Ayuda:Fórmulas Matemáticas
De Wikillerato
(Diferencias entre revisiones)
Línea 231: | Línea 231: | ||
<td><code>\nsupseteqq \varsupsetneq \supsetneqq \varsupsetneqq</code></td> | <td><code>\nsupseteqq \varsupsetneq \supsetneqq \varsupsetneqq</code></td> | ||
<td><math> \nsupseteqq \varsupsetneq \supsetneqq \varsupsetneqq </math></td> | <td><math> \nsupseteqq \varsupsetneq \supsetneqq \varsupsetneqq </math></td> | ||
+ | </tr> | ||
+ | </table> | ||
+ | |||
+ | '''Subíndices, superíndices, integrales''' | ||
+ | |||
+ | <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"> | ||
+ | <tr> | ||
+ | <th rowspan="2"> </th> | ||
+ | <th rowspan="2">Sintaxis</th> | ||
+ | <th colspan="2">Cómo se verá</th> | ||
+ | </tr> | ||
+ | <tr> | ||
+ | <th>HTML</th> | ||
+ | <th>PNG</th> | ||
+ | </tr> | ||
+ | <tr> | ||
+ | <td>Superíndice</td> | ||
+ | <td><code>a^2</code></td> | ||
+ | <td><i>a</i><sup>2</sup></td> | ||
+ | <td><math> a^2 </math></td> | ||
+ | </tr> | ||
+ | <tr> | ||
+ | <td>Subíndice</td> | ||
+ | <td><code>a_2</code></td> | ||
+ | <td>><i>a</i><sub>2</sub></td> | ||
+ | <td><math> a_2 </math></td> | ||
+ | </tr> | ||
+ | <tr> | ||
+ | <td rowspan="2">Agrupar</td> | ||
+ | <td><code>a^{2+2}</code></td> | ||
+ | <td><i>a</i><sup>2 + 2</sup></td> | ||
+ | <td><math> a^{2+2} </math></td> | ||
+ | </tr> | ||
+ | <tr> | ||
+ | <td><code>a_{i,j}</code></td> | ||
+ | <td><i>a</i><sub><i>i</i>,<i>j</i></sub></td> | ||
+ | <td><math> a_{i,j} </math></td> | ||
+ | </tr> | ||
+ | <tr> | ||
+ | <td>Combinar superíndice y subíndice</td> | ||
+ | <td><code>x_2^3</code></td> | ||
+ | <td colspan="2"><math> x_2^3 </math></td> | ||
+ | </tr> | ||
+ | <tr> | ||
+ | <td rowspan="2">Superíndices y subíndices, anteriores, posteriores, arriba y abajo</td> | ||
+ | <td><code>\sideset{_1^2}{_3^4}\prod_a^b</code></td> | ||
+ | <td colspan="2"><math> \sideset{_1^2}{_3^4}\prod_a^b </math></td> | ||
+ | </tr> | ||
+ | <tr> | ||
+ | <td><code>{}_1^2\!\Omega_3^4</code></td> | ||
+ | <td colspan="2"><math> {}_1^2\!\Omega_3^4 </math></td> | ||
+ | </tr> | ||
+ | <tr> | ||
+ | <td rowspan="4">Apilar</td> | ||
+ | <td><code>\overset{\alpha}{\omega}</code></td> | ||
+ | <td colspan="2"><math> \overset{\alpha}{\omega} </math></td> | ||
+ | </tr> | ||
+ | <tr> | ||
+ | <td><code>\underset{\alpha}{\omega}</code></td> | ||
+ | <td colspan="2"><math> \underset{\alpha}{\omega </math></td> | ||
+ | </tr> | ||
+ | <tr> | ||
+ | <td><code>\overset{\alpha}{\underset{\gamma}{\omega}}</code></td> | ||
+ | <td colspan="2"><math> \overset{\alpha}{\underset{\gamma}{\omega}} </math></td> | ||
+ | </tr> | ||
+ | <tr> | ||
+ | <td><code>\stackrel{\alpha}{\omega}</code></td> | ||
+ | <td colspan="2"><math> \stackrel{\alpha}{\omega} </math></td> | ||
+ | </tr> | ||
+ | <tr> | ||
+ | <td>Derivadas ( forzando el PNG)</td> | ||
+ | <td><code>x', y'', f', f''</code></td> | ||
+ | <td colspan="2"><math> x', y'', f', f'' </math></td> | ||
+ | </tr> | ||
+ | <tr> | ||
+ | <td rowspan="3">Subrayado, línea superior, vectores</td> | ||
+ | <td><code>\hat a \ \bar b \ \vec c</code></td> | ||
+ | <td colspan="2"><math> \hat a \ \bar b \ \vec c </math></td> | ||
+ | </tr> | ||
+ | <tr> | ||
+ | <td><code>\overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f}</code></td> | ||
+ | <td colspan="2"><math> \overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f} </math></td> | ||
+ | </tr> | ||
+ | <tr> | ||
+ | <td><code>\overline{g h i} \ \underline{j k l}</code></td> | ||
+ | <td colspan="2"><math> \overline{g h i} \ \underline{j k l} </math></td> | ||
+ | </tr> | ||
+ | <tr> | ||
+ | <td>Flechas</td> | ||
+ | <td><code>A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C</code></td> | ||
+ | <td colspan="2"><math> A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C </math></td> | ||
+ | </tr> | ||
+ | <tr> | ||
+ | <td>Llaves superiores</td> | ||
+ | <td><code>\overbrace{ 1+2+\cdots+100 }^{5050}</code></td> | ||
+ | <td colspan="2"><math> \overbrace{ 1+2+\cdots+100 }^{5050} </math></td> | ||
+ | </tr> | ||
+ | <tr> | ||
+ | <td>Llaves inferiores</td> | ||
+ | <td><code>\underbrace{ a+b+\cdots+z }_{26}</code></td> | ||
+ | <td colspan="2"><math> \underbrace{ a+b+\cdots+z }_{26} </math></td> | ||
+ | </tr> | ||
+ | <tr> | ||
+ | <td>Sumatorios</td> | ||
+ | <td><code>\sum_{k=1}^N k^2</code></td> | ||
+ | <td colspan="2"><math> \sum_{k=1}^N k^2 </math></td> | ||
+ | </tr> | ||
+ | <tr> | ||
+ | <td>Productorio</td> | ||
+ | <td><code>\prod_{i=1}^N x_i</code></td> | ||
+ | <td colspan="2"><math> \prod_{i=1}^N x_i </math></td> | ||
+ | </tr> | ||
+ | <tr> | ||
+ | <td>Coproduct</td> | ||
+ | <td><code>\coprod_{i=1}^N x_i</code></td> | ||
+ | <td colspan="2"><math> \coprod_{i=1}^N x_i </math></td> | ||
+ | </tr> | ||
+ | <tr> | ||
+ | <td>Límite</td> | ||
+ | <td><code>\lim_{n \to \infty}x_n</code></td> | ||
+ | <td colspan="2"><math> \lim_{n \to \infty}x_n </math></td> | ||
+ | </tr> | ||
+ | <tr> | ||
+ | <td>Integral</td> | ||
+ | <td><code>\int_{-N}^{N} e^x\, dx</code></td> | ||
+ | <td colspan="2"><code>\int_{-N}^{N} e^x\, dx</code></td> | ||
+ | </tr> | ||
+ | <tr> | ||
+ | <td>Integral doble</td> | ||
+ | <td><code>\iint_{D}^{W} \, dx\,dy</code></td> | ||
+ | <td colspan="2"><math> \iint_{D}^{W} \, dx\,dy </math></td> | ||
+ | </tr> | ||
+ | <tr> | ||
+ | <td>Integral triple</td> | ||
+ | <td><code>\iiint_{E}^{V} \, dx\,dy\,dz</code></td> | ||
+ | <td colspan="2"><math> \iiint_{E}^{V} \, dx\,dy\,dz </math></td> | ||
+ | </tr> | ||
+ | <tr> | ||
+ | <td>Integral de línea</td> | ||
+ | <td><code>\oint_{C} x^3\, dx + 4y^2\, dy</code></td> | ||
+ | <td colspan="2"><math> \oint_{C} x^3\, dx + 4y^2\, dy </math></td> | ||
+ | </tr> | ||
+ | <tr> | ||
+ | <td>Intersecciones</td> | ||
+ | <td><code>\bigcap_1^{n} p</code></td> | ||
+ | <td colspan="2"><math> \bigcap_1^{n} p </math></td> | ||
+ | </tr> | ||
+ | <tr> | ||
+ | <td>Uniones</td> | ||
+ | <td><code>\bigcup_1^{k} p</code></td> | ||
+ | <td colspan="2"><math> \bigcup_1^{k} p </math></td> | ||
</tr> | </tr> | ||
</table> | </table> | ||
<math>actualizando</math> | <math>actualizando</math> |
Revisión de 11:49 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.
Acentos | |
---|---|
\acute{a} \grave{a} \hat{a} \tilde{a} \breve{a} |
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\check{a} \bar{a} \ddot{a} \dot{a} |
|
Funciones estándar | |
\sin a \cos b \tan c |
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\sec d \csc e \cot f |
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\arcsin h \arccos i \arctan j |
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\sinh k \cosh l \tanh m \coth n |
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\lim u \limsup v \liminf w \min x \max y |
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\inf z \sup a \exp b \ln c \lg d \log e \log_{10} f \ker g |
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Derivadas | |
\nabla \partial x dx \dot x \ddot y |
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Conjuntos | |
\forall \exists \emptyset \varnothing |
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\in \ni \notin \subset \subseteq \supset \supseteq |
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\cap \bigcap \cup \bigcup \biguplus \setminus \smallsetminus |
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\sqsubset \sqsubseteq \sqsupset \sqsupseteq \sqcap \sqcup \bigsqcup |
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Operadores | |
+ \oplus \bigoplus \pm \mp - |
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\times \otimes \bigotimes \cdot \circ \bullet \bigodot |
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\star * / \div \frac{1}{2} |
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Lógica | |
\land \wedge \bigwedge \bar{q} \to p |
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\lor \vee \bigvee \lnot \neg q \And |
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Raíces | |
\sqrt{2} \sqrt[n]{x} |
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Relaciones | |
\sim \approx \simeq \cong |
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\le < \ll \gg \ge > \equiv \not\equiv \ne \mbox{or} \neq \propto |
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Geometría | |
\Diamond \Box \triangle \angle \perp \mid \nmid \| 45^\circ |
|
Flechas | |
\leftarrow \gets \rightarrow \to \not\to \leftrightarrow \longleftarrow \longrightarrow |
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\uparrow \downarrow \updownarrow \rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft |
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\upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \Leftarrow \Rightarrow \Leftrightarrow \Longleftarrow |
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\Longrightarrow \Uparrow \Downarrow \Updownarrow |
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\nLeftrightarrow \longleftrightarrow |
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Especial | |
\eth \S \P \% \dagger \ddagger \ldots \cdots |
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\smile \frown \wr \triangleleft \triangleright \infty \bot \top |
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\vdash \vDash \Vdash \models \lVert \rVert \imath \hbar |
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Otros | |
\vartriangle \triangledown \lozenge \circledS \measuredangle \nexists \Bbbk \backprime \blacktriangle \blacktriangledown |
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\blacksquare \blacklozenge \bigstar \sphericalangle \diagup \diagdown \dotplus \Cap \Cup \barwedge |
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\veebar \doublebarwedge \boxminus \boxtimes \boxdot \boxplus \divideontimes \ltimes \rtimes \leftthreetimes |
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\rightthreetimes \curlywedge \curlyvee \circleddash \circledast \circledcirc \centerdot \intercal \leqq \leqslant |
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\eqslantless \lessapprox \approxeq \lessdot \lll \lessgtr \lesseqgtr \lesseqqgtr \doteqdot |
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\fallingdotseq \backsim \backsimeq \subseteqq \Subset \preccurlyeq \curlyeqprec \precsim \precapprox |
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\Vvdash \bumpeq \Bumpeq \geqq \geqslant \eqslantgtr \gtrsim \gtrapprox \eqsim \gtrdot |
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\ggg \gtrless \gtreqless \gtreqqless \eqcirc \circeq \triangleq \thicksim \thickapprox \supseteqq |
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\Supset \succcurlyeq \curlyeqsucc \succsim \succapprox \vartriangleright \shortmid \shortparallel \between \pitchfork |
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\varpropto \blacktriangleleft \therefore \backepsilon \blacktriangleright \because \nleqslant \nleqq \lneq \lneqq |
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\lvertneqq \lnsim \lnapprox \nprec \npreceq \precneqq \precnsim \precnapprox \nsim \nshortmid |
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\nvdash \nVdash \ntriangleleft \ntrianglelefteq \nsubseteq \nsubseteqq \ngtr |
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\ngeqslant \ngeqq \gneq \gneqq \gvertneqq \gnsim \gnapprox \nsucc \nsucceq \succneqq |
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\succnsim \succnapprox \ncong \nshortparallel \nparallel \nvDash \nVDash \ntriangleright \ntrianglerighteq \nsupseteq |
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\nsupseteqq \varsupsetneq \supsetneqq \varsupsetneqq |
Subíndices, superíndices, integrales
Sintaxis | Cómo se verá | ||
---|---|---|---|
HTML | PNG | ||
Superíndice | a^2 |
a2 | |
Subíndice | a_2 |
>a2 | |
Agrupar | a^{2+2} |
a2 + 2 | |
a_{i,j} |
ai,j | ||
Combinar superíndice y subíndice | x_2^3 |
||
Superíndices y subíndices, anteriores, posteriores, arriba y abajo | \sideset{_1^2}{_3^4}\prod_a^b |
||
{}_1^2\!\Omega_3^4 |
|||
Apilar | \overset{\alpha}{\omega} |
||
\underset{\alpha}{\omega} |
[Unparseable or potentially dangerous latex formula. Error 3 ] | ||
\overset{\alpha}{\underset{\gamma}{\omega}} |
|||
\stackrel{\alpha}{\omega} |
|||
Derivadas ( forzando el PNG) | x', y, f', f |
||
Subrayado, línea superior, vectores | \hat a \ \bar b \ \vec c |
||
\overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f} |
|||
\overline{g h i} \ \underline{j k l} |
|||
Flechas | A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C |
||
Llaves superiores | \overbrace{ 1+2+\cdots+100 }^{5050} |
||
Llaves inferiores | \underbrace{ a+b+\cdots+z }_{26} |
||
Sumatorios | \sum_{k=1}^N k^2 |
||
Productorio | \prod_{i=1}^N x_i |
||
Coproduct | \coprod_{i=1}^N x_i |
||
Límite | \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 |
||
Integral triple | \iiint_{E}^{V} \, dx\,dy\,dz |
||
Integral de línea | \oint_{C} x^3\, dx + 4y^2\, dy |
||
Intersecciones | \bigcap_1^{n} p |
||
Uniones | \bigcup_1^{k} p |
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