \sum_{k=1}^n a_k ``` $$\sum\_{k=1}^n a\_k$$ ### References A complete list is available at