<html><head><title>Brackets and Grouping</title><meta name="filename" content="text/smath/01/03091100"/><meta name="language" content="en-US"/><help:css-file-link xmlns:help="http://openoffice.org/2000/help"/><!--The CSS style header method for setting styles--><style type="text/css">
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<p class="P1"/>
<p class="Head1"><a name="klaugru"/><help:key-word value="brackets and grouping in %PRODUCTNAME Math" tag="kw67338_1" xmlns:help="http://openoffice.org/2000/help"/><help:key-word value="grouping and brackets in %PRODUCTNAME Math" tag="kw67338_2" xmlns:help="http://openoffice.org/2000/help"/><help:link Id="67338" xmlns:help="http://openoffice.org/2000/help">Brackets and Grouping</help:link></p>
<p class="Paragraph">The quotation marks in the examples serve only for emphasis in the text and do not belong to the content of the examples and commands.</p>
<p class="Paragraph">During manual entry of the samples in the command window, please note that spaces are often required for correct structure.</p>
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<p class="Paragraph">As an important bracket symbol, one can use braces - "{}". Using this symbol you can group several other expressions/icons into <span class="T1">one </span>new expression. The example "{a + b}over{c + d} - e" illustrates this. The brackets in this example are not shown in the formula documents also do not need any space.</p>
<p class="Paragraph">Set brackets were previously inserted in the Selection window or directly in the Command window as "left lbrace <?> right rbrace". Now, a left and a right set bracket can also be inserted using "lbrace" and "rbrace", without or without wildcards.</p>
<p class="Paragraph">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 in Computer Science: "lceil -3.7 rceil = -3" or "lfloor -3.7 rfloor = -4".</p>
<p class="Paragraph">Pointed brackets with a vertical line in between them are common in Physics: "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.</p>
<p class="Paragraph">All brackets may only occur in the correct pairing. The brackets have some common characteristics:</p>
<p class="Paragraph">All types of brackets show the same functions in groups as are described for "{}"<span class="T1">-</span> brackets.</p>
<p class="Paragraph">All types of brackets, including those visible, allow the definition of empty groups. The enclosed expression may therefore be empty.</p>
<p class="Paragraph">Another common characteristic of all these brackets is that they do not adjust their size to the enclosed expression, which is true in both directions. 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. The same is true for the different entries and therefore the appropriate results of "(size 3{a over b})" and "left(size 3{a over b}right)". If the brackets themselves are part of the expression whose size is changed, they are also part of the size change: "size 3(a over b)" and "size 12(a over b)"<span class="T1">. </span>Of course, the sizing bracket to bracketed expression ratio does not change in any way.</p>
<p class="Paragraph">Since "left" and "right" ensure unique mutual assignments of the brackets, <span class="T1">every </span>single bracket can be used as an argument for these two brackets, even the right brackets on the left side and vice versa. Instead of one bracket it may say "none" there, which means that there is no bracket shown there and that there is no room reserved for a bracket. Using this, you can create expressions like the following:</p>
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<p class="P2">left lbrace x right none</p>
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<p class="P2">left [ x right )</p>
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<p class="P2">left ] x right [</p>
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<p class="P2">left rangle x right lfloor</p>
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<p class="Paragraph">The same rules apply to "left" and "right" as to the other brackets, specifically, they also work as group builders and may enclose the empty expression.</p>
<p class="Paragraph">The combination of brackets that do not belong together as well as brackets on one side only and repositioning left and right occur often. This is illustrated by an example from math; this, however, <span class="T1">cannot</span> be entered like this:</p>
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<p class="P3">[2, 3) - right open interval</p>
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<p class="Paragraph">Using "left" and "right" you can set individual brackets; 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 is now the possibility of displaying single brackets with a fixed size, by putting a "\" (backslash) in front of normal brackets. These brackets then act like any other symbol and no longer have the special functionality of brackets, i.e. they do <span class="T1">not </span>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"</p>
<p class="Paragraph">The complete overview looks as follows:</p>
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<p class="P4">\{ or \lbrace, \} or \rbrace</p>
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<p class="P5">\(, \)</p>
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<p class="P6">\[, \]</p>
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<p class="P7">\langle, \rangle</p>
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<p class="P8">\lceil, \rceil</p>
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<p class="P9">\lfloor, \rfloor</p>
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<p class="P10">\lline, \rline</p>
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<p class="P11">\ldline, \rdline</p>
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<p class="Paragraph">In this way, intervals like the one above can be built in <span class="T1"><help:productname xmlns:help="http://openoffice.org/2000/help">%PRODUCTNAME</help:productname> Math</span> without any problems: \[2", "3\) or "\]2", "3\[ (Attention: These quotation marks are part of the entry.)</p>
<p class="Paragraph">Please note that the quotation marks must be entered and can be obtained with <span class="T1">(Shift)(2)</span> and not with typographical quotation marks. Generally, punctuation marks (like the comma in this case) should always be set as text; spaces often look good as well. Although it is also possible to use "\[2,~3\)" the above option is preferred. In the example above, "fixed size" always describes a bracket size dependent on the font size used.</p>
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<p class="Paragraph">The cascading of groups is relatively problem-free. For 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}." This is not surprising since these attributes do not compete but rather can be combined.</p>
<p class="Paragraph">This differs slightly for competing or at least mutually influencing attributes. This is often the case for 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 description did basically apply to <help:productname xmlns:help="http://openoffice.org/2000/help">%PRODUCTNAME</help:productname> 4.0; however, this is now the basic resolution rule, which will be followed consistently in the future. In principle, this rule applies to all group operations. This only has a visible effect on the font attributes, like "bold", "ital", "phantom", "size", "color" and "font":</p>
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<p class="P12">Group operations in sequence will be treated as if every single operation was again enclosed by {}. They are grouped in cascades and on every cascade level there is <span class="T1">no more than </span>one operation: "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})}}}}".</p>
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<p class="P13">This is then interpreted from left to right, where an operation only completed the changes for its corresponding group (or expression). There, the operations further to the right "replace" or "combine themselves with" their predecessors.</p>
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<p class="P14">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". See also "a + size *2 (b * size -8 c_1)^2"</p>
<p class="Paragraph">"color ..." and "font ..." as well as "size n" (n is a decimal) replace any preceding operations of the same type,</p>
<p class="Paragraph">for "size +n", "size -n", "size *n", and "size /n" the effects of the operations are combined,</p>
<p class="Paragraph">"size *2 size -5 a" would be double the starting size minus 5</p>
<p class="Paragraph">"font sans ( a + font serif b)"</p>
<p class="Paragraph">"size *2 ( a + size /2 b )"</p>
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<p class="Paragraph">For the StarSymbol Unicode font there are 2 exceptions to these rules:</p>
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<p class="P15">It ignores "font" commands. Otherwise, there would often be different characters from the ones desired, e.g. "font sans (a oplus b)" would then neither have brackets nor an "oplus".</p>
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<p class="P16">The "ital" commands are ignored, e.g. "ital (a + b)". This happens because mathematical symbols are not common; even in combination with text in italics.</p>
<p class="Paragraph">To change the size, you should not use "size n", but rather the versions containing +,-,*,/. These can easily be used in any context. This enables you to copy to other areas by using Copy and Paste, and the result still remains similar. Furthermore, such expressions "survive" a change of the base size in ht menu better than when using "size n". If you use only "size *" and "size /" (e.g. "size *1.24 a or size /0.86 a") the proportions should be kept intact.</p>
<p class="Paragraph">Examples (with a base size of 12 and 50% for indexes):</p>
<p class="Paragraph">Exactly identical proportions with "size 18 a_n" and "size *1.5 a_n".</p>
<p class="Paragraph">This differs in different contexts: "x^{size 18 a_n}" and "x^{size *1.5 a_n}"</p>
<p class="Paragraph">Examples with size +n for a comparison. They look identical:</p>
<p class="Paragraph">a_{size 8 n}</p>
<p class="Paragraph">a_{size +2 n}</p>
<p class="Paragraph">a_{size *1.333 n}</p>
<p class="Paragraph">The following examples, however, do not look identical:</p>
<p class="Paragraph">x^{a_{size 8 n}}</p>
<p class="Paragraph">x^{a_{size +2 n}}</p>
<p class="Paragraph">x^{a_{size *1.333 n}}</p>
<p class="Paragraph">Note that 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)</p>
