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# かっことグループ化

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

コマンドウィンドウに直接入力する場合、多くのコマンドはスペースも正しく入力する必要がありますので注意してください。

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.

かっこは、常に対の形で使用する必要があります。かっこには、次のような共通の特徴があります:

すべての種類のかっこには、"{}" かっこで解説したように、グループにまとめる機能があります。

すべてのかっこには、空白のグループを定義する機能があります。かっこ内は空白でもかまいません。

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.

left と right によってかっこの対がはっきりするため、この２つのコマンドは どんな かっこにも付けることができ、右側のかっこを左側に置いたり、左側のかっこを右側に置いたりすることもできます。かっこのかわりに none を入力すると、そこにはかっこもスペースも表示されないため、次のような式が作成できます:

- left lbrace x right none

- left [ x right )

- left ] x right [

- left rangle x right lfloor

left と right にもほかのかっこと同じ規則が適用されます。つまり、この２つのコマンドにはグループにまとめる機能があり、中に空白の式を入れることもできます。

対でないかっこを組み合わせたり、かっこを片方だけ使ったり、右と左を入れ替えたりすることは、数式でしばしば使われます。そのまま入力することはできないかっこの例に、次のものがあります:

- [2, 3) - 右開区間

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.

まとめると、次のようになります:

- \{ または \lbrace、\} または \rbrace

- \(, \)

- \[, \]

- \langle, \rangle

- \lceil, \rceil

- \lfloor, \rfloor

- \lline, \rline

- \ldline, \rdline

上のような右開区間も、LibreOffice Math では簡単に構成できます: \[2", "3\) または "\]2", "3\[

半角ダブルクオーテーションマーク (") は、Shift+2を押して入力します。印刷用引用符(”)や全角では機能しません。基本的に句読点（この例ではコンマ）はテキストとして設定されます。「\[2,~3\)」と入力することもできますが、上記の方が適切です。上記の例で、かっこの「サイズが固定される」とは、使用するフォントサイズだけにかっこのサイズが調整されるという意味です。

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})}}}}.

- 次に、式全体が左から右へ解釈されます。各演算は、その演算に属するグループ（または式）だけに適用されます。以降に位置する演算は、前の演算を置き換えるか、または組み合わせます。

- 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...、size n（n は数）は、前に同じ種類の演算がある場合、それを置換します。

size +n、size -n、size *n、size /n では、演算の効果が組み合わされます。

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.

例（基本サイズが 12 で、指数は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}

次の例は、表示が異なります:

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)