Parenteser och grupperingar

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.

Alla parenteser får bara förekomma som enhetliga par. Parenteserna har några gemensamma drag:

Alla parentestyper har en grupperande funktion, likt den som beskrivs för "{}"-parenteserna.

Du kan använda alla parentestyper, dvs även de synliga, för att definiera tomma grupper. Det inneslutna uttrycket får alltså vara tomt.

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.

Eftersom "left" och "right" säkerställer en entydig tilldelning av parenteserna till varandra, kan Du använda varje enskild parentes som argument för dessa båda, även för höger parentes på vänster sida och omvänt. I stället för en parentes kan det även stå "none", vilket betyder att det inte visas någon parentes på detta ställe och att det inte heller reserveras utrymme för någon parentes. På så vis kan Du t ex bilda följande uttryck:

• left lbrace x right none

• left [ x right )

• left ] x right [

• left rangle x right lfloor

För "left" och "right" gäller samma regler som för de andra parenteserna. De fungerar även grupperande och får innesluta det tomma uttrycket.

En kombination av parenteser som inte hör till varandra, samt parenteser på bara en sida och positionsbyte av höger och vänster parentes förekommer ofta. Ett exempel från matematiken, som dock inte kan skrivas in så, förtydligar detta:

• [2, 3) - intervall som är öppet till höger

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.

En fullständig översikt ser därför ut som följer:

• \{ eller \lbrace, \} eller \rbrace

• \(, \)

• \[, \]

• \langle, \rangle

• \lceil, \rceil

• \lfloor, \rfloor

• \lline, \rline

• \ldline, \rdline

Därmed kan Du bygga upp sådana intervall som det ovanstående utan problem i LibreOffice Math: \[2", "3\) eller "\]2", "3\[ (Observera: Dessa citattecken hör till inmatningen.)

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})}}}}.

• Den här exempelformeln analyseras från vänster till höger. Operationerna påverkar bara motsvarande grupp (eller uttryck). Operationer som finns längre till höger "ersätter" eller "kombinerar sig själva" med sina föregångare.

• 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 ..." och "font ..." samt "size n" (n är ett decimaltal) ersätter eventuella föregående operationer av samma typ,

för "size +n", "size -n", "size *n" och "size /n" kombineras operationernas effekter,

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 )

Exempel (med basstorlek 12 och 50% för index):

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}

Följande exempel ser däremot inte identiska ut:

x^{a_{size 8 n}}

x^{a_{size +2 n}}

x^{a_{size *1.333 n}}