Created
November 11, 2015 22:46
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Matemáticas de Jero para el curso de LaTeX
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| <!DOCTYPE html> | |
| <html> | |
| <head> | |
| <meta charset="utf-8" /> | |
| <title>matematicas-jero</title> | |
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| .markdown-preview { font-family: Optima; } | |
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| border-bottom: 1px dotted lime; | |
| position: absolute; | |
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| border-bottom: 2px dotted rgba(255, 51, 51, 0.75); | |
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| pre.editor-colors, | |
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| color: #383a42; | |
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| pre.editor-colors .gutter .line-number.cursor-line, | |
| .host .gutter .line-number.cursor-line { | |
| color: #4d5375; | |
| background-color: #f2f2f2; | |
| } | |
| pre.editor-colors .gutter .line-number.cursor-line-no-selection, | |
| .host .gutter .line-number.cursor-line-no-selection { | |
| background-color: transparent; | |
| } | |
| pre.editor-colors .gutter .line-number .icon-right, | |
| .host .gutter .line-number .icon-right { | |
| color: #383a42; | |
| } | |
| pre.editor-colors .gutter:not(.git-diff-icon) .line-number.git-line-removed.git-line-removed::before, | |
| .host .gutter:not(.git-diff-icon) .line-number.git-line-removed.git-line-removed::before { | |
| bottom: -3px; | |
| } | |
| pre.editor-colors .gutter:not(.git-diff-icon) .line-number.git-line-removed::after, | |
| .host .gutter:not(.git-diff-icon) .line-number.git-line-removed::after { | |
| content: ""; | |
| position: absolute; | |
| left: 0px; | |
| bottom: 0px; | |
| width: 25px; | |
| border-bottom: 1px dotted rgba(255, 20, 20, 0.5); | |
| pointer-events: none; | |
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| pre.editor-colors .gutter .line-number.folded, | |
| .host .gutter .line-number.folded, | |
| pre.editor-colors .gutter .line-number:after, | |
| .host .gutter .line-number:after, | |
| pre.editor-colors .fold-marker:after, | |
| .host .fold-marker:after { | |
| color: #4d5375; | |
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| color: #a0a1a7; | |
| font-style: italic; | |
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| .entity.name.type { | |
| color: #c18401; | |
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| color: #50a14f; | |
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| color: #a626a4; | |
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| color: #a626a4; | |
| } | |
| .keyword.operator { | |
| color: #383a42; | |
| } | |
| .keyword.other.special-method { | |
| color: #4078f2; | |
| } | |
| .keyword.other.unit { | |
| color: #986801; | |
| } | |
| .storage { | |
| color: #a626a4; | |
| } | |
| .storage.type.annotation, | |
| .storage.type.primitive { | |
| color: #a626a4; | |
| } | |
| .storage.modifier.package, | |
| .storage.modifier.import { | |
| color: #383a42; | |
| } | |
| .constant { | |
| color: #986801; | |
| } | |
| .constant.variable { | |
| color: #986801; | |
| } | |
| .constant.character.escape { | |
| color: #0184bc; | |
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| .constant.numeric { | |
| color: #986801; | |
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| .constant.other.color { | |
| color: #0184bc; | |
| } | |
| .constant.other.symbol { | |
| color: #0184bc; | |
| } | |
| .variable { | |
| color: #e45649; | |
| } | |
| .variable.interpolation { | |
| color: #ca1243; | |
| } | |
| .variable.parameter { | |
| color: #383a42; | |
| } | |
| .string { | |
| color: #50a14f; | |
| } | |
| .string.regexp { | |
| color: #0184bc; | |
| } | |
| .string.regexp .source.ruby.embedded { | |
| color: #c18401; | |
| } | |
| .string.other.link { | |
| color: #e45649; | |
| } | |
| .punctuation.definition.comment { | |
| color: #a0a1a7; | |
| } | |
| .punctuation.definition.method-parameters, | |
| .punctuation.definition.function-parameters, | |
| .punctuation.definition.parameters, | |
| .punctuation.definition.separator, | |
| .punctuation.definition.seperator, | |
| .punctuation.definition.array { | |
| color: #383a42; | |
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| .punctuation.definition.heading, | |
| .punctuation.definition.identity { | |
| color: #4078f2; | |
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| color: #c18401; | |
| font-weight: bold; | |
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| color: #a626a4; | |
| font-style: italic; | |
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| .punctuation.section.method, | |
| .punctuation.section.class, | |
| .punctuation.section.inner-class { | |
| color: #383a42; | |
| } | |
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| color: #c18401; | |
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| } | |
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| color: #0184bc; | |
| } | |
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| color: #4078f2; | |
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| color: #4078f2; | |
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| .meta.class { | |
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| color: #383a42; | |
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| color: #e45649; | |
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| color: #4078f2; | |
| } | |
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| color: #a626a4; | |
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| background-color: #373b41; | |
| color: #383a42; | |
| } | |
| .meta.tag { | |
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| } | |
| .none { | |
| color: #383a42; | |
| } | |
| .invalid.deprecated { | |
| color: #000000 !important; | |
| background-color: #f2a60d !important; | |
| } | |
| .invalid.illegal { | |
| color: #ffffff !important; | |
| background-color: #ff1414 !important; | |
| } | |
| .markup.bold { | |
| color: #986801; | |
| font-weight: bold; | |
| } | |
| .markup.changed { | |
| color: #a626a4; | |
| } | |
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| color: #e45649; | |
| } | |
| .markup.italic { | |
| color: #a626a4; | |
| font-style: italic; | |
| } | |
| .markup.heading .punctuation.definition.heading { | |
| color: #4078f2; | |
| } | |
| .markup.inserted { | |
| color: #50a14f; | |
| } | |
| .markup.list { | |
| color: #e45649; | |
| } | |
| .markup.quote { | |
| color: #986801; | |
| } | |
| .markup.raw { | |
| color: #50a14f; | |
| } | |
| .source.cs .keyword.operator { | |
| color: #a626a4; | |
| } | |
| .source.css .property-name, | |
| .source.css .property-value { | |
| color: #696c77; | |
| } | |
| .source.css .property-name.support, | |
| .source.css .property-value.support { | |
| color: #383a42; | |
| } | |
| .source.gfm .markup { | |
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| } | |
| .source.gfm .markup.heading { | |
| color: #e45649; | |
| } | |
| .source.gfm .markup.link { | |
| color: #a626a4; | |
| } | |
| .source.gfm .link .entity { | |
| color: #4078f2; | |
| } | |
| .source.ini .keyword.other.definition.ini { | |
| color: #e45649; | |
| } | |
| .source.java .storage.modifier.import { | |
| color: #c18401; | |
| } | |
| .source.java .storage.type { | |
| color: #c18401; | |
| } | |
| .source.java-properties .meta.key-pair { | |
| color: #e45649; | |
| } | |
| .source.java-properties .meta.key-pair > .punctuation { | |
| color: #383a42; | |
| } | |
| .source.json .meta.structure.dictionary.json > .string.quoted.json { | |
| color: #e45649; | |
| } | |
| .source.json .meta.structure.dictionary.json > .string.quoted.json > .punctuation.string { | |
| color: #e45649; | |
| } | |
| .source.json .meta.structure.dictionary.json > .value.json > .string.quoted.json, | |
| .source.json .meta.structure.array.json > .value.json > .string.quoted.json, | |
| .source.json .meta.structure.dictionary.json > .value.json > .string.quoted.json > .punctuation, | |
| .source.json .meta.structure.array.json > .value.json > .string.quoted.json > .punctuation { | |
| color: #50a14f; | |
| } | |
| .source.json .meta.structure.dictionary.json > .constant.language.json, | |
| .source.json .meta.structure.array.json > .constant.language.json { | |
| color: #0184bc; | |
| } | |
| .source.ruby .constant.other.symbol > .punctuation { | |
| color: inherit; | |
| } | |
| .source.python .keyword.operator.logical.python { | |
| color: #a626a4; | |
| } | |
| .source.python .variable.parameter { | |
| color: #986801; | |
| } | |
| </style> | |
| </head> | |
| <body class='markdown-preview'><h1>Matemáticas</h1> | |
| <p>Hay dos formas de escribir matemáticas: en la misma línea o centrado en una línea separada.</p> | |
| <ul> | |
| <li>Para escribir matemáticas <em>en línea</em> agrupamos el texto entre dólares. Por ejemplo,</li> | |
| </ul> | |
| <pre class="editor-colors lang-latex"><div class="line"><span class="text plain null-grammar"><span>$\cos(x+y)^{2}=\sqrt{2+x^2}$</span></span></div></pre> | |
| <p>produce <span class="math"><script type="math/tex">\cos(x+y)^{2}=\sqrt{2+x^2}</script></span>.</p> | |
| <ul> | |
| <li>Para escribir matemáticas centradas en una línea separada, agrupamos la fórmula entre \[ \] o con dólares dobles. Es recomendable la primera opción. Por ejemplo</li> | |
| </ul> | |
| <pre class="editor-colors lang-latex"><div class="line"><span class="text plain null-grammar"><span>\[</span></span></div><div class="line"><span class="text plain null-grammar"><span>\frac{x+y}{2x-1}=\sqrt{\log(x)^2+1}</span></span></div><div class="line"><span class="text plain null-grammar"><span>\]</span></span></div></pre> | |
| <p>produce</p> | |
| <span class="math"><script type="math/tex; mode=display">\frac{x+y}{2x-1}=\sqrt{\log(x)^2+1} | |
| </script></span> | |
| <h3>Espaciado</h3> | |
| <p>Los espacios dentro del modo matemático no se tienen en cuenta.</p> | |
| <p>El espacio dentro las fórmulas es distinto al espacio en modo texto. Compara lo siguiente:</p> | |
| <pre class="editor-colors lang-latex"><div class="line"><span class="text plain null-grammar"><span>Sea $x=1,2$ o $3$ con sea $x=1$, $2$ o $3$</span></span></div></pre> | |
| <p>La forma correcta de escribirlo es la <em>segunda</em> si queremos que LaTeX use el espaciado que se considera correcto.</p> | |
| <h2>Construcciones básicas</h2> | |
| <h3>Operaciones aritméticas, subíndices y superíndices</h3> | |
| <pre class="editor-colors lang-latex"><div class="line"><span class="text plain null-grammar"><span>$a + b$, $a - b$, $-a$, $a / b$, $a b$, $a \cdot b$, $a \times b$, $a \div b$</span></span></div></pre> | |
| <p>produce | |
| <span class="math"><script type="math/tex">a + b</script></span>, <span class="math"><script type="math/tex">a - b</script></span>, <span class="math"><script type="math/tex">-a</script></span>, <span class="math"><script type="math/tex">a / b</script></span>, <span class="math"><script type="math/tex">a b</script></span>, <span class="math"><script type="math/tex">a \cdot b</script></span>, <span class="math"><script type="math/tex">a \times b</script></span>, <span class="math"><script type="math/tex">a \div b</script></span> | |
| Puedes escribir subíndices y superíndices de la siguiente forma:</p> | |
| <pre class="editor-colors lang-latex"><div class="line"><span class="text plain null-grammar"><span>n^{2}, x^{1/x}, x_{n}, lim_{x \to \infty}</span></span></div></pre> | |
| <p>que da como resultado</p> | |
| <span class="math"><script type="math/tex; mode=display">n^{2}, x^{1/x}, x_{n}, \lim_{x \to \infty} | |
| </script></span> | |
| <p>Se pueden anidar y usar subíndices y superíndices al mismo tiempo:</p> | |
| <pre class="editor-colors lang-latex"><div class="line"><span class="text plain null-grammar"><span>\sum_{n=1}^{\infty} x^{x^n}</span></span></div></pre> | |
| <span class="math"><script type="math/tex; mode=display">\sum_{n=1}^{\infty} x^{x^n} | |
| </script></span> | |
| <p>Las fracciones se escriben con el comando <code style="font-family: Courier;">\frac{numerador}{denominador}</code></p> | |
| <pre class="editor-colors lang-latex"><div class="line"><span class="text plain null-grammar"><span>\frac{a}{b}, \tfrac{1}{2},\dfrac{1}{2}</span></span></div></pre> | |
| <p>produce | |
| <span class="math"><script type="math/tex">\frac{a}{b}</script></span>, <span class="math"><script type="math/tex">\tfrac{1}{2}</script></span>, <span class="math"><script type="math/tex">\dfrac{1}{2}</script></span></p> | |
| <p>frac se ajusta su tamaño dependiendo del contexto: si está en una línea es pequeño (como tfrac), si está en una línea separada aumenta (como dfrac). Podemos forzar un comportamiento u otro usando tfrac o dfrac.</p> | |
| <h3>Números binómicos</h3> | |
| <p><code style="font-family: Courier;">\binom{a}{b}</code> produce <span class="math"><script type="math/tex">\binom{a}{b}</script></span>. Al igual que con frac, se | |
| puede alterar su tamaño usando <code style="font-family: Courier;">tbinom{a}{b}</code> o <code style="font-family: Courier;">dbinom{a}{b}</code> y se obtiene <span class="math"><script type="math/tex">\tbinom{a}{b}</script></span> y <span class="math"><script type="math/tex">\dbinom{a}{b}</script></span>.</p> | |
| <h3>Puntos suspensivos</h3> | |
| <p>En lugar de escribir tres puntos seguidos, <code style="font-family: Courier;">\dots, \ldots, \cdots</code> producen puntos suspensivos con el espaciado correcto. <code style="font-family: Courier;">\dots</code> intenta adaptarse al entorno. <code style="font-family: Courier;">\ldots</code> da como resultado puntos “bajos” y <code style="font-family: Courier;">\cdots</code>centrados. Un ejemplo:</p> | |
| <pre class="editor-colors lang-latex"><div class="line"><span class="text plain null-grammar"><span>x=1,2,\ldots 3, x+y+\cdots +z, x\times y \times \dots z</span></span></div></pre> | |
| <p>produce <span class="math"><script type="math/tex">x=1,2,\ldots 3</script></span>, <span class="math"><script type="math/tex">x+y+\cdots +z</script></span>, <span class="math"><script type="math/tex">x\times y \times \dots \times z</script></span></p> | |
| <h3>Integrales</h3> | |
| <p>Varios símbolos de integral</p> | |
| <pre class="editor-colors lang-latex"><div class="line"><span class="text plain null-grammar"><span>$\oint \iint \iiint \iiiint \idotsint$</span></span></div></pre> | |
| <p><span class="math"><script type="math/tex">\oint \iint \iiint \iiiint \idotsint</script></span></p> | |
| <h3>Raíces</h3> | |
| <p><code style="font-family: Courier;">\sqrt{num}</code>y <code style="font-family: Courier;">\sqrt[n]{num}</code> permiten escribir raíces cuadradas y raíces n-ésimas.</p> | |
| <pre class="editor-colors lang-latex"><div class="line"><span class="text plain null-grammar"><span>$\sqrt{3}$, $\sqrt[4]{3}$ $\sqrt[\leftroot{2} \uproot{1} 6]{3}$</span></span></div></pre> | |
| <p><span class="math"><script type="math/tex">\sqrt{3}</script></span>, <span class="math"><script type="math/tex">\sqrt[4]{3}</script></span> <span class="math"><script type="math/tex">\sqrt[\leftroot{2} \uproot{1} 6]{3}</script></span></p> | |
| <h2>Texto en matemáticas</h2> | |
| <p>La orden \text{texto} permite incluir texto dentro de una fórmula con el mismo aspecto que el entorno</p> | |
| <pre class="editor-colors lang-latex"><div class="line"><span class="text plain null-grammar"><span>\[</span></span></div><div class="line"><span class="text plain null-grammar"><span>f(x)=x^2,\text{ si $x>0$ y $\cos(x)$ en otro caso}</span></span></div><div class="line"><span class="text plain null-grammar"><span>\]</span></span></div></pre> | |
| <span class="math"><script type="math/tex; mode=display">f(x)=x^2,\text{ si $x>0$ y $\cos(x)$ en otro caso} | |
| </script></span> | |
| <h3>Acentos, gorros,…</h3> | |
| <p><code style="font-family: Courier;">\hat{a}</code>, <code style="font-family: Courier;">\acute{a}</code>, <code style="font-family: Courier;">\breve{a}</code>, <code style="font-family: Courier;">\dot</code>, <code style="font-family: Courier;">\tilde</code>, <code style="font-family: Courier;">\mathring{A}</code> produce | |
| <span class="math"><script type="math/tex">\hat{a}, \acute{a}, \breve{a}, \dot{a}, \tilde{a}, \mathring{A}</script></span></p> | |
| <p>También se pueden escribir flechas sobre un texto usando <code style="font-family: Courier;">\vec{a}</code> o | |
| <code style="font-family: Courier;">\overrightarrow{abc}</code> <span class="math"><script type="math/tex">\overrightarrow{abc}</script></span></p> | |
| <p>Con el paquete <em>esvect</em> se pueden representar vectores mejor</p> | |
| <pre class="editor-colors lang-latex"><div class="line"><span class="text plain null-grammar"><span>\vv{a}, \; \vv{abc} , \; \vv*{a}{n}</span></span></div></pre> | |
| <h2>Operadores</h2> | |
| <p>LaTeX tiene predefinidos algunas funciones usuales, pero podemos añadir lo que deseemos con la orden <code style="font-family: Courier;">\DeclareMathOperator</code>. Para ello es necesario cargar el paquete amsmath</p> | |
| <p><span class="math"><script type="math/tex">\cos (x)</script></span>, <span class="math"><script type="math/tex">\sin(x)</script></span>, <span class="math"><script type="math/tex">\tan(x)</script></span>, <span class="math"><script type="math/tex">\arccos(x)</script></span>, <span class="math"><script type="math/tex">\log(x)</script></span>, <span class="math"><script type="math/tex">\ln (x)</script></span>, <span class="math"><script type="math/tex">\exp(x)</script></span>,… | |
| Usando</p> | |
| <pre class="editor-colors lang-latex"><div class="line"><span class="text plain null-grammar"><span>\DeclareMathOperator{\dist}{distancia}</span></span></div></pre> | |
| <p>en la cabecera del documento, está disponible el comando <code style="font-family: Courier;">\distancia</code></p> | |
| <h2>Sub y superíndices de nuevo</h2> | |
| <p>El comando <code style="font-family: Courier;">\texttt{substack}</code> para líneas centradas</p> | |
| <pre class="editor-colors lang-latex"><div class="line"><span class="text plain null-grammar"><span>\[</span></span></div><div class="line"><span class="text plain null-grammar"><span>\sum_{\substack{i=1\\j=123}} i+j</span></span></div><div class="line"><span class="text plain null-grammar"><span>\]</span></span></div></pre> | |
| <p>permite incluir subíndices o superíndices que ocupen varias líneas.</p> | |
| <span class="math"><script type="math/tex; mode=display">\sum_{\substack{i=1\\j=123}} i+j | |
| </script></span> | |
| <h2>Llaves y flechas</h2> | |
| <p>overbrace, underbrace, overline, underline</p> | |
| <span class="math"><script type="math/tex; mode=display">\overbrace{a+\underbrace{b+c}_{z}+d}^{n} | |
| </script></span> | |
| <p>overleftarrow, underleftarrow, overrightarrow, underrightarrow, | |
| overleftrightarrow, etc.</p> | |
| <h3>Más flechas</h3> | |
| <p><span class="math"><script type="math/tex">x\xrightarrow[a+b]{a-b+c} y</script></span></p> | |
| <h2>Más matemáticas</h2> | |
| <h3>Espacios</h3> | |
| <p>Se puede añadir o quitar espacio manualmente. Las formas más comunes de | |
| hacerlo son</p> | |
| <ul> | |
| <li>Añadir (poco) \textbackslash ,{} añade un espacio pequeño.</li> | |
| </ul> | |
| <span class="math"><script type="math/tex; mode=display">\int_{0}^{1} f(x)\, dx = \sqrt{x}\, n | |
| </script></span> | |
| <ul> | |
| <li>Añadir (algo más) \textbackslash quad y \textbackslash qquad añade la | |
| longitud de una letra m o de dos. Son espacios dinámicos (pueden variar | |
| un poco para ajustar las líneas).</li> | |
| </ul> | |
| <span class="math"><script type="math/tex; mode=display">f(x)=\cos (x), \quad \forall\, x \in [0,1] | |
| </script></span> | |
| <ul> | |
| <li>Quitar (poco) \textbackslash ! quita un espacio pequeño. Compara</li> | |
| </ul> | |
| <span class="math"><script type="math/tex; mode=display">\sin x/\log x \qquad \sin x /\! \log x | |
| </script></span> | |
| <h2>Entornos multilínea</h2> | |
| <p>Pueden ser de dos tipos: ajustados o alineados.</p> | |
| <h3>Entornos ajustados</h3> | |
| <p>Hay dos: <em>gather</em> y <em>multline</em>. El primero de ellos muestra las ecuaciones | |
| centradas una tras otra. Por ejemplo</p> | |
| <pre class="editor-colors lang-latex"><div class="line"><span class="text plain null-grammar"><span>\[</span></span></div><div class="line"><span class="text plain null-grammar"><span>\begin{gather}</span></span></div><div class="line"><span class="text plain null-grammar"><span>x+y+z_1\\+\int_0^1 f(x)\, \mathrm{d}x +\cos \left( \sqrt{x} \, \right)</span></span></div><div class="line"><span class="text plain null-grammar"><span>\end{gather}</span></span></div><div class="line"><span class="text plain null-grammar"><span>\]</span></span></div></pre> | |
| <span class="math"><script type="math/tex; mode=display">\begin{gather} | |
| x+y+z_1\\+\int_0^1 f(x)\, \mathrm{d}x +\cos \left( \sqrt{x} \, \right) | |
| \end{gather} | |
| </script></span> | |
| <p>El segundo, multline, alinea la primera fórmula a la izquierda, la última a la | |
| derecha y las intermedias, si las hay, las centra.</p> | |
| <pre class="editor-colors lang-latex"><div class="line"><span class="text plain null-grammar"><span>\[</span></span></div><div class="line"><span class="text plain null-grammar"><span>\begin{multline}</span></span></div><div class="line"><span class="text plain null-grammar"><span>x+y+z_1 + \lim_{x \to 0} \int_{0}^{x^2} f(x)\,\mathrm{d}x +</span></span></div><div class="line"><span class="text plain null-grammar"><span>\frac{x-1}{x+1} \\</span></span></div><div class="line"><span class="text plain null-grammar"><span>+x+y+z+\omega+\int_0^1 f(x)\, \mathrm{d}x +\cos \left( \sqrt{x} \, \right)</span></span></div><div class="line"><span class="text plain null-grammar"><span>\end{multline}</span></span></div><div class="line"><span class="text plain null-grammar"><span>\]</span></span></div></pre> | |
| <span class="math"><script type="math/tex; mode=display">\begin{multline} | |
| x+y+z_1 + \lim_{x \to 0} \int_{0}^{x^2} f(x)\,\mathrm{d}x + | |
| \frac{x-1}{x+1} \\ | |
| +x+y+z+\omega+\int_0^1 f(x)\, \mathrm{d}x +\cos \left( \sqrt{x} \, \right) | |
| \end{multline} | |
| </script></span> | |
| <h3>Entornos alineados</h3> | |
| <p>Hay varios entornos de este tipo, dependiendo de cómo estén alineadas | |
| las columnas.</p> | |
| <p>En primer lugar, <em>align</em> muestra las columnas centradas.</p> | |
| <pre class="editor-colors lang-latex"><div class="line"><span class="text plain null-grammar"><span>\[</span></span></div><div class="line"><span class="text plain null-grammar"><span>\left.</span></span></div><div class="line"><span class="text plain null-grammar"><span>\begin{align}</span></span></div><div class="line"><span class="text plain null-grammar"><span> x+y & = 6 \\</span></span></div><div class="line"><span class="text plain null-grammar"><span>2x-3y & = 4</span></span></div><div class="line"><span class="text plain null-grammar"><span>\end{align}</span></span></div><div class="line"><span class="text plain null-grammar"><span>\right\}</span></span></div><div class="line"><span class="text plain null-grammar"><span>\]</span></span></div></pre> | |
| <span class="math"><script type="math/tex; mode=display">\left. | |
| \begin{align} | |
| x+y & = 6 \\ | |
| 2x-3y & = 4 | |
| \end{align} | |
| \right\} | |
| </script></span> | |
| <p><em>flalign</em> es una variante de align que alinea a la izquierda la primera | |
| columna y a la derecha la última</p> | |
| <pre class="editor-colors lang-latex"><div class="line"><span class="text plain null-grammar"><span>\[</span></span></div><div class="line"><span class="text plain null-grammar"><span>\begin{flalign}</span></span></div><div class="line"><span class="text plain null-grammar"><span> x+y +2 z & = 6 & 2u+4v & =8 \\</span></span></div><div class="line"><span class="text plain null-grammar"><span>2x-3y & = 4 & 3u-4v & = 10</span></span></div><div class="line"><span class="text plain null-grammar"><span>\end{flalign}</span></span></div><div class="line"><span class="text plain null-grammar"><span>\]</span></span></div></pre> | |
| <p>Por último, <em>alignat</em>, que tiene un comportamiento un poco distinto: hay | |
| que decir cuántas columnas hay y añadir los espacios entre ellas | |
| manualmente.</p> | |
| <pre class="editor-colors lang-latex"><div class="line"><span class="text plain null-grammar"><span>\[</span></span></div><div class="line"><span class="text plain null-grammar"><span>\begin{alignat}{4}</span></span></div><div class="line"><span class="text plain null-grammar"><span> f(x) &= x + yz & g(x) &= x + y + z\\</span></span></div><div class="line"><span class="text plain null-grammar"><span> h(x) &= xy + xz + yz \qquad & k(x) &= (x+y)(x+z)(y+z)</span></span></div><div class="line"><span class="text plain null-grammar"><span> \notag</span></span></div><div class="line"><span class="text plain null-grammar"><span>\end{alignat}</span></span></div><div class="line"><span class="text plain null-grammar"><span>\]</span></span></div></pre> | |
| <span class="math"><script type="math/tex; mode=display">\begin{alignat}{4} | |
| f(x) &= x + yz & g(x) &= x + y + z\\ | |
| h(x) &= xy + xz + yz \qquad & k(x) &= (x+y)(x+z)(y+z) | |
| \notag | |
| \end{alignat} | |
| </script></span> | |
| <p>Es útil en casos como el siguiente:</p> | |
| <pre class="editor-colors lang-latex"><div class="line"><span class="text plain null-grammar"><span>\[</span></span></div><div class="line"><span class="text plain null-grammar"><span>\begin{alignat}{3}</span></span></div><div class="line"><span class="text plain null-grammar"><span> x &= x (y+z) &</span></span></div><div class="line"><span class="text plain null-grammar"><span> &\quad\text{(propiedad distributiva)}\\</span></span></div><div class="line"><span class="text plain null-grammar"><span> &= (x y) + (x z) & &</span></span></div><div class="line"><span class="text plain null-grammar"><span> \quad\text{(usamos ahora que $x=0$)}\notag\\</span></span></div><div class="line"><span class="text plain null-grammar"><span> &= y z</span></span></div><div class="line"><span class="text plain null-grammar"><span>\end{alignat}</span></span></div><div class="line"><span class="text plain null-grammar"><span>\]</span></span></div></pre> | |
| <span class="math"><script type="math/tex; mode=display">\begin{alignat}{3} | |
| x &= x (y+z) & | |
| &\quad\text{(propiedad distributiva)}\\ | |
| &= (x y) + (x z) & & | |
| \quad\text{(usamos ahora que $x=0$)}\notag\\ | |
| &= y z | |
| \end{alignat} | |
| </script></span> | |
| <h3>Entornos subsidiarios</h3> | |
| <p>align, alignat y gather tienen versiones subsidiarias que tienen que ir dentro de un entorno matemático.</p> | |
| <span class="math"><script type="math/tex; mode=display">\begin{aligned}[c] | |
| x &= 3 + \mathbf{p} + \alpha\\ | |
| y &= 4 + \mathbf{q}\\ | |
| z &= 5 + \mathbf{r}\\ | |
| u &=6 + \mathbf{s} | |
| \end{aligned} | |
| \text{\quad using\quad} | |
| \begin{gathered}[b] | |
| \mathbf{p} = 5 + a + \alpha\\ | |
| \mathbf{q} = 12\\ | |
| \mathbf{r} = 13\\ | |
| \mathbf{s} = 11 + d | |
| \end{gathered} | |
| </script></span> | |
| <span class="math"><script type="math/tex; mode=display">\left. | |
| \begin{aligned}[c] | |
| wx&=u\\ | |
| wy&=v\\ | |
| w&=10 | |
| \end{aligned} | |
| \right\} | |
| \qquad\Longleftrightarrow\qquad | |
| \begin{aligned}[c] | |
| x&=u/w\\ | |
| y&=v/w\\ | |
| \end{aligned} | |
| </script></span> | |
| <p>El entorno más flexible es split. Se puede usar sólo</p> | |
| <pre class="editor-colors lang-latex"><div class="line"><span class="text plain null-grammar"><span>\[</span></span></div><div class="line"><span class="text plain null-grammar"><span>\begin{split}</span></span></div><div class="line"><span class="text plain null-grammar"><span> (x_{1}x_{2}&x_{3}x_{4}x_{5}x_{6})^{2}\\</span></span></div><div class="line"><span class="text plain null-grammar"><span> &+ (x_{1}x_{2}x_{3}x_{4}x_{5}</span></span></div><div class="line"><span class="text plain null-grammar"><span> + x_{1}x_{3}x_{4}x_{5}x_{6}</span></span></div><div class="line"><span class="text plain null-grammar"><span> + x_{1}x_{2}x_{4}x_{5}x_{6}</span></span></div><div class="line"><span class="text plain null-grammar"><span> + x_{1}x_{2}x_{3}x_{5}x_{6})^{2}</span></span></div><div class="line"><span class="text plain null-grammar"><span>\end{split}</span></span></div><div class="line"><span class="text plain null-grammar"><span>\]</span></span></div></pre> | |
| <span class="math"><script type="math/tex; mode=display">\begin{split} | |
| (x_{1}x_{2}&x_{3}x_{4}x_{5}x_{6})^{2}\\ | |
| &+ (x_{1}x_{2}x_{3}x_{4}x_{5} | |
| + x_{1}x_{3}x_{4}x_{5}x_{6} | |
| + x_{1}x_{2}x_{4}x_{5}x_{6} | |
| + x_{1}x_{2}x_{3}x_{5}x_{6})^{2} | |
| \end{split} | |
| </script></span> | |
| <p>o dentro de otro y se alinea como corresponda</p> | |
| <pre class="editor-colors lang-latex"><div class="line"><span class="text plain null-grammar"><span>\[</span></span></div><div class="line"><span class="text plain null-grammar"><span>\begin{align}</span></span></div><div class="line"><span class="text plain null-grammar"><span> \left.</span></span></div><div class="line"><span class="text plain null-grammar"><span> \begin{split}</span></span></div><div class="line"><span class="text plain null-grammar"><span> f(x) & = (x_{1}x_{2} ) \\</span></span></div><div class="line"><span class="text plain null-grammar"><span> & = x+y</span></span></div><div class="line"><span class="text plain null-grammar"><span> \end{split}</span></span></div><div class="line"><span class="text plain null-grammar"><span> \right\}</span></span></div><div class="line"><span class="text plain null-grammar"><span> \implies y+z</span></span></div><div class="line"><span class="text plain null-grammar"><span>\end{align}</span></span></div><div class="line"><span class="text plain null-grammar"><span>\]</span></span></div></pre> | |
| <span class="math"><script type="math/tex; mode=display">\begin{align} | |
| \left. | |
| \begin{split} | |
| f(x) & = (x_{1}x_{2} ) \\ | |
| & = x+y | |
| \end{split} | |
| \right\} | |
| \implies y+z | |
| \end{align} | |
| </script></span></body> | |
| </html> |
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