Zátvorky a Zoskupovanie

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# Zátvorky a zoskupenie

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

Pri písaní vzorcov do okna Príkazy musíte pre zachovanie správnej štruktúry písať medzi príkazy medzery.

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.

Všetky zátvorky môžu byť použité iba v pároch. Zátvorky majú niektoré všeobecné charakteristické vlastnosti:

All types of brackets have the same grouping function as described for "{}" brackets.

Všetky typy zátvoriek, vrátane tých, ktoré sú zrejmé, umožnia prázdne zoskupovanie definícii. Vložený výraz môže byť preto prázdny.

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.

Napísanie "left" alebo "right" zabezpečí jedinečné priradenie zátvorky; každá jednoduchá zátvorka môže byť použitá ako dôvod pre tieto dva príkazy, dokonca ukladajú pravé zátvorky naľavo, alebo ľavé zátvorky vpravo. Namiesto zátvorky môžete použiť "none" označenie, čo znamená, že tam nie je zobrazená zátvorka a že tam nie je ani rezervovaný priestor pre zátvorku. Použitím tohto príkazu môžete vytvoriť nasledovné kombinácie znakov:

- left lbrace x right none

- left [ x right )

- left ] x right [

- left rangle x right lfloor

Tie isté pravidlá aplikujú "left" a "right" na druhú zátvorku: tiež pracujú ako skupinové nadstavby a môžu uzavierať prázdne kombinácie znakov.

Nevhodná kombinácia zátvoriek, jednoduchých zátvoriek a premiestnenie ľavých a pravých zátvoriek nastane často v matematických vzorcoch. Následkom toho je vzorec, ktorý vygeneruje chybovú hlášku:

- [2, 3) - right open interval

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.

Nasleduje kompletný prehľad

- \{ alebo \lbrace, \} alebo \rbrace

- \(, \)

- \[, \]

- \langle, \rangle

- \lceil, \rceil

- \lfloor, \rfloor

- \lline, \rline

- \ldline, \rdline

Takto možno v LibreOffice Math bez problémov zapísať intervaly (ako bol ten vyššie): \[2", "3\) alebo "\]2", "3\[ (Pozor: tieto úvodzovky sú súčasťou vzorca.)

Poznámka: je potrebné zadávať štandardné úvodzovky, kroré môžu byť získané pomocou Shift+2 a nie úvodzovky typografické. Obecne sa interpunkčné znamienka (napr. v tomto prípade čiarka) zadávajú ako text. Tiež je možné napísať "\[2,~3\)", ale vyššie uvedený príklad je lepší. V predchádzajúcich príkladoch znamená "pevná veľkosť", že veľkosť je závislá na použitom písme.

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})}}}}.

- Tento príklad vzorca je potom interpretovaný zľava doprava. Operácie iba pôsobia na jeho príslušnú skupinu (alebo výraz). Operácie ďalej doprava "replace" alebo "combine themselves with" ich predchádzajú.

- 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 ..." a "font ..." ako aj "size n" (n je desatinné číslo) ktoré nahradí niektoré predošlé operácie rovnakého typu

za "size +n", "size -n", "size *n", a "size /n" efektivita operácií je kombinovaná,

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.

Príklad (so základnou veľkosťou 12 a 50% pre indexy):

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}

Nasledujú príklady, ktoré nevyzerajú rovkano:

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)

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