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Ayuda:Fórmulas Matemáticas

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(Diferencias entre revisiones)
Línea 515: Línea 515:
<td> \left ( \frac{1}{2} \right )</td>
<td> \left ( \frac{1}{2} \right )</td>
<td><math> \left ( \frac{1} {2} \right ) </math></td>
<td><math> \left ( \frac{1} {2} \right ) </math></td>
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</tr>
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</table>
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<table style="border: 1px solid rgb(170, 170, 170); margin: 1em 1em 1em 0pt; background: rgb(249, 249, 249) none repeat scroll 0%;border-collapse: collapse;" border="2" cellpadding="4" cellspacing="0">
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<tr>
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<th>&nbsp;</th>
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<th>Sintaxis</th>
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<th>Cómo se verá</th>
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</tr>
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<tr>
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<td>Paréntesis</td>
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<td>\left ( \frac{a}{b} \right )</td>
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<td><math> \left ( \frac{a}{b} \right ) </math></td>
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</tr>
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<tr>
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<td>Corchetes</td>
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<td>\left [ \frac{a}{b} \right ] \quad \left \lbrack \frac{a}{b} \right \rbrack</td>
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<td><math> \left [ \frac{a}{b} \right ] \quad \left \lbrack \frac{a}{b} \right \rbrack </math></td>
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</tr>
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<tr>
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<td>Llaves</td>
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<td>\left \{ \frac{a}{b} \right \} \quad \left \lbrace \frac{a}{b} \right \rbrace</td>
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<td><math> \left \{ \frac{a}{b} \right \} \quad \left \lbrace \frac{a}{b} \right \rbrace </math></td>
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</tr>
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<tr>
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<td>Barras y dobles barras</td>
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<td>\left | \frac{a}{b} \right \vert \left \Vert \frac{c}{d} \right \|</td>
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<td><math> \left | \frac{a}{b} \right \vert \left \Vert \frac{c}{d} \right \| </math></td>
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</tr>
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<td>Barras invertidas</td>
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<td>\left / \frac{a}{b} \right \backslash</td>
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<td><math> \left / \frac{a}{b} \right \backslash </math></td>
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</tr>
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<tr>
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<td>Flechas arriba y abajo</td>
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<td>\left \uparrow \frac{a}{b} \right \downarrow \quad \left \Uparrow \frac{a}{b} \right \Downarrow \quad \left \updownarrow \frac{a}{b} \right \Updownarrow</td>
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<td><math> \left \uparrow \frac{a}{b} \right \downarrow \quad \left \Uparrow \frac{a}{b} \right \Downarrow \quad \left \updownarrow \frac{a}{b} \right \Updownarrow </math></td>
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</tr>
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<tr>
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<td>Los delimitadores pueden mezclarse</td>
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<td>\left [ 0,1 \right )</td>
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<td><math> \left [ 0,1 \right ) </math></td>
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</tr>
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<tr>
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<td>Usa \left. y \right. si no quieres que un delimitador aparezca</td>
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<td>\left . \frac{A}{B} \right \} \to X</td>
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<td><math> \left . \frac{A}{B} \right \} \to X </math></td>
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</tr>
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<tr>
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<td rowspan="5">Tamaño de los delimitadores</td>
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<td>\big( \Big( \bigg( \Bigg( ... \Bigg] \bigg] \Big] \big]</td>
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<td><math> \big( \Big( \bigg( \Bigg( ... \Bigg] \bigg] \Big] \big] </math></td>
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</tr>
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<tr>
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<td>\big\{ \Big\{ \bigg\{ \Bigg\{ ... \Bigg\rangle \bigg\rangle \Big\rangle \big\rangle</td>
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<td><math> \big\{ \Big\{ \bigg\{ \Bigg\{ ... \Bigg\rangle \bigg\rangle \Big\rangle \big\rangle </math></td>
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</tr>
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<tr>
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<td>\big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow ... \Bigg\Downarrow \bigg\Downarrow \Big\Downarrow \big\Downarrow</td>
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<td><math> \big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow ... \Bigg\Downarrow \bigg\Downarrow \Big\Downarrow \big\Downarrow </math></td>
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</tr>
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<tr>
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<td>\big\updownarrow \Big\updownarrow \bigg\updownarrow \Bigg\updownarrow ... \Bigg\Updownarrow \bigg\Updownarrow \Big\Updownarrow \big\Updownarrow</td>
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<td><math> \big\updownarrow \Big\updownarrow \bigg\updownarrow \Bigg\updownarrow ... \Bigg\Updownarrow \bigg\Updownarrow \Big\Updownarrow \big\Updownarrow </math></td>
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</tr>
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<tr>
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<td>\big / \Big / \bigg / \Bigg / ... \Bigg\backslash \bigg\backslash \Big\backslash \big\backslash</td>
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<td><math> \big / \Big / \bigg / \Bigg / ... \Bigg\backslash \bigg\backslash \Big\backslash \big\backslash </math></td>
</tr>
</tr>
</table>
</table>

Revisión de 15:31 6 nov 2007

Ayuda A continuación ofrecemos un cuadro de referencia con nociones básicas y ejemplos que sirven de ayuda para escribir fórmulas utilizando el código LaTeX.

Tabla de contenidos

Básicos

Acentos
\acute{a} \grave{a} \hat{a} \tilde{a} \breve{a} \acute{a} \grave{a} \hat{a} \tilde{a} \breve{a}
\check{a} \bar{a} \ddot{a} \dot{a}  \check{a} \bar{a} \ddot{a} \dot{a}
Funciones estándar
\sin a \cos b \tan c  \sin a \cos b \tan c
\sec d \csc e \cot f  \sec d \csc e \cot f
\arcsin h \arccos i \arctan j  \arcsin h \arccos i \arctan j
\sinh k \cosh l \tanh m \coth n  \sinh k \cosh l \tanh m \coth n
\lim u \limsup v \liminf w \min x \max y  \lim u \limsup v \liminf w \min x \max y
\inf z \sup a \exp b \ln c \lg d \log e \log_{10} f \ker g  \inf z \sup a \exp b \ln c \lg d \log e \log_{10} f \ker g
Derivadas
\nabla \partial x dx \dot x \ddot y  \nabla \partial x dx \dot x \ddot y
Conjuntos
\forall \exists \emptyset \varnothing  \forall \exists \emptyset \varnothing
\in \ni \notin \subset \subseteq \supset \supseteq  \in \ni \notin \subset \subseteq \supset \supseteq
\cap \bigcap \cup \bigcup \biguplus \setminus \smallsetminus  \cap \bigcap \cup \bigcup \biguplus \setminus \smallsetminus
\sqsubset \sqsubseteq \sqsupset \sqsupseteq \sqcap \sqcup \bigsqcup  \sqsubset \sqsubseteq \sqsupset \sqsupseteq \sqcap \sqcup \bigsqcup
Operadores
+ \oplus \bigoplus \pm \mp -  + \oplus \bigoplus \pm \mp -
\times \otimes \bigotimes \cdot \circ \bullet \bigodot  \times \otimes \bigotimes \cdot \circ \bullet \bigodot
\star * / \div \frac{1}{2}  \star * / \div \frac{1}{2}
Lógica
\land \wedge \bigwedge \bar{q} \to p  \land \wedge \bigwedge \bar{q} \to p
\lor \vee \bigvee \lnot \neg q \And  \lor \vee \bigvee \lnot \neg q \And
Raíces
\sqrt{2} \sqrt[n]{x}  \sqrt{2} \sqrt[n]{x}
Relaciones
\sim \approx \simeq \cong  \sim \approx \simeq \cong
\le < \ll \gg \ge > \equiv \not\equiv \ne \mbox{or} \neq \propto  \le < \ll \gg \ge > \equiv \not\equiv \ne \mbox{or} \neq \propto
Geometría
\Diamond \Box \triangle \angle \perp \mid \nmid \| 45^\circ  \Diamond \Box \triangle \angle \perp \mid \nmid \| 45^\circ
Flechas
\leftarrow \gets \rightarrow \to \not\to \leftrightarrow \longleftarrow \longrightarrow  \leftarrow \gets \rightarrow \to \not\to \leftrightarrow \longleftarrow \longrightarrow
\uparrow \downarrow \updownarrow \rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft  \uparrow \downarrow \updownarrow \rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft
\upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \Leftarrow \Rightarrow \Leftrightarrow \Longleftarrow  \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \Leftarrow \Rightarrow \Leftrightarrow \Longleftarrow
\Longrightarrow \Uparrow \Downarrow \Updownarrow  \Longrightarrow \Uparrow \Downarrow \Updownarrow
\nLeftrightarrow \longleftrightarrow  \nLeftrightarrow \longleftrightarrow
Especial
\eth \S \P \% \dagger \ddagger \ldots \cdots  \eth \S \P \% \dagger \ddagger \ldots \cdots
\smile \frown \wr \triangleleft \triangleright \infty \bot \top  \smile \frown \wr \triangleleft \triangleright \infty \bot \top
\vdash \vDash \Vdash \models \lVert \rVert \imath \hbar  \vdash \vDash \Vdash \models \lVert \rVert \imath \hbar
Otros
\vartriangle \triangledown \lozenge \circledS \measuredangle \nexists \Bbbk \backprime \blacktriangle \blacktriangledown  \vartriangle \triangledown \lozenge \circledS \measuredangle \nexists \Bbbk \backprime \blacktriangle \blacktriangledown
\blacksquare \blacklozenge \bigstar \sphericalangle \diagup \diagdown \dotplus \Cap \Cup \barwedge  \blacksquare \blacklozenge \bigstar \sphericalangle \diagup \diagdown \dotplus \Cap \Cup \barwedge
\veebar \doublebarwedge \boxminus \boxtimes \boxdot \boxplus \divideontimes \ltimes \rtimes \leftthreetimes  \veebar \doublebarwedge \boxminus \boxtimes \boxdot \boxplus \divideontimes \ltimes \rtimes \leftthreetimes
\rightthreetimes \curlywedge \curlyvee \circleddash \circledast \circledcirc \centerdot \intercal \leqq \leqslant  \rightthreetimes \curlywedge \curlyvee \circleddash \circledast \circledcirc \centerdot \intercal \leqq \leqslant
\eqslantless \lessapprox \approxeq \lessdot \lll \lessgtr \lesseqgtr \lesseqqgtr \doteqdot  \eqslantless \lessapprox \approxeq \lessdot \lll \lessgtr \lesseqgtr \lesseqqgtr \doteqdot
\fallingdotseq \backsim \backsimeq \subseteqq \Subset \preccurlyeq \curlyeqprec \precsim \precapprox  \fallingdotseq \backsim \backsimeq \subseteqq \Subset \preccurlyeq \curlyeqprec \precsim \precapprox
\Vvdash \bumpeq \Bumpeq \geqq \geqslant \eqslantgtr \gtrsim \gtrapprox \eqsim \gtrdot  \Vvdash \bumpeq \Bumpeq \geqq \geqslant \eqslantgtr \gtrsim \gtrapprox \eqsim \gtrdot
\ggg \gtrless \gtreqless \gtreqqless \eqcirc \circeq \triangleq \thicksim \thickapprox \supseteqq  \ggg \gtrless \gtreqless \gtreqqless \eqcirc \circeq \triangleq \thicksim \thickapprox \supseteqq
\Supset \succcurlyeq \curlyeqsucc \succsim \succapprox \vartriangleright \shortmid \shortparallel \between \pitchfork  \Supset \succcurlyeq \curlyeqsucc \succsim \succapprox \vartriangleright \shortmid \shortparallel \between \pitchfork
\varpropto \blacktriangleleft \therefore \backepsilon \blacktriangleright \because \nleqslant \nleqq \lneq \lneqq  \varpropto \blacktriangleleft \therefore \backepsilon \blacktriangleright \because \nleqslant \nleqq \lneq \lneqq
\lvertneqq \lnsim \lnapprox \nprec \npreceq \precneqq \precnsim \precnapprox \nsim \nshortmid  \lvertneqq \lnsim \lnapprox \nprec \npreceq \precneqq \precnsim \precnapprox \nsim \nshortmid
\nvdash \nVdash \ntriangleleft \ntrianglelefteq \nsubseteq \nsubseteqq \ngtr  \nvdash \nVdash \ntriangleleft \ntrianglelefteq \nsubseteq \nsubseteqq \ngtr
\ngeqslant \ngeqq \gneq \gneqq \gvertneqq \gnsim \gnapprox \nsucc \nsucceq \succneqq  \ngeqslant \ngeqq \gneq \gneqq \gvertneqq \gnsim \gnapprox \nsucc \nsucceq \succneqq
\succnsim \succnapprox \ncong \nshortparallel \nparallel \nvDash \nVDash \ntriangleright \ntrianglerighteq \nsupseteq  \succnsim \succnapprox \ncong \nshortparallel \nparallel \nvDash \nVDash \ntriangleright \ntrianglerighteq \nsupseteq
\nsupseteqq \varsupsetneq \supsetneqq \varsupsetneqq  \nsupseteqq \varsupsetneq \supsetneqq \varsupsetneqq

Subíndices, superíndices, integrales

  Sintaxis Cómo se verá
Superíndice a^2  a^2
Subíndice a_2  a_2
Agrupar a^{2+2}  a^{2+2}
a_{i,j}  a_{i,j}
Combinar superindice y subíndice x_2^3  x_2^3
Superíndices y subíndices, anteriores, posteriores, arriba y abajo \sideset {_1^2} {_3^4} \prod_a^b  \sideset {_1^2} {_3^4} \prod_a^b
{}_1^2 \! \Omega_3^4  {}_1^2 \! \Omega_3^4
Apilar \overset { \alpha} { \omega}  \overset { \alpha} { \omega}
\overset { \alpha} { \underset { \gamma} { \omega}}  \overset { \alpha} { \underset { \gamma} { \omega}}
\stackrel { \alpha} { \omega}  \stackrel { \alpha} { \omega}
Derivadas x', y, f', f  x', y'', f', f''
Subrayado, línea superior, vectores \hat a \ \bar b \ \vec c  \hat a \ \bar b \ \vec c
\overrightarrow {a b} \overleftarrow {c d} \widehat {d e f}  \overrightarrow {a b} \overleftarrow {c d} \widehat {d e f}
\overline {g h i} \underline {j k l}  \overline {g h i} \underline {j k l}
Flechas A \xleftarrow {n+ \mu-1} B \xrightarrow[T] {n \pm i-1} C  A \xleftarrow {n+ \mu-1} B \xrightarrow[T] {n \pm i-1} C
Llaves superiores \overbrace{ 1+2+ \cdots+100 } ^ {5050}  \overbrace{ 1+2+ \cdots+100 } ^ {5050}
Llaves inferiores \underbrace { a+b+ \cdots+z }_{26}  \underbrace { a+b+ \cdots+z }_{26}
Sumatorios \sum_{k=1}^N k^2  \sum_{k=1}^N k^2
Productorio \prod_{i=1}^N x_i  \prod_{i=1}^N x_i
Coproducto \coprod_{i=1}^N x_i  \coprod_{i=1}^N x_i
Límite \lim_{n \to \infty}x_n  \lim_{n \to \infty}x_n
Integral \int_{-N}^{N} e^x\, dx \int_{-N}^{N} e^x\, dx
Integral doble \iint_{D}^{W} \, dx\,dy  \iint_{D}^{W} \, dx\,dy
Integral triple \iiint_{E}^{V} \, dx\,dy\,dz  \iiint_{E}^{V} \, dx\,dy\,dz
Integral de línea \oint_{C} x^3\, dx + 4y^2\, dy  \oint_{C} x^3\, dx + 4y^2\, dy
Intersecciones \bigcap_1^{n} p  \bigcap_1^{n} p
Uniones \bigcup_1^{k} p  \bigcup_1^{k} p

Fracciones, matrices, multilíneas

  Sintaxis Cómo se verá
Fracciones \frac{2}{4}=0.5 \frac{2}{4}=0.5
Coeficiente binomial \binom{n}{k} \binom{n}{k}
Matrices \begin{matrix}
x & y \\
z & v
\end{matrix}
 \begin{matrix} x & y \\ z & v \end{matrix}
\begin{vmatrix}
x & y \\
z & v
\end{vmatrix}
 \begin{vmatrix} x & y \\ z & v \end{vmatrix}
\begin{Vmatrix
x & y \\
z & v
\end{Vmatrix}
 \begin{Vmatrix} x & y \\ z & v \end{Vmatrix}
\begin{bmatrix}
0 & \cdots & 0 \\
\vdots & \ddots & \vdots \\
0 & \cdots & 0
\end{bmatrix}
 \begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0 \end{bmatrix}
\begin{Bmatrix}
x & y \\
z & v
\end{Bmatrix}
 \begin{Bmatrix} x & y \\ z & v \end{Bmatrix}
\begin{pmatrix}
x & y \\
z & v
\end{pmatrix}
 \begin{pmatrix} x & y \\ z & v \end{pmatrix}
\bigl( \begin{smallmatrix}
a&b\\ c&d
\end{smallmatrix} \bigr)
 \bigl( \begin{smallmatrix} a&b\\ c&d \end{smallmatrix} \bigr)
Distinción de casos f(n) =
\begin{cases}
n/2, & \mbox{if }n\mbox{ is even} \\
3n+1, & \mbox{if }n\mbox{ is odd}
\end{cases}
 f(n) = \begin{cases} n/2, & \mbox{if }n\mbox{ is even} \\ 3n+1, & \mbox{if }n\mbox{ is odd} \end{cases}
Ecuaciones multilínea (se debe definir el número de columnas con {lcl}) \begin{array}{lcl}
z & = & a \\
f(x,y,z) & = & x + y + z
\end{array}
 \begin{array}{lcl} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}
\begin{array}{lclcl}
z & = & a & = & \sqrt 2\\
f(x,y,z) & = & x + y + z & = & t^2\\
f(z) & = & x+y & = & 2 \pi
\end{array}
 \begin{array}{lclcl}   z        & = & a & = & \sqrt 2\\  f(x,y,z) & = & x + y + z & = & t^2\\ f(z) & = & x+y & = & 2 \pi \end{array}
Romper largas expresiones para hacer más legible el código <math>f(x) \,\!</math>
<math>= \sum_{n=0}^\infty a_n x^n </math>
<math>= a_0+a_1x+a_2x^2+\cdots</math>

 f(x) \,\!  = \sum_{n=0}^ \infty a_n x^n  = a_0+a_1x+a_2x^2+ \cdots

Ecuaciones simultáneas \begin{cases}
3x + 5y + z \\
7x - 2y + 4z \\
-6x + 3y + 2z
\end{cases}
 \begin{cases} 3x + 5y + z \\ 7x - 2y + 4z \\ -6x + 3y + 2z \end{cases}

Alfabetos

Alfabeto griego
\Delta \Theta \Lambda  \Delta \Theta \Lambda
\Xi \Pi \Sigma \Xi \Pi \Sigma
\Upsilon \Phi \Psi \Omega  \Upsilon \Phi \Psi \Omega
\alpha \beta \gamma \delta \epsilon \zeta  \alpha \beta \gamma \delta \epsilon \zeta
\eta \theta \iota \kappa \lambda \mu  \eta \theta \iota \kappa \lambda \mu
\nu \xi \pi \rho \sigma \tau  \nu \xi \pi \rho \sigma \tau
\upsilon \phi \chi \psi \omega  \upsilon \phi \chi \psi \omega
\varepsilon \digamma \vartheta \varkappa  \varepsilon \digamma \vartheta \varkappa
\varpi \varrho \varsigma \varphi  \varpi \varrho \varsigma \varphi

Añadiendo paréntesis a grandes expresiones

  Sintaxis Cómo se verá
Mal ( \frac{1}{2} )  ( \frac{1}{2} )
Bien \left ( \frac{1}{2} \right )  \left ( \frac{1} {2} \right )

</tr>

  Sintaxis Cómo se verá
Paréntesis \left ( \frac{a}{b} \right )  \left ( \frac{a}{b} \right )
Corchetes \left [ \frac{a}{b} \right ] \quad \left \lbrack \frac{a}{b} \right \rbrack  \left [ \frac{a}{b} \right ] \quad \left \lbrack \frac{a}{b} \right \rbrack
Llaves \left \{ \frac{a}{b} \right \} \quad \left \lbrace \frac{a}{b} \right \rbrace  \left \{ \frac{a}{b} \right \} \quad \left \lbrace \frac{a}{b} \right \rbrace
Barras y dobles barras \left | \frac{a}{b} \right \vert \left \Vert \frac{c}{d} \right \|  \left | \frac{a}{b} \right \vert \left \Vert \frac{c}{d} \right \|
Barras invertidas \left / \frac{a}{b} \right \backslash  \left / \frac{a}{b} \right \backslash
Flechas arriba y abajo \left \uparrow \frac{a}{b} \right \downarrow \quad \left \Uparrow \frac{a}{b} \right \Downarrow \quad \left \updownarrow \frac{a}{b} \right \Updownarrow  \left \uparrow \frac{a}{b} \right \downarrow \quad \left \Uparrow \frac{a}{b} \right \Downarrow \quad \left \updownarrow \frac{a}{b} \right \Updownarrow
Los delimitadores pueden mezclarse \left [ 0,1 \right )  \left [ 0,1 \right )
Usa \left. y \right. si no quieres que un delimitador aparezca \left . \frac{A}{B} \right \} \to X  \left . \frac{A}{B} \right \} \to X
Tamaño de los delimitadores \big( \Big( \bigg( \Bigg( ... \Bigg] \bigg] \Big] \big]  \big( \Big( \bigg( \Bigg( ... \Bigg] \bigg] \Big] \big]
\big\{ \Big\{ \bigg\{ \Bigg\{ ... \Bigg\rangle \bigg\rangle \Big\rangle \big\rangle  \big\{ \Big\{ \bigg\{ \Bigg\{ ... \Bigg\rangle \bigg\rangle \Big\rangle \big\rangle
\big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow ... \Bigg\Downarrow \bigg\Downarrow \Big\Downarrow \big\Downarrow  \big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow ... \Bigg\Downarrow \bigg\Downarrow \Big\Downarrow \big\Downarrow
\big\updownarrow \Big\updownarrow \bigg\updownarrow \Bigg\updownarrow ... \Bigg\Updownarrow \bigg\Updownarrow \Big\Updownarrow \big\Updownarrow  \big\updownarrow \Big\updownarrow \bigg\updownarrow \Bigg\updownarrow ... \Bigg\Updownarrow \bigg\Updownarrow \Big\Updownarrow \big\Updownarrow
\big / \Big / \bigg / \Bigg / ... \Bigg\backslash \bigg\backslash \Big\backslash \big\backslash  \big / \Big / \bigg / \Bigg / ... \Bigg\backslash \bigg\backslash \Big\backslash \big\backslash

Espaciado

Colores

Ejemplos

actualizando

   
 
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