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diff --git a/macros/inrstex/inrsdoc/thmateq.tex b/macros/inrstex/inrsdoc/thmateq.tex deleted file mode 100644 index e894a666e9..0000000000 --- a/macros/inrstex/inrsdoc/thmateq.tex +++ /dev/null @@ -1,480 +0,0 @@ -%-*-tex-*- -\ifundefined{writestatus} \input status \relax \fi % -\chcode{mateq} - -\def\cqu{\cquote{Having got our equations, we must proceed to -carry out such operatins as we have neglected, taking care never to multiply -when we can divide}{Rules for the Direction of the Mind, Rule XX, -Ren\'e~Descartes (1596-1650)}} - -\chapterhead{mateq}{MATHEMATICS:\cr EQUATION\cr SETUP} -\tex\ makes the typesetting of the most difficult expressions relatively -easy. This chapter lists and shows examples of the special forms supplied by -{\it plain}. For the finer points of mathematic equation setup, the reader is -referred to the \texbook~[\cite{[Knut84]}]. For more advanced mathematics macro -and accenting capabilities, the AMS\tex~[\cite{[Amst84]}] package is -recommended. - -\intex\ supplies all that is in {\it plain} plus -\beginlist -\li $\bullet$ an autonumbering feature, using |\aneq|, |\aneqtag|, or |\autoeqnum| -for equations, -\li $\bullet$ a |\math| and |\displaymath| -for those who don't like |$|, -\li $\bullet$ a -|\leftequationnumbering| and |\rightequationnumbering| that will magically -shift all the equation numbers from the side specified by the form, -\li $\bullet$ and a |\mathopen| command that will cause aligned equations to increase -their spacing. -\endlist - - -The two basic commands |\math| and |\displaymath| can be used to invoke either -scriptstyle or displaystyle mathematics in running text. For instance -|\math{\sum_0^n}| gives \math{\sum_0^n} while |\displaymath{\sum_0^n}| gives -\displaymath{\sum_0^n}. - -In addition there is a tagging mechanism that enables the -symbolic referencing of equations, both forward and backward. - - - -\shead{eqcoms}{Command List} -\begintwocolumn -\hfuzz = 20pt %temporary -\pla|\abovewithdelims| -\pla|\atop| -\pla|\atopwithdelims| -\ext|\aneq \aneqtag| -\ext|\autoeqnum| -\pla|\bordermatrix| -\pla|\cases| -\pla|\cdot| -\pla|\cdots| -\pla|\choose| -\pla|\ddots| -\ext|\displaymath| -\pla|\eqalign| -\pla|\eqalignno| -\pla|\eqno| -\pla|\ldots| -\ext|\leftequationnumbering| -\pla|\leqno| -\pla|\leqalignno| -\ext|\math| -\ext|\mathopen| -\pla|\matrix| -\pri|\noalign| -\pla|\openup| -\pla|\over| -\pla|\overbrace| -\pla|\overline| -\pla|\overwithdelims| -\pla|\phantom| -\pla|\pmatrix| -\ext|\rightequationnumbering| -\pla|\smash| -\ext|\sphantom| -\pla|\sqrt| -\pla|\underbrace| -\pla|\underline| -\pla|\vphantom| -\endthreecolumn - -\shead{eqbasics}{Mathematic Equation Basics} -To put some mathematics, either symbols or expressions, in running text you -must surround them by a pair of single |$| like |$<expression>$|. An example -is |$x^y$| gives $x^y$. Mathematics in running text will be broken at the end -of line at spaces in the expression. To prevent a break but preserve a space -insert the tie |~| into the expression. Thus |$x~=~y+1$|, giving $x~=~y+1$ -will prevent a break around the $=$ sign. To obtain display equations use -form -\begintt -$$ -<display mathematics forms> -$$ -\endtt -There should be {\bf no} blank lines or |\par| within -|<display mathematics>|. Mysterious errors will result. To have a -display expression end a sentence, the last character before the equation -number should be a period. - -Superscripting and subscripting can occur only in mathematics mode. The |\@| -is the superscript character and |_| is the subscript character. The braces -|{<super,subscript characters>}| are necessary to tell \tex\ what material -goes where. The example below shows the result of different use of braces. - -$$ -2^xyz_uvw : 2^{xyz}_{uvw} : 2^{xyz_uvw} : 2^{xyz_{uvw}}. -$$ -is given by -\begintt -$$ -2^xyz_uvw : 2^{xyz}_{uvw} : 2^{xyz_uvw} : 2^{xyz_{uvw}}. -$$ -\endtt - -Finally, in commands that produce alignments, the |&| is used to separate -items and the |\cr| to end a line. Examples of their use will be found in -such commands as |\matrix| and |\eqalign|. Equation numbers are put in using -either the automatic numbering commands |\aneq|, |\aneqtag|, |\autoeqnum|, or -the normal manual numbering forms |\eqno| for right hand numbers or |\leqno| -for lefthand numbers. - - - - -\shead{mateqcomforms}{Command Forms} -This is a list of commands that are given in {\it plain}, along with some -examples and the form of the parameters for their use. -\beginblockmode - -\mbr -\pla\@|\above.. \atop.. \over.. functions - {<parm1> \atop <parm2>} - {<parm1> \choose <parm2>} - {<parm1> \over <parm2>} - {<parm1> \atopwithdelims<left delim><right delim> <parm2>} - {<parm1> \overwithdelims<left delim><right delim> <parm2>} - {<parm1> \abovewithdelims<left delim><right delim> - <bar thickness> <parm2>}| -\nbr -These forms are all used for putting |<parm1>| on top of |<parm2>| as might -happen in a fraction. The difference between them is that |\atop| puts no -line or bar between the |<parms>| while |\over| does, and |\choose| puts in -no bar but does enclose the |<parms>| in large parens as is normally done in -a binomial coefficient. The forms |\...delims| allow for the specifcation of -delimiters around the |<parms>| that may be different than parens. Finally -the |<bar thickness>| in the |\abovewithdelims| allows for the thickness of -the line or bar between the |<parms>| to be a specified |<dimen>|. As an -example -$$ -{37 \over 45} : {n \atop \alpha} : {10 \choose r} -: {f(x) \overwithdelims\{\} g(y)} -: {\alpha \atopwithdelims][ \beta} -: {209 \abovewithdelims\langle\rangle 2pt h(y)} -$$ -is given by -\begintt -$$ -{37 \over 45} : {n \atop \alpha} : {10 \choose r} -: {f(x) \overwithdelims\{\} g(y)} -: {\alpha \atopwithdelims][ \beta} -: {209 \abovewithdelims\langle\rangle 2pt h(y)} -$$ -\endtt -\mbr -\ext|\aneq \aneqtag{<tag>}| -\nbr -\ext|\autoeqnum{<tag>}| -\nbr -When |autonumbering| is on these commands will automatically number -equations. |\aneq| and |\aneqtag{<tag>}| inserts a bracketed equation number -in the correct place in the equation depending on whether it is an -|\eqalign|, |\eqalignno|, or |\leqalignno|. The |\autonumeq{<tag>}| inserts a -number without brackets. The |<tag>| allows for references to the equation. - -If |autonumbering| is off, the |\aneq| results in nothing and the two forms -with |<tag>| insert the |<tag>| --- without the |< >| of course. - -For example, |autonumbering| is on, -$$ -x \equiv y \aneq -$$ -is given by -\begintt -$$ -x \equiv y \aneq -$$ -\endtt -and -$$ -\eqalignno{ f(x)&\approx K x^{-3/2} & (\autoeqnum{eqfx}.a) \cr - &\approx 0 \qquad x \gg 0 & (\ref{eqfx}.b) \cr} -$$ -is given by -\begintt -$$ -\eqalignno{ f(x)&\approx K x^{-3/2} & (\autoeqnum{eqfx}.a) \cr - &\approx 0 \qquad x \gg 0 & (\ref{eqfx}.b) \cr} -$$ -\endtt -The |eqfx| is the equation tag. However, the -tag for |eqfx| does not make it to the margin! A better way to do this, and -one that guarantees that the tag for |eqfx| makes it to the margin is as -follows: -\begintt -{\silenttrue \autoeqnum{eqfx}} -$$ -\eqalignno{ f(x)&\approx K x^{-3/2} & (\ref{eqfx}.a) \cr - &\approx 0 \qquad x \gg 0 & (\ref{eqfx}.b) \cr} -$$ -\endtt -The \@|\silenttrue| turns on a switch in |\autoeqnum{<...>}| that prevents it -from writing out its value. -In this case, the |\autoeqnum{<...>}| is in vertical mode -so that the tag for |eqfx| will now make it to the margin. -The command |\ref{eqfx}| will produce the -(equation) number corresponding to |eqfx|. This construction allows -both lines of the equation to have the same main equation number. - -\mbr -\pla\@|\bordermatrix{<top 0>&<top 1>&<top 2>&...&<top n>\cr - <side 1>&<first row>\cr - ... - <side m>&<last row>\cr}| -\nbr -The |\bordermatrix| places parens around the |<rows>| in the same way as -|\pmatrix| and then places the |<top i>| items above and the |<side i>| items -to the left hand side outside the parens. Thus -$$ -\bordermatrix{ R\backslash C& Col 1 & Col 2 & Col 3 \cr - Row 1 & a & b & c \cr - Row 2 &\sum_{\ell=1}^n & & \alpha \cr - Row 3 & v=0 &\gamma & 1000.0\cr} -$$ -is given by -\begintt -$$ -\bordermatrix{ R\backslash C& Col 1 & Col 2 & Col 3 \cr - Row 1 & a & b & c \cr - Row 2 &\sum_{\ell=1}^n & & \alpha \cr - Row 3 & v=0 &\gamma & 1000.0\cr} -$$ -\endtt - -\mbr -\pla\@|\cases{<first math>&<first condition>\cr - ... - <last math>&<last condition>\cr}| -\nbr -This allows for a very simple way of stacking a set of possibilities in an -equation and putting a large brace on the left hand side. The |<...math>| is -the mathematics, and is in display math mode, and the |<...condition>| -is the condition and is in internal horizontal mode \dots\ not -math mode. Thus -$$ -G(x) = \cases{\vert x\vert & for $x<0$ \cr - x^2 & for $x\ge 0$ \cr} -$$ -is given by -\begintt -$$ -G(x) = \cases{\vert x\vert & for $x<0$ \cr - x^2 & for $x\ge 0$ \cr} -$$ -\endtt -\mbr -\pla\@|\eqalign ... - \eqalign{ <left first row> &<right first row>\cr - ... - <left last row> &<right last row>\cr} - \eqalignno{<left first row> &<right first row>&<first eq.no>\cr - ... - <left last row> &<right last row>&<last eq.no>\cr} - \leqalignno{<left first row>&<right first row>&<first eq.no>\cr - ... - <left last row> &<right last row>&<last eq.no>\cr}| -\nbr -All three of these commands allow for a list of equations, or expressions to -be aligned on a {\bf single} point within the expression. This is usually a -relation such as $=$ or $\gg$ although any point is possible. The -|\eqalignno| and |\leqalignno| have an extra field at the end of each row for -an equation number, which will be printed on the right for the former and on -the left for the latter. Note that in both cases the actual |<eq.no>| field -appears on the right. Any of the |<left ...>| or |<right ...>| or -|<... eq.no.>| may be omitted. -A major difference between |\eqalign| and |\eqalignno| is that the latter -always is as wide as the page while the former is its natural width. -|\openup<dimen>|, immediately after the opening |$$|, -is used to increase the spacing between the lines of an -|\eqalign| or its relatives by |<dimen>|. A font relative -|<unit of measure>| such as |ex| is recommended with |1ex| to start. -To obtain a lefthand equation number with -|\eqalign|, or ordinary display mathematics, use |\leqno|. - -\intex\ supplies automatic equation numbering and ways of having a document -change from left to right hand equation numbering or vice versa. See -|\lefhandequationnumbering| and |\righthandequationnumbering|. -For automatic equation numbering use |\autoeqnum{tag}|, |\aneq| and -|\aneqtag|. - -An example of an |\eqalign| is -$$ -\eqalign{F(x) &=\int_{-\infty}^x H(y)dy \cr - &=x^{3/2} \cr - G(z) &\ll 1 \cr} - \eqno (12) -$$ -which is given by -\begintt -$$ -\eqalign{F(x) &=\int_{-\infty}^x H(y)dy \cr - &=x^{3/2} \cr - G(z) &\ll 1 \cr} - \eqno (12) -$$ -\endtt -Notice the equation number is centered on the right hand side. An example -for |\eqalignno| is -$$ -\openup 1ex -\eqalignno{F(x) &=\int_{-\infty}^x H(y)dy \cr - &=x^{3/2} &(2.i)\cr -\noalign{and} - G(z) &\ll 1 &(2.ii)\cr} -$$ -is given by -\begintt -$$ -\openup 1ex -\eqalignno{F(x) &=\int_{-\infty}^x H(y)dy \cr - &=x^{3/2} &(2.i)\cr -\noalign{and} - G(z) &\ll 1 &(2.ii)\cr} -$$ -\endtt -The use of |\noalign {<text>}| places the |and| at the margin and maintains -the alignment of the $=$ and $\ll$. This technique will not work with -|\eqalign| because it does not necessarily take up the full width of the page. -Note again the placement of the equation numbers. - -\mbr -\pri\@|\eqno <reference> \leqno <reference>| -\nbr -|\eqno| and |\leqno| are used to put an equation |<reference>|, usually a -number, at the right or left hand side, respectively, of an equation. It can -be used with any display mathematics except |\[l]eqalignno|. - -\mbr -\ext\@|\leftequationnumbering \rightequationnumbering| -\nbr -These commands when used with the auto equation numbering commands |\aneq|, -|\aneqtag{<tag>}| or |\autoeqnum{<tag>}| will result in completely left or -right hand equation numbers whether |\eqalignno| or -|\leqalignno| is used. However |\eqno| and |\leqno| still result in right and -left hand equation numbers respectively.\footnote{\dagger}{These defaults are -subject to negotiation and change. It is quite easy to make the equation -sides independent of |\eqno| and |\leqno|.} - - - -\mbr -\pri\@|\noalign {<text>}| -\nbr -This is used in mathematics to insert text that you want at the left hand -margin between lines in an |\eqalignno| or |\leqalignno|. See the -|\eqalignno| example. - -\mbr -\pla\@|\openup <dimen>| -\nbr -This is used in display mathematics |$$\openup ... $$| to increase spacing -between lines in an |\eqalign|, |\eqalignno|, or |\leqalignno|. The dimension -should be |<decimal number>ex| for font size independence. It does not work -with |\cases| or |\matrix|. - -\mbr -\pri\@|\over ... \under ... - \overline{<math>} \underline{<math>} - \overbrace{<math>} \underbrace{<math>}| -\nbr -These commands put lines and braces on top or under the |<math>| expressions. -Thus -$$ -\overline{\alpha\beta\gamma} : \underline{2^x_y} : -\underbrace{\overbrace{H(x)=u+g(x,y)}} -$$ -is given by -\begintt -$$ -\overline{\alpha\beta\gamma} : \underline{2^x_y} : -\underbrace{\overbrace{H(x)=u+g(x,y)}} -$$ -\endtt - - -\mbr -\pla\@|\dots ... \cdot \cdots \ldots \ddots| -\nbr -These produce dots of various flavours. Thus -$$ -[\cdot] : [\cdots] : [\ldots] : [\ddots] -$$ -are given by -\begintt -$$ -[\cdot] : [\cdots] : [\ldots] : [\ddots] -$$ -\endtt -\mbr -\ext\@|\mathopen{<dimen or glue>}| -\nbr -This will cause all of the horizontal alignments, such as |\eqalign|, -|\eqalignno|, |\halign|, |\cases|, |\matrix|, |\bordermatrix|, |\pmatrix|, -and the table macros within the {\bf group} to be spread apart by -|<dimen or glue>|. Its effect on tables with rules or lines is probably -undesirable. {\bf It should be used only within a group such as that implied -by |$$ ... $$|.} - -\mbr - - -\mbr -\pla\@|\matrix{<entry 11>&<entry 12>&...&<entry 1n>\cr - <second row>\cr - ... - <last row> \cr} - \pmatrix{<several rows>\cr}| -\nbr -The |\matrix| entry allows for the production of matrices or arrays with an -arbitrary number of rows and columns. Thus -$$ -\left\{ - \matrix{ a & b & c \cr - \sum_{\ell=1}^n & & \alpha \cr - v=0 &\gamma & 1000.0\cr} -\right\} -$$ -is given by -\begintt -$$ -\left\{ - \matrix{ a & b & c \cr - \sum_{\ell=1}^n & & \alpha \cr - v=0 &\gamma & 1000.0\cr} -\right\} -$$ -\endtt -Note that the braces |{..}| were in addition to the rows generated by -|\matrix|. |\pmatrix| is identical to |\left( \matrix{<rows>\cr} \right)|. -This just saves the placement of the braces. - - -\mbr -\pla\@|\phantom{<math>} \vphantom{<math>} \sphantom{<hlist>}| -\nbr -|\phantom| builds a box the same size as |<math>| but prints a blank. -|\vphantom| is a box of the same height and depth as |<math>| but of zero -width \dots\ a custom made strut. |\sphantom| is used when -strange expansions such as messages create errors using a |\vphantom|. -All three are used for controlling spacing. - -\mbr -\pla\@|\sqrt{<math>}| -\nbr -This puts a square root sign around a |<math>| expression. Thus |$\sqrt{2}$| -gives $\sqrt{2}$. - -\mbr -\pla\@|\smash{<math>}| -\nbr -This leaves the |<math>| expression in a box of height and depth zero. It is -useful for certain kinds of superposition. - -\endblockmode -\ejectpage - - - -\done |