ይዞታዎች

# ቅንፎች እና ቡድን

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

የ መቀመሪያ ምሳሌዎች በሚጽፉ ጊዜ በ ትእዛዞችመስኮት ውስጥ ያስታውሱ ክፍተት አስፈላጊ ነው ለ ትክክለኛ አካል

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.

ቀደም ብሎ ቅንፎች ገብተዋል በ አካላቶች ክፍል ውስጥ:ወይንም በ ቀጥታ በ ትእዛዞች መስኮት ውስጥ እንደ "በ ግራ የ ግራ ጠምዛዛ <?> በ ቀኝ የ ቀኝ ጠምዛዛ": አሁን: የ ግራ እና የ ቀኝ ጥንድ ቅንፍ ማስገባት ይቻላል በ መጠቀም: "የ ግራ ጠምዛዛ" እና "የ ቀኝ ጠምዛዛ": በ ወይንም ያለ ሁለ ገብ ካርድ

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.

ሁሉንም ቅንፎች የሚጠቀሙት በ ጥንድ ነው: ቅንፎች የ ተለመዱ ባህሪዎች አላቸው:

ሁሉም አይነት ቅንፎች ተመሳሳይ በ ቡድን ማድረጊያ ተግባሮች አላቸው እንደ ተገለጸው በ "{}" ቅንፎች

ሁሉም አይነት ቅንፎች: የሚታዩትንም አካትቶ: ባዶ ቡድን መግለጽ ይፈቅዳሉ: የ ተከበበው አገላለጽ ምናልባት ባዶ ሊሆን ይችላል

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.

ከ "ግራ" እና "ቀኝ" ያረጋግጣል የ ተለዩ ስራዎች ለ ቅንፎች: እያንዳንዱን ነጠላ ቅንፍ መጠቀም ይቻላል እንደ ክርክር ለ እነዚህ ሁለት ትእዛዞች: የ ቀኝ ቅንፍ በ ግራ ቅንፍ በኩል ቢያደርጉ: ወይንም የ ግራ ቅንፍ በ ቀኝ ቅንፍ በኩል ቢያደርጉ: በ ቅንፍ ፋንታ እርስዎ መጠቀም ይችላሉ የ "ምንም" ያሟላል: ይህ ማለት የሚታይ ቅንፍ የለም ማለት ነው እና ለ ቅንፍ የ ተያዘ ምንም ቦታ የለም ማለት ነው: ይህን በ መጠቀም: እርስዎ የሚቀጥለውን መግለጫ መፍጠር ይችላሉ

- left lbrace x right none

- left [ x right )

- left ] x right [

- left rangle x right lfloor

ተመሳሳይ ህግ ይፈጸማል ለ "ግራ" እና "ቀኝ" እንደ ሌሎቹ ቅንፎች: እንዲሁም ይሰራሉ እንደ ቡድን ገንቢዎች እና ባዶ መግለጫዎችን ይከባሉ

መቀላቀያ ለማይመሳሰሉ ቅንፎች: ነጠላ ቅንፎች እና ቦታውን መቀየሪያ ወደ ግራ እና ወደ ቀኝ ቅንፎች በ ሂሳብ መቀመሪያዎች ውስጥ ይፈጠራል: የሚቀጥለው መቀመሪያ በሚጻፍ ጊዜ ስህተት ይፈጥራል

- [2, 3) - በ ቀኝ ክፍተት መክፈቻ

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.

ባጠቃላይ ሙሉ መመልከቻው እንደሚከተለው ነው

- \{ or \በ ግራ ጠምዛዛ: \} ወይንም \በ ቀኝ ጠምዛዛ

- \(, \)

- \[, \]

- \langle, \rangle

- \lceil, \rceil

- \lfloor, \rfloor

- \lline, \rline

- \ldline, \rdline

በዚህ መንገድ ክፍተት ከ ላይ በኩል እንዳለው መገንባት ይቻላል በ LibreOffice ሂሳብ ያለ ምንም ችግር: \[2", "3\) ወይንም "\]2", "3\[ (ማስጠንቀቂያ: እነዚህ የ ጥቅስ ምልክቶች የ ማስገቢያ አካል ናቸው)

እባክዎን ያስታውሱ የ ጥቅስ ምልክቶች መግባት አለባቸው እና ማግኘት ይቻላል በ Shift+2 እና በ ጽሁፍ የ ጥቅስ ምልክት አይደልም: ባጠቃላይ: ነጥቦች እንደ (ኮማ በዚህ ጉዳይ ውስጥ) የሚሰናዱት እንደ ጽሁፍ ነው: ነገር ግን እንዲሁም መጻፍ ይችላሉ "\[2,~3\)" የ ላይኛው ምርጫ ይመረጣል: ያለፈው ምሳሌ: "የ ተወሰነ መጠን" ሁልጊዜ የሚገልጸው የ ቅንፍ መጠን ነው: ጥገኛ የሆነ በሚጠቀሙት የ ፊደል መጠን

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})}}}}.

- ይህ የ መቀመሪያ ምሳሌ የሚተረጎመው ከ ግራ ወደ ቀኝ ነው: አንቀሳቃሹ ተጽእኖ የሚፈጥረው በ ተመሳሳይ ቡድን ውስጥ ነው (ወይንም መግለጫ). አንቀሳቃሹ ይቀጥላል ወደ ቀኝ "መቀየሪያ" ወይንም "መቀላቀያ ራሳቸውን በ" በ ቅድሚያ በ ቦታው የነበረውን

- 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

"ቀለም ..." እና "ፊደል ..." እንዲሁም "መጠን n" (n ዴሲማል ነው) መቀየሪያ የ ነበረውን ተግባር ወይንም ተመሳሳይ አይነት

ለ "መጠን +n", "መጠን -n", "መጠን *n", እና "መጠን /n" ውጤቱ ለ ተግባሮች የ ተቀላቀለ ነው

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.

ለምሳሌ (በ መሰረታዊ መጠን በ 12 እና 50% ለ ማውጫዎች):

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}

የሚቀጥሉት ምሳሌዎች: ነገር ግን ተመሳሳይ አይመስሉም:

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)

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