括號與分組

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# 括號及群組

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

當您在「指令」視窗中手動輸入範例時，請注意，空白字元是正確結構不可或缺的一部分。

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.

所有括號只能成對使用，它們具有一些共同的特徵：

所有的括號類型會像之前說明的「{}」一樣具群組功能。

所有的括號形式，包括看得見的，都可定義空白群組。封閉的表示式也可以是空白的。

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.

由於「left」和「right」彼此確認括號的指定，故可讓這兩個中的每個單獨括號作為參數，右括號也可以放在左側或是倒過來。以「none」來替代括號，也就是在那裡不設括號也不預留空位，如此就出現了以下的表示式：

- left lbrace x right none

- left [ x right )

- left ] x right [

- left rangle x right lfloor

「left」和「right」適用與其他括號一樣的排序規則，特別是它也有群組功能以及空白表示式。

不同類括號的合併，例如，只有一邊的括號以及左右交換位置的情況是常有的。當然是不能這樣輸入的。一下的數學的示例只是用來說明這種情況：

- [2, 3) - 右側開放的間隔

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.

完整的摘要如下：

- \{ 或 \lbrace，\} 或 \rbrace

- \(, \)

- \[, \]

- \langle, \rangle

- \lceil, \rceil

- \lfloor, \rfloor

- \lline, \rline

- \ldline, \rdline

藉此可在 LibreOffice Math 中毫無困難地建立上述區間：\[2","3\) 或"\]2",「3\[ (請注意：這些引號屬於輸入的一部分。)

請注意，必須輸入引號 (只要按 Shift+2 即可)，且不能使用印刷字體的引號。一般而言，標點符號 (如本例中的逗號) 會被設為文字。雖然也可以輸入 "\[2,~3\)"，但最好還是使用上述方法。在上例中，"fixed size" 一律表示括號大小視使用的字型大小而定。

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})}}}}.

- 本範例公式從左向右解譯。此運算只會影響其對應群組 (或表示式)。最右邊的運算「替代」或「組合」了其前一個結果。

- 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 ...」、「font ...」以及「size n」(n 是十進位數字) 最終會替代之前相同的操作，

操作效果會在「size +n」、「size -n」、「size *n」與「size /n」時組合，

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.

範例 (基本大小為 12 以及標誌為 50%)：

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}

以下的範例看起來則不一致：

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)