mirror of https://github.com/texmacs/doc.git
257 lines
8.6 KiB
Tcl
257 lines
8.6 KiB
Tcl
<TeXmacs|1.99.11>
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<style|<tuple|tmdoc|old-spacing>>
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<\body>
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<tmdoc-title|Mathematical primitives>
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<\explain>
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<explain-macro|left|large-delimiter>
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<explain-macro|left|large-delimiter|size>
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<explain-macro|left|large-delimiter|bottom|top>
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<explain-macro|mid|large-delimiter|<math|\<cdots\>>>
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<explain-macro|right|large-delimiter|<math|\<cdots\>>><explain-synopsis|large
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delimiters>
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<|explain>
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These primitives are used for producing large delimiters, like in the
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formula
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<\equation*>
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<around*|\<langle\>|<frac|1|a<rsub|1>><mid|\|><frac|1|a<rsub|2>><mid|\|>\<cdots\><mid|\|><frac|1|a<rsub|n>>|\<rangle\>>.
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</equation*>
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Matching left and right delimiters are automatically sized so as contain
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the enclosed expression. Between matching left and right delimiters, the
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formula may contain an arbitrary number of middle delimiters, which are
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sized in a similar way. Contrary to <TeX>, the depth of a large delimiter
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is not necessarily equal to its height, so as to correctly render
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formulas like
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<\equation*>
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f<around*|(|<frac|1|x+<frac|1|y+<frac|1|z>>>|)>
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</equation*>
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The user may override the automatically determined size by specifying
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additional length parameters <src-arg|size> or <src-arg|bottom> and
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<src-arg|top>. For instance,
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<\tm-fragment>
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<inactive*|f<left|(|-8mm|4mm>x<mid|\||8mm>y<right|)|-4mm|8mm>>
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</tm-fragment>
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is rendered as
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<\equation*>
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f<left|(|-8mm|4mm>x<mid|\||8mm>y<right|)|-4mm|8mm>
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</equation*>
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The <src-arg|size> may also be a number <math|n>, in which case the
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<math|n>-th available size for the delimiter is taken. For instance,
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<\tm-fragment>
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<inactive*|g<left|(|0><left|(|1><left|(|2><left|(|3>z<right|)|3><right|)|2><right|)|1><right|)|0>>
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</tm-fragment>
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is rendered as
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<\equation*>
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g<left|(|0><left|(|1><left|(|2><left|(|3>z<right|)|3><right|)|2><right|)|1><right|)|0>
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</equation*>
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</explain>
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\;
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<\explain>
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<explain-macro|big|big-symbol><explain-synopsis|big symbols>
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<|explain>
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This primitive is used in order to produce big operators as in
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<\equation>
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<label|big-example><big|sum><rsub|i=0><rsup|\<infty\>>a<rsub|i>*z<rsup|i>
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</equation>
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The size of the operator depends on whether the formula is rendered in
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``display style'' or not. Formulas in separate equations, like
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(<reference|big-example>), are said to be rendered in display style,
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contrary to formulas which occur in the main text, like
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<math|<big|sum><rsub|i=0><rsup|\<infty\>>a<rsub|i>*z<rsup|i>>. The user
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may use <menu|Format|Display style> to override the current settings.
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Notice that the formula (<reference|big-example>) is internally
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represented as
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<\tm-fragment>
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<inactive*|<big|sum><rsub|i=0><rsup|\<infty\>>a<rsub|i>*z<rsup|i><big|.>>
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</tm-fragment>
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The invisible big operator <inactive*|<big|.>> is used to indicate the
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end of the scope of <inactive*|<big|sum>>.
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</explain>
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<\explain>
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<explain-macro|frac|num|den><explain-synopsis|fractions>
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<|explain>
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The <markup|frac> primitive is used in order to render fractions like
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<math|<frac|x|y>>. In display style, the numerator <src-arg|num> and
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denominator <src-arg|den> are rendered in the normal size, but display
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style is turned of when typesetting <src-arg|num> and <src-arg|den>. When
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the display style is turned of, then the arguments are rendered in script
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size. For instance, the content
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<\tm-fragment>
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<inactive*|<frac|1|a<rsub|0>+<frac|1|a<rsub|1>+<frac|1|a<rsub|2>+\<ddots\>>>>>
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</tm-fragment>
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is rendered in display style as
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<\equation*>
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<frac|1|a<rsub|0>+<frac|1|a<rsub|1>+<frac|1|a<rsub|2>+\<ddots\>>>>
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</equation*>
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</explain>
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<\explain>
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<explain-macro|sqrt|content>
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<explain-macro|sqrt|content|n><explain-synopsis|roots>
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<|explain>
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The <markup|sqrt> primitive is used in order to render square roots like
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<math|<sqrt|x>> or <src-arg|n>-th roots like <math|<sqrt|x|3>>. The root
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symbol is automatically sized so as to encapsulate the <src-arg|content>:
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<\equation*>
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<sqrt|<frac|f<around|(|x|)>|y<rsup|2>+z<rsup|2>>|i+j>
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</equation*>
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</explain>
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<\explain>
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<explain-macro|lsub|script>
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<explain-macro|lsup|script>
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<explain-macro|rsub|script>
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<explain-macro|rsup|script><explain-synopsis|scripts>
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<|explain>
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These primitives are used in order to attach a <src-arg|script> to the
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preceding box in a horizontal concatenation (in the case of right
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scripts) or the next one (in the case of left scripts). When there is no
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such box, then the script is attached to an empty box. Moreover, when
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both a subscript and a superscript are specified on the same side, then
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they are merged together. For instance, the expression
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<\tm-fragment>
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<inactive*|<rsub|a><rsup|b>+<lsub|1><lsup|2>x<rsub|3><rsup|4>=y<rsub|1>+<lsub|c>>
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</tm-fragment>
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is rendered as
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<\equation*>
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<rsub|a><rsup|b>+<lsub|1><lsup|2>x<rsub|3><rsup|4>=y<rsub|1>+<lsub|c>
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</equation*>
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When a right script is attached to an operator (or symbol) which accepts
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limits, then it is rendered below or above instead of beside the
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operator:
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<\equation*>
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lim<rsub|n\<rightarrow\>\<infty\>>a<rsub|n>
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</equation*>
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Scripts are rendered in a smaller font in non-display style.
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Nevertheless, in order to keep formulas readable, the size is not reduced
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below script-script-size.
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</explain>
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<\explain>
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<explain-macro|lprime|prime-symbols>
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<explain-macro|rprime|prime-symbols><explain-synopsis|primes>
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<|explain>
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Left and right primes are similar to left and right superscripts, except
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that they behave in a different way when being edited. For instance, when
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your cursor is behind the prime symbol in <math|f<rprime|'>> and you
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press backspace, then the prime is removed. If you are behind
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<math|f<rsup|n>> and you press backspace several times, then you first
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enter the superscript, next remove <math|n> and finally remove the
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superscript. Notice also that <src-arg|prime-symbols> is necessarily a
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string of concatenated prime symbols. For instance,
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<math|f<rprime|'\<dag\>>> is represented by
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<inactive*|f<rprime|'\<dag\>>>.
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</explain>
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<\explain>
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<explain-macro|below|content|script>
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<explain-macro|above|content|script><explain-synopsis|scripts above and
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below>
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<|explain>
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The <markup|below> and <markup|above> tags are used to explicitly attach
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a <src-arg|script> below or above a given <src-arg|content>. Both can be
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mixed in order to produce content with both a script below and above:
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<\equation*>
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<above|<below|xor|i=1>|\<infty\>> x<rsub|i>
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</equation*>
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can be produced using
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<\tm-fragment>
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<inactive*|<above|<below|xor|i=1>|\<infty\>> x<rsub|i>>
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</tm-fragment>
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</explain>
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<\explain>
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<explain-macro|wide|content|wide-symbol>
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<explain-macro|wide*|content|wide-symbol><explain-synopsis|wide symbols>
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<|explain>
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These primitives can be used in order to produce wide accents above or
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below some mathematical <src-arg|content>. For instance
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<math|<wide|x+y|\<bar\>>> corresponds to the markup
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<inactive*|<wide|x+y|\<bar\>>>.
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</explain>
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<\explain>
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<explain-macro|neg|content><explain-synopsis|negations>
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<|explain>
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This primitive is mainly used for producing negated symbols or
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expressions, such as <math|<neg|\<rightarrowtail\>>> or <math|<neg|a>>.
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</explain>
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<\explain>
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<explain-macro|tree|root|child-1|<math|\<cdots\>>|child-n><explain-synopsis|trees>
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<|explain>
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This primitive is used to produce a tree with a given <src-arg|root> and
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children <src-arg|child-1> until <src-arg|child-n>. The primitive should
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be used recursively in order to produce trees. For instance,
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<\equation*>
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<tree|+|x|y|<tree|\<times\>|2|y|z>>
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</equation*>
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corresponds to the markup
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<\tm-fragment>
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<inactive*|<tree|+|x|y|<tree|\<times\>|2|y|z>>>
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</tm-fragment>
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In the future, we plan to provide further style parameters in order to
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control the rendering.
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</explain>
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<tmdoc-copyright|2004|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|<\collection>
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</collection>> |