Sulud ja rühmitamine
The quotation marks in the examples are used to emphasize text and do not belong to the content of the formulas and commands.
Valemite sisestamisel konsooliaknasse pea meeles, et korrektse struktuuri tagamiseks on sageli vaja kasutada tühikuid.
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.
Kõik sulud on mõeldud kasutamiseks paaridena. Sulgudel on teatud ühised omadused:
Kõigil sulutüüpidel on sama rühmitamisfunktsioon, mida on kirjeldatud looksulgude '{}' jaoks.
Kõik sulud, ka nähtavad, võivad sisaldada tühja rühma. Seega sulud ei pruugi avaldist tingimata sisaldada.
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.
Kuna koodid "left" ja "right" muudavad sulu unikaalseks, siis võib nende argumendiks olla iga sulg, võimalik on paigutada parempoolseid sulge vasakule ja vasakpoolseid paremale. Sulu asemel võib kasutada argumenti "none", mis tähendab, et sulgu ei näidata ja ruumi sellele ei reserveerita. Antud meetodi abil saab luua järgnevaid avaldisi:
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left lbrace x right none
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left [ x right )
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left ] x right [
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left rangle x right lfloor
Koodidele "left" ja "right" laienevad samad reeglid, mis teistele sulgudele: need töötavad samuti rühmitajatena ja võivad sisaldada tühja avaldist.
Paariliseta sulgude, üksikute sulgude ja vahetatud parempoolsete ja vasakpoolsete sulgude kombinatsioone kasutatakse tihti matemaatilistes avaldistes. Järgnev valem annab sisestamisel veateate:
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[2, 3) - paremalt avatud intervall
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.
Järgnevalt täielik ülevaade:
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\{ või \lbrace, \} või \rbrace
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\(, \)
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\[, \]
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\langle, \rangle
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\lceil, \rceil
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\lfloor, \rfloor
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\lline, \rline
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\ldline, \rdline
Nii saab ülaltoodud näite intervalli koostada LibreOffice Math'is ilma probleemideta: \[2", "3\) või "\]2", "3\[ (Märkus: jutumärgid on kirje osa.)
Jutumärkide sisestamiseks tuleb kasutada klahve Shift+2 ja mitte trükitehnilisi jutumärke. Üldiselt käsitletakse kirjavahemärke (nagu koma antud näites) kui teksti. Ehkki on võimalik kirjutada ka "\[2,~3\)", on ülaltoodud näide eelistatav. Selles näites tähendab "fikseeritud suurus" alati, et sulgude suurus sõltub kasutatava fondi suurusest.
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":
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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})}}}}.
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Näidisvalemit käsitletakse vasakult paremale. Toimingud mõjutavad ainult neile vastavaid rühmi (või avaldisi). Paremal asuvad koodid "asendavad" või "kombineeruvad" eelnevatega.
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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 ..." ja "font ...", samuti "size n" (n on arv) tühistavad eelneva sama tüüpi koodi
koodides "size +n", "size -n", "size *n" ja "size /n" on atribuutide efektid kombineeritud,
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.
Näited (baassuurus on 12 ja indeksite kõrgus 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}
Järgnevad näited ei näe paraku samasugused välja:
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)