mirror of https://github.com/texmacs/doc.git
107 lines
6.1 KiB
Plaintext
107 lines
6.1 KiB
Plaintext
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<TeXmacs|1.0.7.9>
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<style|tmdoc>
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<\body>
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<tmdoc-title|Semantics of mathematical symbols>
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The mathematical symbols in <TeXmacs> all come with a certain number of
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properties which correspond to their intended meaning. For instance,
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<TeXmacs> is aware that <math|<op|+>> is an infix operator, whereas ! is
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rather a postfix, and , a separator.
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<TeXmacs> has special symbols <math|\<mathe\>=2.71828\<cdots\>>,
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<math|\<mathpi\>=3.14159\<cdots\>> and <math|\<mathi\>> for important
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mathematical constants, which display differently from the mere characters
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<math|e>, <math|\<pi\>> and <math|i>, and which can be entered using the
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shortcuts <shortcut|\<mathe\>>, <shortcut|\<mathpi\>> and
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<shortcut|\<mathi\>>. We recommend to systematically use these shortcuts.
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Inversely, semantically distinct symbols may display in a similar way. For
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instance, the comma separator, as in <math|f<around|(|x,y|)>>, is different
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from the decimal comma, as in <math|3\<comma\>14159\<cdots\>>. Notice that
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the two symbols admit different spacing rules. Semantically distinct
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symbols which are rendered by the same glyph are called <em|homoglyphs>.
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Notice that our semantics is purely syntactic: for instance,
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the<nbsp><math|+> infix is commonly used for addition, but sometimes also
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for the concatenation of strings. Nevertheless, these two uses do not
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differ from a syntactical point of view, since the<nbsp><math|+> symbol
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remains a binary infix with the same precedence with respect to other
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symbols.
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The most confusing homoglyphs are the various invisible symbols supported
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by <TeXmacs>:
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<\itemize>
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<item>The multiplication, entered by <key|*>. Example: <math|a*b>.
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<item>Function application, entered by <key|space>. Example: <math|sin
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x>.
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<item>An invisible separator, entered by <shortcut|\<nocomma\>>. Example:
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the matrix <math|A=<around|(|a<rsub|i\<nocomma\>j>|)>>.
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<item>An invisible addition, entered by <shortcut|\<noplus\>>. Example:
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<math|17\<noplus\><frac*|3|8>>.
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<item>An invisible symbol, entered by <shortcut|\<nosymbol\>>. Example:
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the increment <math|\<nosymbol\>+1>.
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<item><label|nobracket>An invisible bracket (mainly for internal use). A
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matching pair of invisible brackets is entered using <key|( space>.
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</itemize>
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Again it is recommended that authors carefully enter these various
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invisible symbols when appropriate. It is particularly important to
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distinguish between multiplication and function application, since there is
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no 100% safe automatic way to make this distinction (we already mentioned
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the formulas <math|a<around|(|b+c|)>> and <math|f<around|(|x+y|)>> before).
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<TeXmacs> supports two quite general schemes for entering homoglyphs. On
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the one hand, we often rely on the standard variant system. For instance,
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<math|\<times\>> and <math|\<ast\>> are obtained using <shortcut|\<times\>>
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and <shortcut|\<ast\>>. When applicable, we also support the following
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convention: first type the character with a similar semantics and then type
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the character which corresponds to the rendering. This convention was
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already used above for the invisible homoglyphs, and often allows for
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shorter shortcuts. In table<nbsp><reference|homoglyph-table> we have given
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the complete list of homoglyphs supported by <TeXmacs>.
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<big-table|<block|<tformat|<table|<row|<cell|Shortcut>|<cell|Glyph>|<cell|Example>|<cell|Semantics>>|<row|<cell|<key|*>>|<cell|>|<cell|<math|a*b>>|<cell|Multiplication>>|<row|<cell|<key|space>>|<cell|>|<cell|<math|sin
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x>>|<cell|Function application>>|<row|<cell|<key|,
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space>>|<cell|>|<cell|<math|a<rsub|i\<nocomma\>j>=a<rsub|j\<nocomma\>i>>>|<cell|Invisible
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separator>>|<row|<cell|<key|+ space>>|<cell|>|<cell|<with|mode|math|17\<noplus\><frac*|3|8>>>|<cell|Invisible
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addition>>|<row|<cell|<key|. space>>|<cell|>|<cell|<math|\<nosymbol\>+1>>|<cell|Invisible
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symbol>>|<row|<cell|<key|( space>>|<cell|>|<cell|<math|\<Phi\>\<equiv\><around*|\<nobracket\>|\<forall\>x,P<around*|(|x|)>|\<nobracket\>>>>|<cell|Invisible
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bracket(s)>>|<row|<cell|<key|\|>>|<cell|<math|\|>>|<cell|<math|<around*|\||-x|\|>=<around*|\||x|\|>>>|<cell|Absolute
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value>>|<row|<cell|<key|\| var>>|<cell|<math|\|>>|<cell|<math|<around*|{|x\<in\>\<bbb-R\>\|x\<gtr\>0|}>>>|<cell|Separating
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bar>>|<row|<cell|<key|\| var var>>|<cell|<math|\|>>|<cell|<math|<around*|\<langle\>|a<rsub|i><rsup|2><mid|\|>a<rsub|j><rsup|2>|\<rangle\>>>>|<cell|Extensible
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middle bar>>|<row|<cell|<key|\| var var var
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var>>|<cell|<math|\|>>|<cell|<math|11\<divides\>1001>>|<cell|Divides
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relation>>|<row|<cell|<key|,>>|<cell|<math|,>>|<cell|<math|f<around*|(|x,y|)>>>|<cell|Comma
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separator>>|<row|<cell|<key|, var>>|<cell|<math|,>>|<cell|<math|123\<comma\>456>>|<cell|Decimal
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comma>>|<row|<cell|<key|.>>|<cell|<math|.>>|<cell|<math|123.456>>|<cell|Decimal
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point>>|<row|<cell|<key|. var>>|<cell|<math|.>>|<cell|<math|\<mathlambda\>x\<point\>x<rsup|2>>>|<cell|Dot
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connector>>|<row|<cell|<key|* var var var>>|<cell|<math|\<cdot\>>>|<cell|<math|\<b-v\>\<cdot\>\<b-w\>>>|<cell|Dot
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multiplication>>|<row|<cell|<key|. var var>>|<cell|<math|\<cdummy\>>>|<cell|<math|\<cdummy\>+1>>|<cell|Dummy
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widcard>>|<row|<cell|<key|\\ var>>|<cell|<math|\\>>|<cell|<math|\\x>>|<cell|Backslash>>|<row|<cell|<key|\\
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var var>>|<cell|<math|\\>>|<cell|<math|\<bbb-N\><rsup|\<gtr\>>=\<bbb-N\>\<setminus\><around*|{|0|}>>>|<cell|Set
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minus>>|<row|<cell|<key|&>>|<cell|<math|\<wedge\>>>|<cell|<math|1=1\<wedge\>2=2>>|<cell|Logical
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and>>|<row|<cell|<key|* &>>|<cell|<math|\<exterior\>>>|<cell|<math|\<mathd\>x\<exterior\>\<mathd\>y>>|<cell|Wedge
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product>>>>>|<label|homoglyph-table>Homoglyphs supported by <TeXmacs>.>
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<tmdoc-copyright|2010|Joris van der Hoeven>
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<tmdoc-license|Permission is granted to copy, distribute and/or modify this
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document under the terms of the GNU Free Documentation License, Version 1.1
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or any later version published by the Free Software Foundation; with no
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Invariant Sections, with no Front-Cover Texts, and with no Back-Cover
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Texts. A copy of the license is included in the section entitled "GNU Free
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Documentation License".>
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</body>
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<\initial>
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<\collection>
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<associate|language|english>
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</collection>
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</initial>
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