# Paréntesis y grupos

The quotation marks in the examples are used to emphasize text and do not belong to the content of the formulas and commands.

Al introducir les fórmules d'exemplu na ventana Comandos, nun escaeza que los espacios son necesarios pa xenerar una estructura correcta.

Braces "{}" are used to group expressions together to form one new expression. For example, sqrt {x * y} is the square root of the entire product x*y, while sqrt x * y is the square root of x multiplied by y. Braces do not require an extra space.

Set brackets were previously inserted in the Elements pane or directly in the Commands window as "left lbrace <?> right rbrace". Now, a left and a right set bracket can also be inserted using "lbrace" and "rbrace", with or without wildcards.

There are a total of eight (8) different types of brackets available. The "ceil" and "floor" brackets are often used for rounding up or down the argument to the next integer: lceil -3.7 rceil = -3 or lfloor -3.7 rfloor = -4.

Operator brackets, also known as Bra-kets (angle brackets with a vertical line in between), are common in Physics notation: langle a mline b rangle or langle a mline b mline c over d mline e rangle. The height and positioning of the vertical lines always corresponds exactly to the enclosing brackets.

Los paréntesis namái podrán utilizase cola correspondiente pareya. Los paréntesis tienen los siguientes puntos de mancomún:

Tolos paréntesis tienen una función d'agrupación, tal como se describió nel casu de los paréntesis "{}".

Tolos paréntesis, los visibles tamién, dexen definir grupos baleros. En tal casu, la espresión que zarren pue tar balera.

Brackets do not adjust their size to the enclosed expression. For example, if you want ( a over b ) with a bracket size adjusted to a and b you must insert "left" and "right". Entering left(a over b right) produces appropriate sizing. If, however, the brackets themselves are part of the expression whose size is changed, they are included the size change: size 3(a over b) and size 12(a over b). The sizing of the bracket-to-expression ratio does not change in any way.

Como "left" y "right" garanticen una asignación única de los paréntesis, cada paréntesis individual pue utilizase como argumentu pa estos dos comandos, inda poner paréntesis drechos nel llau izquierdu, o paréntesis izquierdos a la drecha. En llugar d'un paréntesis tamién pue apaecer "none", lo que significa que nun s'amuesa nengún paréntesis y, nun se reserva espaciu pa nengunu. D'esta miente, ye posible crear les siguientes espresiones:

• left lbrace x right none

• left [ x right )

• left ] x right [

• left rangle x right lfloor

Para "left" y "right" aplíquense les mesmes regles que pa los demás paréntesissobremou, presenten un efeutu agrupador y puen zarrar la espresión balera.

La combinación de paréntesis ensin rellacionar ente sigo, como de paréntesis en namái una páxina o'l cambéu de posición de derecha y esquierda, producir con frecuencia. A mou d'esplicación, presentamos un exemplu matemáticu que sicasí nun pue introducise asina:

• [2, 3) - intervalu abiertu a la derecha

Using "left" and "right" makes the above expression valid in LibreOffice Math: left [2, 3 right ). However, the brackets do not have any fixed size because they adjust to the argument. Setting a single bracket is a bit cumbersome. Therefore, there you can display single brackets with a fixed size by placing a "\" (backslash) in front of normal brackets. These brackets then act like any other symbol and no longer have the special functionality of brackets; that is they do not work as group builders and their orientation corresponds to that of other symbols. See size *2 \langle x \rangle and size *2 langle x rangle.

El resume completu ye'l siguiente:

• \{ o \lbrace, \} o \brace

• $$,$$

• $,$

• \langle, \rangle

• \lceil, \rceil

• \lfloor, \rfloor

• \lline, \rline

• \ldline, \rdline

D'esta miente puen crease ensin problemes intervalos como'l que s'esplicó enantes nel casu de LibreOffice Math: $2", "3\) o "$2", "3\[ (Atención: estes comines pertenecen a la entrada).

Utilice estes comines, que se llogren con Mayús+2, y non les tipográfiques. Polo xeneral, los signos de puntuación (como la coma nesti casu) inclúyense como testu. Anque tamién pue escribise "\[2,~3\)", ye preferible la opción anterior. Nel exemplu anterior, "tamañu fixu" siempres describe un tamañu de paréntesis que depende del tamañu de lletra que s'utiliza

Nesting groups within each other is relatively problem-free. In the formula hat "{a + b}" the "hat" is displayed simply over the center of "{a + b}". Also, color red lceil a rceil and grave hat langle x * y rangle work as expected. The result of the latter can be compared to grave {hat langle x * y rangle}. These attributes do not compete, but rather can be combined.

This differs slightly for competing or mutually influencing attributes. This is often the case with font attributes. For example, which color does the b have in color yellow color red (a + color green b), or which size does it have in size *4 (a + size /2 b)? Given a base size of 12, does it have the size 48, 6 or even 24 (which could be seen as a combination)? The following are basic resolution rules, which will be followed consistently in the future. In general, the rules apply to all group operations. This only has a visible effect on the font attributes, like "bold", "ital", "phantom", "size", "color" and "font":

• Group operations in sequence are treated as if every single operation is enclosed by braces. They are nested, and in every level there can be no more than one operation. Here is an example of a formula with many group operations:

size 12 color red font sans size -5 (a + size 8 b)" like "{size 12{color red{font sans{size -5 (a + {size 8 b})}}}}.

• Esta fórmula d'exemplu interprétase entós d'esquierda a derecha. Les operaciones namái afecten al so grupu (o espresión) correspondiente. Les operaciones más a la derecha "sustitúin" o "combinar con" les que les anteceden.

• A group operation does not have any effect on higher-level operations but rather affects only lower-level groups and expressions, including their brackets and super-/subscripts. For example,

a + size *2 (b * size -8 c_1)^2

"color ..." y "font ..." al igual que "size n" (n ye un númberu decimal) sustitúin, nel so casu, les operaciones precedentes del mesmu tipu,

nel casu de "size +n", "size -n", "size *n" y "size /n" combínense los efeutos de les operaciones,

size *2 size -5 a would be double the starting size minus 5

font sans ( a + font serif b)

size *2 ( a + size /2 b )

To change the size of a formula, use "size +" or -,*,/. Do not use "size n". These can easily be used in any context. This enables you to copy to other areas by using Copy and Paste, and the result remains the same. Furthermore, such expressions survive a change of base size in the menu better than when using "size n". If you use only size * and size / (for example, size *1.24 a or size /0.86 a) the proportions remain intact.

Exemplos (col tamañu básicu 12 y 50 % pa los índices):

Exactly identical proportions with size 18 a_n and size *1.5 a_n.

This differs in different contexts: x^{size 18 a_n} and x^{size *1.5 a_n}

Examples with size +n for a comparison. They look identical:

a_{size 8 n}

a_{size +2 n}

a_{size *1.333 n}

Otra mou, los siguientes exemplos amuesen un aspeutu distintu:

x^{a_{size 8 n}}

x^{a_{size +2 n}}

x^{a_{size *1.333 n}}

All n here have different sizes. The size 1.333 results from 8/6, the desired size divided by the default index size 6. (Index size 50% with a base size of 12)