ltex - xbook.in

ltex

\begin{center} \textbf{{\large Powerful Mathematics Editor}} {\footnotesize \underline{for inputing and sharing your formulas with people! }} Input your mathematics formula inline: $\vec{F} \ =\ m\vec{a}$ or new line \end{center} \begin{gather*} \frac{a}{b} +\sqrt[3]{a+b} +\int _{b}^{a} dx+\overbrace{a-b}^{n+1} +\wideparen{ABC} +\widehat{ABC} +\Uparrow H_{2} 0\Uparrow \\ \end{gather*} \begin{center} Matrices, cases, layouts \end{center} \begin{equation*} \begin{pmatrix} a_{1} & b_{1}\\ c_{1} & d_{1} \end{pmatrix} \ \ \ \begin{bmatrix} 1 & \cdots & 1\\ \vdots & \iddots & \vdots \\ 1 & \cdots & 1 \end{bmatrix} \ \ \ \ \begin{array}{ c|c|c|c } fx & a_{1} & \nearrow & a_{2}\\ \hline & b_{1} & \swarrow & b_{2} \end{array} \ \ \ fx=\begin{cases} \alpha & \mathrm{if,} \ a=b\\ \beta & \mathrm{if,} \ a\neq b \end{cases} \end{equation*} \begin{center} Fonts \end{center} \begin{equation*} \mathcal{L} ,\boldsymbol{a} ,n\subset (\mathbb{R\cap N}) \ < \mathrm{gen,diff,min}> \end{equation*} \begin{center} Diagram \end{center} \tikzset{every picture/.style={line width=0.75pt}} %set default line width to 0.75pt \begin{tikzpicture}[x=0.75pt,y=0.75pt,yscale=-1,xscale=1] %uncomment if require: \path (0,235); %set diagram left start at 0, and has height of 235 %Straight Lines [id:da9313950171592851] \draw [color={rgb, 255:red, 74; green, 144; blue, 226 } ,draw opacity=1 ] (274,30) -- (274,103.29) ; \draw [shift={(274,103.29)}, rotate = 90] [color={rgb, 255:red, 74; green, 144; blue, 226 } ,draw opacity=1 ][fill={rgb, 255:red, 74; green, 144; blue, 226 } ,fill opacity=1 ][line width=0.75] (0, 0) circle [x radius= 3.35, y radius= 3.35] ; \draw [shift={(274,30)}, rotate = 90] [color={rgb, 255:red, 74; green, 144; blue, 226 } ,draw opacity=1 ][fill={rgb, 255:red, 74; green, 144; blue, 226 } ,fill opacity=1 ][line width=0.75] (0, 0) circle [x radius= 3.35, y radius= 3.35] ; %Straight Lines [id:da0072983473385641595] \draw [color={rgb, 255:red, 74; green, 144; blue, 226 } ,draw opacity=1 ] (427.58,100) -- (269.5,100) ; \draw [shift={(269.5,100)}, rotate = 180] [color={rgb, 255:red, 74; green, 144; blue, 226 } ,draw opacity=1 ][fill={rgb, 255:red, 74; green, 144; blue, 226 } ,fill opacity=1 ][line width=0.75] (0, 0) circle [x radius= 3.35, y radius= 3.35] ; \draw [shift={(427.58,100)}, rotate = 180] [color={rgb, 255:red, 74; green, 144; blue, 226 } ,draw opacity=1 ][fill={rgb, 255:red, 74; green, 144; blue, 226 } ,fill opacity=1 ][line width=0.75] (0, 0) circle [x radius= 3.35, y radius= 3.35] ; %Straight Lines [id:da0611422079179329] \draw [color={rgb, 255:red, 74; green, 144; blue, 226 } ,draw opacity=1 ] (270.5,32) -- (427.5,100) ; \draw [shift={(427.5,100)}, rotate = 23.42] [color={rgb, 255:red, 74; green, 144; blue, 226 } ,draw opacity=1 ][fill={rgb, 255:red, 74; green, 144; blue, 226 } ,fill opacity=1 ][line width=0.75] (0, 0) circle [x radius= 3.35, y radius= 3.35] ; \draw [shift={(270.5,32)}, rotate = 23.42] [color={rgb, 255:red, 74; green, 144; blue, 226 } ,draw opacity=1 ][fill={rgb, 255:red, 74; green, 144; blue, 226 } ,fill opacity=1 ][line width=0.75] (0, 0) circle [x radius= 3.35, y radius= 3.35] ; %Straight Lines [id:da6902289836929021] \draw [color={rgb, 255:red, 74; green, 144; blue, 226 } ,draw opacity=1 ] (271.5,31) -- (321.5,103) ; \draw [shift={(321.5,103)}, rotate = 55.22] [color={rgb, 255:red, 74; green, 144; blue, 226 } ,draw opacity=1 ][fill={rgb, 255:red, 74; green, 144; blue, 226 } ,fill opacity=1 ][line width=0.75] (0, 0) circle [x radius= 3.35, y radius= 3.35] ; \draw [shift={(271.5,31)}, rotate = 55.22] [color={rgb, 255:red, 74; green, 144; blue, 226 } ,draw opacity=1 ][fill={rgb, 255:red, 74; green, 144; blue, 226 } ,fill opacity=1 ][line width=0.75] (0, 0) circle [x radius= 3.35, y radius= 3.35] ; %Shape: Arc [id:dp012460516914444497] \draw [draw opacity=0][fill={rgb, 255:red, 74; green, 144; blue, 226 } ,fill opacity=0.22 ] (311.81,87.37) .. controls (313.42,87.12) and (315.12,86.99) .. (316.87,87) .. controls (327.75,87.07) and (336.54,92.5) .. (336.5,99.12) .. controls (336.5,99.34) and (336.49,99.56) .. (336.47,99.78) -- (316.8,99) -- cycle ; \draw [color={rgb, 255:red, 74; green, 144; blue, 226 } ,draw opacity=1 ] (311.81,87.37) .. controls (313.42,87.12) and (315.12,86.99) .. (316.87,87) .. controls (327.75,87.07) and (336.54,92.5) .. (336.5,99.12) .. controls (336.5,99.34) and (336.49,99.56) .. (336.47,99.78) ; %Straight Lines [id:da012774030553635018] \draw [color={rgb, 255:red, 74; green, 144; blue, 226 } ,draw opacity=1 ] (274,90) -- (287.04,90) -- (287.04,100.78) ; %Shape: Axis 2D [id:dp048941842347560494] \draw [color={rgb, 255:red, 73; green, 135; blue, 206 } ,draw opacity=1 ][line width=1.5] (41,177) -- (280,177)(61,16) -- (61,199) (273,172) -- (280,177) -- (273,182) (56,23) -- (61,16) -- (66,23) (92,172) -- (92,182)(123,172) -- (123,182)(154,172) -- (154,182)(185,172) -- (185,182)(216,172) -- (216,182)(247,172) -- (247,182)(56,146) -- (66,146)(56,115) -- (66,115)(56,84) -- (66,84)(56,53) -- (66,53) ; \draw ; %Shape: Polynomial [id:dp29246577559714826] \draw [color={rgb, 255:red, 70; green, 155; blue, 36 } ,draw opacity=1 ][line width=1.5] (42,193) .. controls (93.67,-47) and (145.33,333) .. (197,93) ; %Shape: Parabola [id:dp636758281566334] \draw [color={rgb, 255:red, 209; green, 53; blue, 53 } ,draw opacity=1 ][line width=1.5] (123,35) .. controls (164.67,221.67) and (206.33,221.67) .. (248,35) ; %Straight Lines [id:da5751643928734858] \draw [color={rgb, 255:red, 141; green, 34; blue, 137 } ,draw opacity=1 ][line width=1.5] (16,34) -- (300,196) ; %Shape: Brace [id:dp8862990797251067] \draw [dash pattern={on 0.84pt off 2.51pt}] (190,125) .. controls (192.21,120.89) and (191.25,117.73) .. (187.14,115.52) -- (181.62,112.56) .. controls (175.75,109.41) and (173.91,105.77) .. (176.12,101.66) .. controls (173.91,105.77) and (169.87,106.25) .. (164,103.1)(166.64,104.52) -- (158.48,100.14) .. controls (154.37,97.93) and (151.21,98.89) .. (149,103) ; % Text Node \draw (339,84) node [font=\footnotesize,color={rgb, 255:red, 74; green, 144; blue, 226 } ,opacity=1 ,rotate=-333.43] {$\alpha $}; % Text Node \draw (264,19) node [font=\footnotesize,color={rgb, 255:red, 74; green, 144; blue, 226 } ,opacity=1 ] {$C$}; % Text Node \draw (273,114) node [font=\footnotesize,color={rgb, 255:red, 74; green, 144; blue, 226 } ,opacity=1 ] {$D$}; % Text Node \draw (320,114) node [font=\footnotesize,color={rgb, 255:red, 74; green, 144; blue, 226 } ,opacity=1 ] {$A$}; % Text Node \draw (429,112) node [font=\footnotesize,color={rgb, 255:red, 74; green, 144; blue, 226 } ,opacity=1 ] {$B$}; % Text Node \draw (451,71) node {$A_{1}$}; % Text Node \draw (501,21) node {$A_{2}$}; % Text Node \draw (451,171) node {$A'_{1}$}; % Text Node \draw (581,21) node {$B_{2}$}; % Text Node \draw (661,21) node {$C_{2}$}; % Text Node \draw (541,71) node {$B_{1}$}; % Text Node \draw (621,71) node {$C_{1}$}; % Text Node \draw (501,111) node {$A'_{2}$}; % Text Node \draw (581,111) node {$B'_{2}$}; % Text Node \draw (661,111) node {$C'_{2}$}; % Text Node \draw (541,171) node {$B'_{1}$}; % Text Node \draw (621,171) node {$C'_{1}$}; % Text Node \draw (721,21) node {$0$}; % Text Node \draw (701,71) node {$0$}; % Text Node \draw (81,53) node [color={rgb, 255:red, 146; green, 29; blue, 130 } ,opacity=1 ,rotate=-30.96] {$A_{1}$}; % Text Node \draw (264,155) node [color={rgb, 255:red, 145; green, 25; blue, 123 } ,opacity=1 ,rotate=-30.96] {$A_{2}$}; % Text Node \draw (29,197) node [color={rgb, 255:red, 36; green, 114; blue, 18 } ,opacity=1 ,rotate=-14.47] {$y=x^{3}$}; % Text Node \draw (160,46) node [color={rgb, 255:red, 179; green, 35; blue, 24 } ,opacity=1 ,rotate=-344.74] {$y=x^{2}$}; % Text Node \draw (181,92) node [font=\footnotesize,rotate=-22.93] {$d$}; % Connection \draw (515,21) -- (566,21) ; \draw [shift={(568,21)}, rotate = 180] [color={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.75] (10.93,-3.29) .. controls (6.95,-1.4) and (3.31,-0.3) .. (0,0) .. controls (3.31,0.3) and (6.95,1.4) .. (10.93,3.29) ; % Connection \draw (594,21) -- (645.5,21) ; \draw [shift={(647.5,21)}, rotate = 180] [color={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.75] (10.93,-3.29) .. controls (6.95,-1.4) and (3.31,-0.3) .. (0,0) .. controls (3.31,0.3) and (6.95,1.4) .. (10.93,3.29) ; % Connection \draw (464,58) -- (486.59,35.41) ; \draw [shift={(488,34)}, rotate = 495] [color={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.75] (10.93,-3.29) .. controls (6.95,-1.4) and (3.31,-0.3) .. (0,0) .. controls (3.31,0.3) and (6.95,1.4) .. (10.93,3.29) ; % Connection \draw (465,71) -- (526,71) ; \draw [shift={(528,71)}, rotate = 180] [color={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.75] (10.93,-3.29) .. controls (6.95,-1.4) and (3.31,-0.3) .. (0,0) .. controls (3.31,0.3) and (6.95,1.4) .. (10.93,3.29) ; % Connection \draw (554,71) -- (605.5,71) ; \draw [shift={(607.5,71)}, rotate = 180] [color={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.75] (10.93,-3.29) .. controls (6.95,-1.4) and (3.31,-0.3) .. (0,0) .. controls (3.31,0.3) and (6.95,1.4) .. (10.93,3.29) ; % Connection \draw (551.4,58) -- (569.35,35.56) ; \draw [shift={(570.6,34)}, rotate = 488.66] [color={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.75] (10.93,-3.29) .. controls (6.95,-1.4) and (3.31,-0.3) .. (0,0) .. controls (3.31,0.3) and (6.95,1.4) .. (10.93,3.29) ; % Connection \draw (631.4,58) -- (649.35,35.56) ; \draw [shift={(650.6,34)}, rotate = 488.66] [color={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.75] (10.93,-3.29) .. controls (6.95,-1.4) and (3.31,-0.3) .. (0,0) .. controls (3.31,0.3) and (6.95,1.4) .. (10.93,3.29) ; % Connection \draw (451,84) -- (451,156) ; \draw [shift={(451,158)}, rotate = 270] [color={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.75] (10.93,-3.29) .. controls (6.95,-1.4) and (3.31,-0.3) .. (0,0) .. controls (3.31,0.3) and (6.95,1.4) .. (10.93,3.29) ; % Connection \draw (465,171) -- (526,171) ; \draw [shift={(528,171)}, rotate = 180] [color={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.75] (10.93,-3.29) .. controls (6.95,-1.4) and (3.31,-0.3) .. (0,0) .. controls (3.31,0.3) and (6.95,1.4) .. (10.93,3.29) ; % Connection \draw (554,171) -- (605.5,171) ; \draw [shift={(607.5,171)}, rotate = 180] [color={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.75] (10.93,-3.29) .. controls (6.95,-1.4) and (3.31,-0.3) .. (0,0) .. controls (3.31,0.3) and (6.95,1.4) .. (10.93,3.29) ; % Connection \draw (629.67,158) -- (651.22,125.66) ; \draw [shift={(652.33,124)}, rotate = 483.69] [color={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.75] (10.93,-3.29) .. controls (6.95,-1.4) and (3.31,-0.3) .. (0,0) .. controls (3.31,0.3) and (6.95,1.4) .. (10.93,3.29) ; % Connection \draw (549.67,158) -- (571.22,125.66) ; \draw [shift={(572.33,124)}, rotate = 483.69] [color={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.75] (10.93,-3.29) .. controls (6.95,-1.4) and (3.31,-0.3) .. (0,0) .. controls (3.31,0.3) and (6.95,1.4) .. (10.93,3.29) ; % Connection \draw (461.83,158) -- (488.89,125.54) ; \draw [shift={(490.17,124)}, rotate = 489.81] [color={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.75] (10.93,-3.29) .. controls (6.95,-1.4) and (3.31,-0.3) .. (0,0) .. controls (3.31,0.3) and (6.95,1.4) .. (10.93,3.29) ; % Connection \draw (515,111) -- (533.95,111)(541.95,111) -- (566,111) ; \draw [shift={(568,111)}, rotate = 180] [color={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.75] (10.93,-3.29) .. controls (6.95,-1.4) and (3.31,-0.3) .. (0,0) .. controls (3.31,0.3) and (6.95,1.4) .. (10.93,3.29) ; % Connection \draw (594,111) -- (615.25,111)(624.25,111) -- (645.5,111) ; \draw [shift={(647.5,111)}, rotate = 180] [color={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.75] (10.93,-3.29) .. controls (6.95,-1.4) and (3.31,-0.3) .. (0,0) .. controls (3.31,0.3) and (6.95,1.4) .. (10.93,3.29) ; % Connection \draw (501,34) -- (501,64.72)(501,72.72) -- (501,96) ; \draw [shift={(501,98)}, rotate = 270] [color={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.75] (10.93,-3.29) .. controls (6.95,-1.4) and (3.31,-0.3) .. (0,0) .. controls (3.31,0.3) and (6.95,1.4) .. (10.93,3.29) ; % Connection \draw (581,34) -- (581,64.72)(581,72.72) -- (581,96) ; \draw [shift={(581,98)}, rotate = 270] [color={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.75] (10.93,-3.29) .. controls (6.95,-1.4) and (3.31,-0.3) .. (0,0) .. controls (3.31,0.3) and (6.95,1.4) .. (10.93,3.29) ; % Connection \draw (661,34) -- (661,64.22)(661,73.22) -- (661,96) ; \draw [shift={(661,98)}, rotate = 270] [color={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.75] (10.93,-3.29) .. controls (6.95,-1.4) and (3.31,-0.3) .. (0,0) .. controls (3.31,0.3) and (6.95,1.4) .. (10.93,3.29) ; % Connection \draw (541,84) -- (541,156) ; \draw [shift={(541,158)}, rotate = 270] [color={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.75] (10.93,-3.29) .. controls (6.95,-1.4) and (3.31,-0.3) .. (0,0) .. controls (3.31,0.3) and (6.95,1.4) .. (10.93,3.29) ; % Connection \draw (621,84) -- (621,156) ; \draw [shift={(621,158)}, rotate = 270] [color={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.75] (10.93,-3.29) .. controls (6.95,-1.4) and (3.31,-0.3) .. (0,0) .. controls (3.31,0.3) and (6.95,1.4) .. (10.93,3.29) ; % Connection \draw (674.5,21) -- (710,21) ; \draw [shift={(712,21)}, rotate = 180] [color={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.75] (10.93,-3.29) .. controls (6.95,-1.4) and (3.31,-0.3) .. (0,0) .. controls (3.31,0.3) and (6.95,1.4) .. (10.93,3.29) ; % Connection \draw (634.5,71) -- (690,71) ; \draw [shift={(692,71)}, rotate = 180] [color={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.75] (10.93,-3.29) .. controls (6.95,-1.4) and (3.31,-0.3) .. (0,0) .. controls (3.31,0.3) and (6.95,1.4) .. (10.93,3.29) ; \end{tikzpicture} \begin{center} Brackets \end{center} \begin{equation*} \left(\frac{xdx}{dy} -\frac{ydy}{dx}\right)^{2} \ ,\ [\vec{F} =m\vec{a}] \ ,\ \left| \frac{a}{b}\right| \ \left\Vert \frac{a}{b}\right\Vert \ \left< \frac{a}{b}\right> \left\{\sqrt{a+\sqrt{a+\sqrt{a}}}\rightarrow \infty \right\} \end{equation*} \begin{center} Complex display \end{center} \begin{gather*} \begin{array}{ c c c } ! & \int _{b}^{a} f'( x) dx=f( b) -f( a) & \underbrace{\frac{1}{4} W_{\mu \nu } \cdot W^{\mu \nu } -\frac{1}{4} B_{\mu \nu } B^{\mu \nu } -\frac{1}{4} G_{\mu \nu }^{a} G_{a}^{\mu \nu }}_{\mathrm{kinetic\ energies\ and\ self-interactions\ of\ the\ gauge\ bosons}}\\ & \Vert x+y\Vert \geq \bigl|\Vert x\Vert -\Vert y\Vert \bigr| & \nabla \cdot \mathbf{D} =\rho \ \mathrm{and} \ \nabla \cdot \mathbf{B} =0\ \\ & & \nabla \times \mathbf{E} =-\frac{\partial \mathbf{B}}{\partial t} \ \mathrm{and} \ \nabla \times \mathbf{H} =\mathbf{J} +\frac{\partial \mathbf{D}}{\partial t}\\ & y=\frac{\sum\limits _{i} w_{i} y_{i}}{\sum\limits _{i} w_{i}} \ \ ,i=1,2...k & e=\lim\limits _{n\rightarrow \infty }\left( 1+\frac{1}{n}\right)^{n}\\ & & \end{array}\\ \dot{x}_{i} =a_{i} x_{i'} -( d+a_{i0} +a_{i1}) x_{i} +rx_{i}( f_{i} -\phi ) \end{gather*}

No comments