Parenteser och grupperingar

Symbolen Info

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


Varningssymbol

NÀr du skriver exempel i kommandofönstret manuellt bör du tÀnka pÄ att du ofta mÄste anvÀnda blanksteg för ge exemplen korrekt uppbyggnad.


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 fÄr bara förekomma som enhetliga par. Parenteserna har nÄgra gemensamma drag:

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

Du kan anvÀnda alla parentestyper, dvs Àven de synliga, för att definiera tomma grupper. Det inneslutna uttrycket fÄr alltsÄ 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" sÀkerstÀller en entydig tilldelning av parenteserna till varandra, kan Du anvÀnda varje enskild parentes som argument för dessa bÄda, Àven för höger parentes pÄ vÀnster sida och omvÀnt. I stÀllet för en parentes kan det Àven stÄ "none", vilket betyder att det inte visas nÄgon parentes pÄ detta stÀlle och att det inte heller reserveras utrymme för nÄgon parentes. PÄ sÄ vis kan Du t ex bilda följande uttryck:

För "left" och "right" gÀller samma regler som för de andra parenteserna. De fungerar Àven grupperande och fÄr innesluta det tomma uttrycket.

En kombination av parenteser som inte hör till varandra, samt parenteser pÄ bara en sida och positionsbyte av höger och vÀnster parentes förekommer ofta. Ett exempel frÄn matematiken, som dock inte kan skrivas in sÄ, förtydligar detta:

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 fullstÀndig översikt ser dÀrför ut som följer:

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

Symbolen Info

Observera att citattecknen mĂ„ste anges och ska infogas med Skift+2. Det ska inte vara typografiska citattecken. Interpunktionstecken (till exempel komma i det hĂ€r fallet) ska vanligtvis anges som text. Även om det gĂ„r att skriva "\[2,~3\)" bör du skriva som i alternativet ovan. I föregĂ„ende exempel beskriver "fixed size" en parentesstorlek som Ă€r beroende av den teckensnittsstorlek som anvĂ€nds.


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":

"color ..." och "font ..." samt "size n" (n Àr ett decimaltal) ersÀtter eventuella föregÄende 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 )

Symbolen Tips

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.


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 dÀremot inte identiska ut:

x^{a_{size 8 n}}

x^{a_{size +2 n}}

x^{a_{size *1.333 n}}

Symbolen Info

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)


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