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TeX

$$ \def\aaa{a} \alpha \aaa $$

$$ \sqrt 2 \quad \sqrt{x + y} \quad \sqrt [ 3 ] 2 \quad \root 3^2 \of 4^5 $$

$$ \begin{pmatrix} a & b \\[0.5ex] c & d \\ \end{pmatrix} $$

$$ \left\langle a \over b \middle| c \over d \right\rangle $$

$$ { a \over^2 b } $$

$$ { a \over b \over c } $$

$$ \# \& \% \quad { a + b \over c + d} \quad \binom n 3 \quad { n+m \choose k} \quad \frac a b \quad \tfrac a b \quad \genfrac \{ \} {2pt} {0} ab \quad \genfrac \{ \} {} {1} ab \quad \genfrac \{ \} {} {2} ab \quad \genfrac \{ \} {} {3} ab \quad {a \atop b} \quad {a \brace b} \quad {a \brack b} \quad { a \above {1pt} b } $$

$$ =\not= \quad \equiv\not\equiv \quad \in\not\in \quad \ni\not\ni \quad \divides\not\divides \quad \parallel\not\parallel \quad \approx\not\approx \quad \exists\not\exists \quad \wp\not\wp \quad \alpha\not\alpha \quad \not\mathfrak R \quad \not h \quad \not H \quad 3\not 3 $$

$$ & \quad \\ \quad #1 \quad \middle | $$

$$ \genfrac . . {1pt}{0} 23 \sqrt{\smash[b] 3} $$

$$ \text{text} \textsf{text san-serif} \textit{text italic} $$

$$ \operatorname{s} s \quad \mathfrak{f} \mathfrak{\operatorname{f}} \mathbf{f} $$

$$ a / b \quad {x \mod a \over b} $$

$$ {dz} = \left({\partial F} \over {\partial y}\right)^{-1} {dx} = - \left({\partial F} \over {\partial x} \right)^{-1} {dy} $$

$$ \begin{aligned} h_3(\omega_1) \left(\frac {h_3(\omega_1)h_2} {h_1 h_3} \space + \space \frac {h_1 h_3} {h_3(\omega_1) h_2}\right) \enspace &= \enspace h_3(\omega_2) \left(\frac {h_3(\omega_2)h_1} {h_2 h_3} \space + \space \frac {h_2 h_3} {h_3(\omega_2) h_1}\right) \\\\ h_3(\omega_1)^2 h_2^2 \space + \space h_1^2 h_3^2 \enspace &= \enspace h_3(\omega_2)^2 h_1^2 \space + \space h_2^2 h_3^2 \\\\ (e_1 - e_3)(\wp - e_2) \space + \space (\wp - e_1)(\wp - e_3) \enspace &= \enspace (e_2 - e_3)(\wp - e_1) \space + \space (\wp - e_2)(\wp - e_3) \\\\ \wp^2 \space - \space 2e_3\wp \space + \space e_1e_3 + e_2e_3 - e_1e_2 \enspace &= \enspace \wp^2 \space - \space 2e_3\wp \space + \space e_1e_3 + e_2e_3 - e_1e_2 \qquad \checkmark \end{aligned} $$

$$ \sum_{\substack { m_1 \ne m_2 \mod 2 \\ [1em] \tfrac 79 \\[1em] m_1,m_2 \in Z} } $$

$ g' g'' g''' g'''' $ $ g''''' $

$$ A \hspace{-1em} A \! A \, A \> A \; A \enspace A \quad A \qquad A \hspace{4em} A $$

$$ ( \big( \Big( \bigg( \Bigg( $$

$$ \alpha\beta\gamma\delta\epsilon\zeta\eta\theta\iota\kappa\lambda\mu\nu\xi\omicron\pi\rho\sigma\tau\upsilon\psi\chi\phi\omega $$ $$ \Alpha\Beta\Gamma\Delta\Epsilon\Zeta\Eta\Theta\Iota\Kappa\Lambda\Mu\Nu\Xi\Omicron\Pi\Rho\Sigma\Tau\Upsilon\Psi\Chi\Phi\Omega $$ $$ \mathbb{0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz} $$ $$ \mathbf{0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz} $$ $$ \mathcal{0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz} $$ $$ \mathfrak{0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz} $$

$$ \overline{\sum_{i=1}^n x_i} \quad \hat{\prod\limits_{i=1}^n x_i} \quad \underline{\lim_{i \rightarrow \infty} x_i} $$

$$ \begin{bmatrix} a & b \\ c & d \\ \end{bmatrix} \quad \begin {matrix} a & b \\ c & d \\ \end{matrix} \quad \begin{pmatrix} a & b \\ c & d \\ \end{pmatrix} \quad \begin{vmatrix} a & b \\ c & d \\ \end{vmatrix} \quad \begin{Vmatrix} a & b \\ c & d \\ \end{Vmatrix} $$ $$ \sqrt [2] 3 4 $$ $$ \sqrt [[2] 3 $$ $$ \sqrt [2]] 3 $$ <$$ \sqrt [2] 3 $$

$$ \def \n {12} \def \d {34} \def \f#1#2{\frac #1 #2} \f \n \d X \f \n {34} X \f \n {{34}} X \f \n {\d} X \frac {\f \n \d} 5 X \frac x y^2 X {\frac x y}^2 X \frac {\f x y z} W \bar x^2 X {\bar x}^2 X \overline {x^2} X \lt^2 X \mathfrak {x^2} $$ Rules are that inbuilt functions are auto-grouped \frac x y => {\frac x y} but the macro \f{\frac x y} is spread. So when you hit a func\macro grab the next nargs using grouping. If macro the group args are spread then evaluated. But if function group args are groups.

MathML

This example demonstrates effect of font on MathML render quality.

$$ \wp^{-1}(x) = \int_{-\infty}^x {1 \over \sqrt{4x^3 - g_2x - g_3}} dx $$
$$ \prod_{0 \le i,j,k,l \le 2} \begin{vmatrix} \sqrt[3]{x_1-e_1} & \phantom{\zeta^0} \sqrt[3]{x_1-e_2} & \phantom{\zeta^0} \sqrt[3]{x_1-e_3} \\ \sqrt[3]{x_2-e_1} & \zeta^i \sqrt[3]{x_2-e_2} & \zeta^j \sqrt[3]{x_2-e_3} \\[1em] \sqrt[3]{x_3-e_1} & \zeta^k \sqrt[3]{x_3-e_2} & \zeta^l \sqrt[3]{x_3-e_3} \\ \end{vmatrix} = 3^{36} \cdot \begin{vmatrix} 1 & x_1 & x_1^2 \\ 1 & x_2 & x_2^2 \\ 1 & x_3 & x_3^2 \\ \end{vmatrix}^9 \cdot \begin{vmatrix} 1 & e_1 & e_1^2 \\ 1 & e_2 & e_2^2 \\ 1 & e_3 & e_3^2 \\ \end{vmatrix}^9 \cdot \left(\left(\mathfrak{R},\left(\mathfrak{R},\mathfrak{S}\right)_2\right)_2,\left(\mathfrak{S},\left(\mathfrak{S},\mathfrak{R}\right)_2\right)_2\right)_1^3 $$

Response Math

#flow

#flow \Delta(a,b,c,d,e) = 256a^3e^3 - 192a^2bde^2 - 128a^2c^2e^2 + 144a^2cd^2e - 27a^2d^4 + 144ab^2ce^2 - 6ab^2d^2e - 80abc^2de + 18abcd^3 + 16ac^4e - 4ac^3d^2 - 27b^4e^2 + 18b^3cde - 4b^3d^3 - 4b^2c^3e + b^2c^2d^2

#flow,left

#flow,left \Delta(a,b,c,d,e) = 256a^3e^3 - 192a^2bde^2 - 128a^2c^2e^2 + 144a^2cd^2e - 27a^2d^4 + 144ab^2ce^2 - 6ab^2d^2e - 80abc^2de + 18abcd^3 + 16ac^4e - 4ac^3d^2 - 27b^4e^2 + 18b^3cde - 4b^3d^3 - 4b^2c^3e + b^2c^2d^2

#flow,indent,rowgap=1em

#flow,indent,rowgap=1em \Delta(a,b,c,d,e) = 256a^3e^3 - 192a^2bde^2 - 128a^2c^2e^2 + 144a^2cd^2e - 27a^2d^4 + 144ab^2ce^2 - 6ab^2d^2e - 80abc^2de + 18abcd^3 + 16ac^4e - 4ac^3d^2 - 27b^4e^2 + 18b^3cde - 4b^3d^3 - 4b^2c^3e + b^2c^2d^2

#flow,left,indent,fold=500

#flow,left,indent,fold=500 \Delta(a,b,c,d,e) = 256a^3e^3 - 192a^2bde^2 - 128a^2c^2e^2 + 144a^2cd^2e - 27a^2d^4 + 144ab^2ce^2 - 6ab^2d^2e - 80abc^2de + 18abcd^3 + 16ac^4e - 4ac^3d^2 - 27b^4e^2 + 18b^3cde - 4b^3d^3 - 4b^2c^3e + b^2c^2d^2

#list

#list \alpha, \frac 1 {\alpha}, 1 - \alpha, \frac {\alpha} {\alpha - 1}, \frac {\alpha - 1} {\alpha}, \frac 1 {1 - \alpha}, \beta, \frac 1 {\beta}, 1 - \beta, \frac {\beta} {\beta - 1}, \frac {\beta - 1} {\beta}, \frac 1 {1 - \beta}, \lambda, \frac 1 {\lambda}, 1 - \lambda, \frac {\lambda} {\lambda - 1}, \frac {\lambda - 1} {\lambda}, \frac 1 {1 - \lambda}

fold

#fold

#fold \sqrt[30] {\discrim(a,b,c,d,e,f,g)}\int_{C} \frac 1 {\sqrt[3]{ax^6 + bx^5 + cx^4 + dx^3 + ex^2 + fx + g}} dx = \sqrt[30] {\discrim(p,q,r,s,t,u,v)} \int_{C'} \frac 1 {\sqrt[3]{py^6 + qy^5 + ry^4 + sy^3 + ty^2 + uy + v}} dy

#fold,end

#fold \sqrt[30] {\discrim(a,b,c,d,e,f,g)} \int_{C} \frac 1 {\sqrt[3]{ax^6 + bx^5 + cx^4 + dx^3 + ex^2 + fx + g}} dx = $ \sqrt[30] {\discrim(p,q,r,s,t,u,v)} $ \int_{C'} \frac 1 {\sqrt[3]{py^6 + qy^5 + ry^4 + sy^3 + ty^2 + uy + v}} dy

#fold

#fold \sqrt[30] {\discrim(a,b,c,d,e,f,g)} $ \int_{C} \frac 1 {\sqrt[3]{ax^6 + bx^5 + cx^4 + dx^3 + ex^2 + fx + g}} dx = $ \sqrt[30] {\discrim(p,q,r,s,t,u,v)} $ \int_{C'} \frac 1 {\sqrt[3]{py^6 + qy^5 + ry^4 + sy^3 + ty^2 + uy + v}} dy

#fold2 with 2 parts - doesn't look good

#fold2 \sqrt[30] {\discrim(a,b,c,d,e,f,g)} $ \int_{C} \frac 1 {\sqrt[3]{ax^6 + bx^5 + cx^4 + dx^3 + ex^2 + fx + g}} dx = $$ \sqrt[30] {\discrim(p,q,r,s,t,u,v)} $ \int_{C'} \frac 1 {\sqrt[3]{py^6 + qy^5 + ry^4 + sy^3 + ty^2 + uy + v}} dy

#fold2 with 3 parts - doesn't look good

#fold2 \beta \space = \space \zeta^i \alpha, \quad$ \frac 1 {\zeta^i \alpha}, \quad$ \zeta^j \frac {1 - \zeta^i\alpha} {1 + \zeta^i\alpha} $$ \qquad \textsf{where} \qquad $$ i=0\ldots 3, \enspace j=0 \ldots 3

train

#train,width=1200,flow,fold

#train,width=1200,flow,fold \small{\begin{vmatrix} a & b & c \\ p & q & r \\ q & r & s \\ \end{vmatrix}} $ = $ a(qs - r^2) + b(qr - ps) + $ c(pr - q^2) $$ = $ - \tfrac 1 {18} ap^2\big[ $ (\alpha - \mu)(\beta - \mu)(\nu - \omega)^2 + $ (\alpha - \nu)(\beta - \nu)(\mu - \omega)^2 + $ (\alpha - \omega)(\beta - \omega)(\mu - \nu)^2\big]

#train,width=1200,flow,fold=430

#train,width=1200,flow,fold=430 \small{\begin{vmatrix} a & b & c \\ p & q & r \\ q & r & s \\ \end{vmatrix}} $ = $ a(qs - r^2) + b(qr - ps) + c(pr - q^2) $$ = $ - \tfrac 1 {18} ap^2\big[ $ (\alpha - \mu)(\beta - \mu)(\nu - \omega)^2 + $ (\alpha - \nu)(\beta - \nu)(\mu - \omega)^2 + $ (\alpha - \omega)(\beta - \omega)(\mu - \nu)^2\big]