Zátvorky a zoskupenie

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


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Pri p├şsan├ş vzorcov do okna Pr├şkazy mus├şte pre zachovanie spr├ívnej ┼ítrukt├║ry p├şsa┼ą medzi pr├şkazy 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.

V┼íetky z├ítvorky m├┤┼żu by┼ą pou┼żit├ę iba v p├íroch. Z├ítvorky maj├║ niektor├ę v┼íeobecn├ę charakteristick├ę vlastnosti:

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

V┼íetky typy z├ítvoriek, vr├ítane t├Żch, ktor├ę s├║ zrejm├ę, umo┼żnia pr├ízdne zoskupovanie defin├şcii. Vlo┼żen├Ż v├Żraz m├┤┼że by┼ą preto pr├ízdny.

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.

Nap├şsanie "left" alebo "right" zabezpe─Ź├ş jedine─Źn├ę priradenie z├ítvorky; ka┼żd├í jednoduch├í z├ítvorka m├┤┼że by┼ą pou┼żit├í ako d├┤vod pre tieto dva pr├şkazy, dokonca ukladaj├║ prav├ę z├ítvorky na─żavo, alebo ─żav├ę z├ítvorky vpravo. Namiesto z├ítvorky m├┤┼żete pou┼żi┼ą "none" ozna─Źenie, ─Źo znamen├í, ┼że tam nie je zobrazen├í z├ítvorka a ┼że tam nie je ani rezervovan├Ż priestor pre z├ítvorku. Pou┼żit├şm tohto pr├şkazu m├┤┼żete vytvori┼ą nasledovn├ę kombin├ície znakov:

Tie ist├ę pravidl├í aplikuj├║ "left" a "right" na druh├║ z├ítvorku: tie┼ż pracuj├║ ako skupinov├ę nadstavby a m├┤┼żu uzaviera┼ą pr├ízdne kombin├ície znakov.

Nevhodn├í kombin├ícia z├ítvoriek, jednoduch├Żch z├ítvoriek a premiestnenie ─żav├Żch a prav├Żch z├ítvoriek nastane ─Źasto v matematick├Żch vzorcoch. N├ísledkom toho je vzorec, ktor├Ż vygeneruje chybov├║ hl├í┼íku:

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 kompletn├Ż preh─żad

Takto mo┼żno v LibreOffice Math bez probl├ęmov zap├şsa┼ą intervaly (ako bol ten vy┼í┼íie): \[2", "3\) alebo "\]2", "3\[ (Pozor: tieto ├║vodzovky s├║ s├║─Źas┼ąou vzorca.)

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Pozn├ímka: je potrebn├ę zad├íva┼ą ┼ítandardn├ę ├║vodzovky, kror├ę m├┤┼żu by┼ą z├şskan├ę pomocou Shift+2 a nie ├║vodzovky typografick├ę. Obecne sa interpunk─Źn├ę znamienka (napr. v tomto pr├şpade ─Źiarka) zad├ívaj├║ ako text. Tie┼ż je mo┼żn├ę nap├şsa┼ą "\[2,~3\)", ale vy┼í┼íie uveden├Ż pr├şklad je lep┼í├ş. V predch├ídzaj├║cich pr├şkladoch znamen├í "pevn├í ve─żkos┼ą", ┼że ve─żkos┼ą je z├ívisl├í na pou┼żitom p├şsme.


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 ..." a "font ..." ako aj "size n" (n je desatinn├ę ─Ź├şslo) ktor├ę nahrad├ş niektor├ę predo┼íl├ę oper├ície rovnak├ęho typu

za "size +n", "size -n", "size *n", a "size /n" efektivita oper├íci├ş je kombinovan├í,

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 )

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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.


Pr├şklad (so z├íkladnou ve─żkos┼ąou 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}

Nasleduj├║ pr├şklady, ktor├ę nevyzeraj├║ rovkano:

x^{a_{size 8 n}}

x^{a_{size +2 n}}

x^{a_{size *1.333 n}}

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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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