From 9a5f9a8fbaf534d7f2b0afa74d07e45ea5fada89 Mon Sep 17 00:00:00 2001
From: Karl Berry
+
+
+
+Author: F. Bosisio
+
+
+
+Package graphfig
+
+
+
+This is version 2.0, last revised 1997/15/12; documentation date 1997/15/12
+
+
+
+E-mail:
+ bosisio@mate.polimi.it
+
+Web page:
+ http://ftp.mate.polimi.it/~bosisio/LaTeX
+
+CTAN location:
+ CTAN:macros/latex/contrib/supported/bosisio/
+
+
+
+Abstract
+
+
+
+Table of contents
+
+
+This package provides some commands to make the use of graphic files +in LaTeX simpler. +
+ ++It declares the ``Figure'' environment (capitalized!) and the two +commands ``\graphfile'' and ``\graphfile*''. +Combining this commands, it is possible to include graphic files in a +LaTeX document very simply. +
+ ++This package uses the ``\includegraphics*'' command defined in +the standard graphics package. +Moreover, it uses the package subfigure when the +subfigure option is specified, and the +float package if the AllowH option +is used. +
+ ++At now, two options are available: ``subfigure'' and +``AllowH''. +
+ ++The ``subfigure'' option allow the use of sub-figures inside a +Figure environment, in order to place +multiple pictures in a single LaTeX figure (cfr. the subfigure +standard package). +
+ ++The ``AllowH'' option allow the use of the ``H'' float +specifier for the Figure environment, +in order to place the figure exaclty where the command is placed +(cfr. the float standard package). +
+ ++The ``Figure'' environment (capitalized!) is somewhat different from +the standard LaTeX ``figure'' environment: besides an optional +argument used to specify the placement parameters (which now defaults to +``[htbp]''), it has a mandatory agrument specifying the ``caption'' +and another optional argument, used as a ``label'' for cross-referencies: +
+ \begin{Figure}[+ + +]{<caption>}[<label>] + ... + \end{Figure} +
+The use of the ``H'' specifier (i.e. ``I want my float here!'') is +possible only if the ``AllowH'' option has +been specified. +
+ ++Inside the ``Figure'' environment, are available the commands: +
+ \graphfile[+which are a simplified version of the ``\includegraphics*'' +command (which is automatically included by this package; see the +graphics package for reference), since you don't have to worry +about scaling: the mandatory argument is the name of the graphic file to +include, whereas the first optional argument specifies the desired width +(in the non *-form) or heigth (in the *-form) of the figure as a fraction +of ``\linewidth'' (e.g. ``|50|'' means +``.50\linewidth'', i.e. half a line! ), so no unit of measure +(as ``cm'' or ``pt'') is required. + + +]{ }[ ] + \graphfile*[ ]{ }[ ] +
+Moreover, since the ``*-form'' of ``\includegraphics'' is used, +the regions outside the bounding-box of postscript files are not drawn. +
+ ++Another advantage of the combined use of the +``Figure'' environment and the +``\graphfile'' commands is that the picture is automatically +centered horizontally, so no ``\centering'' or similar +declartion is required. +
+ \begin{Figure}[+ + +]{<caption>}[<label>] + \graphfile[ ]{ } + \end{Figure} +
+If you want to include more than one file in a single figure, you may +specify the ``subfigure'' option, which +includes the subfigure package and provides the authomatic +placement of a sub-caption below each picture. +
+ ++If the ``subfigure'' option is not specified, multiple graphs are +still allowed but no sub-caption will appear. +
+ \graphfile[+This is a combined version of ``\subfigure'' and +``\includegraphics*'' (see the subfigure and +graphics packages for reference): +the last optional argument specify a ``caption'' for the sub-figure under +consideration, while the first two arguments work exactly like as described +above in the case of one only picture (indeed, you can use the last optional +argument even if the subfigure option was not specified, in which +case it is simply ignored). + + +]{ }[ ] + ... + \graphfile[ ]{ }[ ] +
+Each individual caption is printed preceded by a bracketed letter, which is +the sub-figure counter and is printed even if no caption is specified. +Using only a series of ``\graphfile[...]{...}[...]'' commands +inside a ``Figure'' environment provides an equal spacing beetween +the pictures and around them, without the need for any extra command. +
+ ++Finally, if a ``<label>'' was specified as the last optional +argument to the ``Figure'' environment, +you can reference to each individual sub-figure by the labels +``<label>:a'', ``<label>:b'', and so on, without +the need for declaring them. +
+ \begin{Figure}[+ + +]{<caption>}[<label>] + \graphfile[ ]{ }[ ] + \graphfile[ ]{ }[ ] + : + : + \end{Figure} +
+ +
+This page describes the LaTeX packages developed and mantained
+by F. Bosisio at the "Politecnico di Milano", Italy.
+
+For informations on the whole LaTeX packages see any +CTAN archive, like + +http://www.tex.ac.uk +
+ ++At now the available packages are +
+This package provides some environments and commands which I found very +useful in math-mode. +
+ ++The new math environments are used to make multi-line formulas and systems +of equations, both numbered or unnumbered. +Also the standard equation environment may be redefined so that +it has the same optional argument as the other ones (this optional argument +is simply a label for cross-referencies). +
+ ++Also a very simple way of making adjustable-size matching braces is +available. +
+ ++For more informations, see the on-line +documentation or +download the documentation file. +
+ ++The source file is mathenv.dtx, which also +deserves as an installation driver: simply run it through LaTeX in order +to get the corresponding mathenv.sty file +and also the documentation driver mathenv.drv (which you +must run throught LaTeX to get the documentation). +
+ ++This package provides some commands which I found very useful in math-mode. +
+ ++The new commands include derivatives, vectors operators, arrow-limits, +integrals and sums. +
+ ++For more informations, see the on-line +documentation or +download the documentation file. +
+ ++The source file is mathcmd.dtx, which also +deserves as an installation driver: simply run it through LaTeX in order +to get the corresponding mathcmd.sty file +and also the documentation driver mathcmd.drv (which you +must run throught LaTeX to get the documentation). +
+ ++This package provides some commands which I found very useful when +dealing with higher Mathematics that envolves the use of Hilbert and +Sobolev spaces. +
+ ++The new commands include norm, semi-norm, scalar products, crochet symbols, +besides the various Sobolev spaces. +
+ ++For more informations, see the on-line +documentation or +download the documentation file. +
+ ++The source file is sobolev.dtx, which also +deserves as an installation driver: simply run it through LaTeX in order +to get the corresponding sobolev.sty file +and also the documentation driver sobolev.drv (which you +must run throught LaTeX to get the documentation). +
+ ++This package provides some very powerful commands to deal with figures +and graphics files in LaTeX. +
+ ++It provides a new Figure environment and a +\graphfile command: the combined use of these authomatically +produce a correct centering of the graph(s) with respect to the page. +Moreover, subfigures can be handled in the same way and hard-to-discover +errors (such as a \label preceding a \caption) +are eliminated. +
+ ++For more informations, see the on-line +documentation or +download the documentation file. +
+ ++The source file is graphfig.dtx, which also +deserves as an installation driver: simply run it through LaTeX in order +to get the corresponding graphfig.sty file +and also the documentation driver graphfig.drv (which you +must run throught LaTeX to get the documentation). +
+ ++This package provides a simple way to define new commands whose goal +is to print a letter in the blackboard-bold font. +
+ ++For more informations, see the +documentation +file. +
+ ++The source file is dblfont.dtx, which also +deserves as an installation driver: simply run it through LaTeX in order +to get the corresponding dblfont.sty file +and also the documentation driver dblfont.drv (which you +must run throught LaTeX to get the documentation). +
+ ++This package provides a shorter version of the accents-making commands +of LaTeX. +They were explicitly build for Italian language, so that only the accents +that occurr in it are handled (the standard LaTeX accents commands still +remains available, though): for this reason this was not made a +standard package available throught CTAN archives. +
+ ++Nevertheless, I let it here since italian writers may find it useful, +expecially if they work with an italian keyboard (i.e. one without +a key for the backquote character). +In such a case, a suitable option is given to let LaTeX understand the +extended ASCII characters that represents accented letters: however, +if you use it remember that this may fail on some systems (e.g. when +copying the file on a UNIX machine). +
+ ++For more informations, see the +documentation +file. +
+ ++The source file is accenti.dtx, which also +deserves as an installation driver: simply run it through LaTeX in order +to get the corresponding accenti.sty file +and also the documentation driver accenti.drv (which you +must run throught LaTeX to get the documentation). +
+ + +
+
+Author: F. Bosisio
+
+E-mail:
+ bosisio@mate.polimi.it
+
+Web page:
+ http://ftp.mate.polimi.it/~bosisio/LaTeX
+
+CTAN location:
+ CTAN:macros/latex/contrib/supported/bosisio/
+
+
+
+
+ +
+ +
+
+ +
+In particular the ``\d'' command is +redefined, so care should be taken, expecially when including this package +in an already existent LaTeX file. + +
+The original work of ``\d'' (i.e. place a dot under its argument) +is now done by the ``\UnderDot'' command. + +
+At now, six options are available with the mathcmd package, which +comes out in matched pairs. + +
+The ``ThreeSubscrSum'' and ``TwoSubscrSum'' options control +the placement of subscripts for +the ``\Sum'' command: the latter +(which is the default) puts the index under the simbol toghether with the +starting point, while the former puts the index on the lower right corner. + +
+The ``ProdVettWedge'' and ``ProdVettTimes'' options +select which symbol is to be used for the +vector product: the first one uses +a ``\wedge'' (default), whilst the second uses a ``\times". + +
+Finally, the ``VectOpStr'' and ``VectOpSymb'' options +controls whether the vector-operator commands +``\Grad'', ``\Div'' and ``\Rot'' should produce +a roman string (default) or a ``\nabla" symbol followed by an +operator, respectively. + +
+The mathcmd package defines a number of math-mode commands. + +
+The ``\text...'' command is defined to be equivalent to +``\mbox'' (except when the ``amstext" package is also used, +since this package already defines this command in a better way). + +
+It is intended for inserting pieces of text in a formula. + +
+The ``\Int'' (capitalized) differs from the LaTeX command +``\int'' in that it is always printed in displaystyle and +if it has only a subscript, this is somewhat lowered so that it looks better. +
+ \Int_{...}^{...} ... \d{...} ++ +
+The ``\d...'' command is for making the +differential symbol at the end of integrals: it simply prints a ``d'' +followed by its argument and preceded by a little space, which seems prettier. + +
+The ``\Sum{...=...,...}'' command works differently, depending on +which option between ``TwoSubscrSum'' +(default) and ``ThreeSubscrSum'' has been +specified. + +
+In the first case, it expands to +``\displaystyle\sum_{...}={...}^{...}'', whereas in the second +case the second and third argument are treated in the same way as before +(i.e. as a subscript and superscript, respectively), but the first argument +(the one before the ``='') is placed near the lower-left edge of the +``\sum'' symbol and the ``='' is not printed. + +
+There is also a ``\SUM...'' command which is useful when only a +subscript is desired, irrespectively of the option specified: in fact, it +is equivalent to ``\displaystyle\sum_...". + +
+The commands ``\DerTot{...}{...}'', ``\DerPar{...}{...}'' and +``\DerNorm{...}'' generate the symbols of total derivative, partial +derivative and normal derivative, respectively. + +
+In other words, they are the same as: +
+ \displaystyle\frac{d...}{d...} + \displaystyle\frac{\partial ...}{\partial ...} + \displaystyle\frac{\partial ...}{\partial n} ++ +
+The command ``\TendsTo[...,...]'' generates a right-arrow with +optionally an underscript wich is another smaller right-arrow between the +two comma-separeted arguments inside the square brackets. + +
+For example, the command ``f(x) \TendsTo[x,0] 1'' generates +the following output: +
+ f(x) ----------> 1 + x --> 0 ++ +
+Finally, the commands ``\Grad'', ``\Div'' and +``\Rot'' generates the strings ``grad'', ``div'' and ``rot'' +in roman type and with small spaces added before and after, if the +``VectOpStr'' option is in effect (default). +If, instead, the option ``VectOpSymb'' was specified, +they generate ``\nabla", ``\nabla\cdot'' and +``\nabla\ProdVett'' respectively. + +
+The command ``\ProdVett'' is intended for making the symbol of +vector product, and evaluates to ``\times'' with the option +``ProdVettTimes'' and to ``\wedge'' +with the (default) option ``ProdVettWedge''. + +
+ +
+
+Author: F. Bosisio
+
+E-mail:
+ bosisio@mate.polimi.it
+
+Web page:
+ http://ftp.mate.polimi.it/~bosisio/LaTeX
+
+CTAN location:
+ CTAN:macros/latex/contrib/supported/bosisio/
+
+
+
+
+ +
+
+ + ++This package provides some useful math-commands and enviroments, which +are simpler to use and prettier then their standard LaTeX counterpart. +
+ ++In particular some commands are redefined +(see next section if you don't want them to be +redefined), so care should be taken, expecially when including this package +in an already existent LaTeX file. + +
+The redefined commands are:
+\(, \),
+\[, \],
+\{ and \}.
+The effect of ``\( ...\)'' can still be achieved by
+the LaTeX equivalent commands ``\begin{math} ... \end{math}''
+or ``$...$''.
+
+Similarly, the effect of ``\[...\]'' can be achieved by the +LaTeX equivalent commands +``\begin{displaymath}...\end{displaymath}'' or +``$$...$$''. +
+ ++The ``\{'' and ``\}'' commands are the more +error-prone, since one may try to use ``\left\{'', which now +is incorrect, because the ``\{'' command already contains a +``\left'' declaration. +In the rare occasions where a brace of normal size is needed, one can use +the LaTeX commands ``\lbrace'' and ``\rbrace''. +
+ ++Also the ``equation'' environment has been +changed, but it is completly compatible with the original definition, so it +should be safe, perhaps except when the first character of the equation is +an open square bracket or it is placed in a moving argument: +in fact, the new version of this command is fragile, and this is true also +for most of the commands defined by this package. +
+ ++At now, five options are available with the mathenv package. +
+ ++The ``RedefEquation''/``StdEquation'' and +``RedefBrackets''/``StdBrackets'' options control +whether the ``equation'' environment and the brace commands +``\('', ``\)'', ``\['', +``\]'', ``\{'' and ``\}'' should +be redefined or retain their original LaTeX meaning. +
+ ++More precisely, ``RedefEquation'' (default) redefines the +``equation'' environment to have an optional argument (used as a label), +while ``StdEquation'' leaves it unchanged. +In the first case, the ``equation'' environment will be equivalent to the +``Equation'' environment (capitalized!) described +below, whereas in the second case they will be different. +
+ ++Similarly, the ``RedefBrackets'' option (default) makes the + bracket commands to be redefined, whilst +``StdBrackets'' leave them their original meaning. +
+ ++Also a ``Standard'' option exists, which amounts to specify both +the ``StdEquation'' and ``StdBrackets'' options, thus making +the package fully standard, which may be useful when sending your +LaTeX files to someone else. +
+ ++This package provides some math-mode environments, each with a ``*-form'' +which does not generates numbers (or produce sub-numbering). +
+ ++The ``Equation'' environment has an optional argument which is used +as a label to reference it. +
+ \begin{Equation}[<label>] + ... + \end{Equation} ++ + +
+If the ``RedefEquation'' option is in effect (default), then +the ``equation'' environment is redefined to have the same optional +argument as ``Equation''. +
+ ++There is also a *-form, which does not generate a number (so this *-form is +really a ``displaymath'' and not an equation, but it has been added for +simmetry and for making it easier to add or remove the number to a formula). +
+ ++The *-form has an optional argument like the non-* form, which is +disregarded by the environment and is added only for simmetry reasons. +
+ \begin{equation*}[<disregarded-label>] + ... + \end{equation*} ++ + +
+The ``MultiLine'' environment is intended for formulas that don't +fit on a single line, and so must be broken across lines. +
+ ++As for the Equation environment above, +it has an optional argument which is used as a label. +
+ ++All the lines but the first are automatically indented by the lenght +``\MultiLineIndent'', which is rougthly what one expects, but +can be changed at any time by the user with +``\setlenght\MultiLineIndent{...}''. +You can also control the alignment of the continuation rows by placing an +optional & in the first row: is such a case all the others line +will not be indented by ``\MultiLineIndent'' but wil behave +as if there were an ampersand in front of them (i.e. they will be +left-aligned at the right of the & in the first row). +
+ ++Each line but the last must end with a ``\\'' command +(which can have an optional argument to add some vertical space between +lines). +When the line is broken in the middle (e.g. after a ``+'' sign) and not at +the end (i.e. after a ``='' or similar), the *-form ``\\*'' +may be used to indicate the line-break, the difference being in an extra +space added at the beginning of the next line. +The width of a this space defaults to 1em and can be changed by the user +with ``\setlenght\MultiLineStarIndent{...}''. +
+ ++
+ \begin{MultiLine}[<label>] + ... [&]= ... = \\ + = ... + \\* + + ... = \\ + = ... + \end{MultiLine} ++ + +
+Also this environment has a *-form which differs only in that it does not +generate an equation number. +
+ \begin{MultiLine*}[<disregarded-label>] + ... [&]= ... = \\ + = ... + \\* + + ... = \\ + = ... + \end{MultiLine*} ++ + +
+The ``System'' environment is used for grouping a set of equations +together inside a left brace, with one only equation number. +
+ ++Again there is an optional argument to indicate a label and each equation +is separated by a ``\\'' or ``\\*'' command, +as for the ``MultiLine'' environment. +
+ ++The rows (except the ones ended with the *-form ``\\*'') +may optionally contain one ``&'', which is usually used when +some text should be added to the equation. +
+ \begin{System}[<label>] + ... = ... [& ...] \\ + ... = ... + \\* + + ... [& ...] \\ + ... = ... [& ...] + \end{System} ++ + +
+A *-form which does not generate any number is also provided. +
+ \begin{System*}[<disregarded-label>] + ... = ... [& ...] \\ + ... = ... + \\* + + ... [& ...] \\ + ... = ... [& ...] + \end{System*} ++ + +
+The ``EqSystem'' environment is used for grouping a set of equations +together inside a left brace, each with its own equation number. +
+ ++Again there is an optional argument to indicate a label and each equation is +separated by a ``\\'' or ``\\*'' command. +
+ ++The rows may optionally contain one ``&'', which is usually used +when some text should be added to the equation. +
+ \begin{EqSystem}[<label>] + ... = ... [& ...] \\ % (1.1) + ... = ... + \\* % + + ... [& ...] \\ % (1.2) + ... = ... [& ...] % (1.3) + \end{EqSystem} ++ + +
+A *-form is also provided: it differs in that each equation is numbered with +the same number but with a lowercase letter added, i.e. like (1.1a), (1.1b), +etc. instead of (1.1), (1.2) and so on. +
+ \begin{EqSystem*}[<label>] + ... = ... [& ...] \\ % (1.5a) + ... = ... + \\* % + + ... [& ...] \\ % (1.5b) + ... = ... [& ...] % (1.5c) + \end{EqSystem*} ++In both cases, if the optional argument is present, each equation can be +referenced by \ref{<label>:a}, +\ref{<label>:b}, ..., where <label>, +stands for the string used as optional argument. +In the case of the *-form, a reference of the kind +\ref{<label>} will print the equation number without +any letter, thus referring to the system as a whole, whereas such a +reference is meaningless (and indeed does not exists) when dealing with +the non *-form. + + +
+In addition to the previously mentioned environments, the mathenv +package defines also some of math-mode commands which considerably simplify +the use of adjustable-size parentheses. +
+ ++The ``\('', ``\['', ``\{'', +``\)'', ``\]'' and ``\}'' generates +the corresponding parenthesis but with a ``\left'' or +``\right'' declaration (respectively) added, so they must come +in matched pairs or coupled with a ``\left.'' or +``\rigtht.'' or another adjustable-size delimiter. +
+ ++ +
+
+Author: F. Bosisio
+
+E-mail:
+ bosisio@mate.polimi.it
+
+Web page:
+ http://ftp.mate.polimi.it/~bosisio/LaTeX
+
+CTAN location:
+ CTAN:macros/latex/contrib/supported/bosisio/
+
+
+
+
+
+This package provides some commands which are useful when dealing with +Sobolev spaces and their relatives. + +
+In particular some commands are redefined, so care should be taken, +expecially when including this package in an already existent LaTeX file. + +
+The redefined commands are \H and \L. +The effect of ``\H'' (which is a type of accent) can now be achieved +by the command ``\HAccent'', whilst the job of ``\L'' +(i.e. print an ``L'' with a superimposed bar) is now done by the command +``\Lbar''. + +
+Two options are available at the moment: DivInBrackets and +DivAsExponent. +They only affect the output of the ``\Hdiv'' command. + +
+The firt options (DivInBrackets, which is the default) makes +\Hdiv behave like ``H(div;...)'', while the +second one (DivAsExponent) makes \Hdiv expand to +``H^{div}(...)''. + +
+Most of the subsequent space-generating commands have mandatory arguments to +indicate the type of the space. +Often this argument consists of a single digit: in this case it is not +necessary to enclose it in brackets, since in LaTeX the names of commands +consists of letters only, and so a digit following it is certainly an argument. +This saves a lot of typing and is the only reason that makes these commans +useful (if you always had to type the brackets, then it would have been simpler +to type the expansion of the command than the command itself !). +In other words, you can think as if several commands exist (like \H, +\H1, \H10, etc.), the ones with the digit beeing a sort of +abbreviation for the general one. + +
+The \H command is used to generate the symbol of sobolev spaces. +It takes a mandatory argument, which is used as a superscript, and an optional +argument, which is used as a subscript. + +
+As explained above, if the mandatory argument is a digit, it need not be +enclosed in brackets. +Moreover, if the optional argument is the digit ``0'', it can be typed without +the square brackets. + +
+Here are some examples (whith the \DefaultSet set to its default +value \Omega): +
+ \H2 ==> H^2(\Omega) + \H10 ==> H^1_0(\Omega) + \H1[\Gamma_D] ==> H^1_{\Gamma_D}(\Omega) + \H^{-1/2} ==> H^{-1/2}(\Omega) ++ +
+The \Hdiv command is used to generate the sobolev space +called ``H div''. +It takes only an optional argument, which is used as a subscript and which +need not to be surrounded by the square brackets if it is the digit ``0''. + +
+If the (default) option DivInBrackets is in effect, it differs from +the command \H in that the word ``div'' is printed (in roman type) +inside brackets, before the set. +If, instead, the option DivAsExponent is active, then it is simply +an abbreviation for \Hdiv. + +
+Here are some examples: +
+ DivInBrackets DivAsExponent + \Hdiv ==> H(\mathrm{div};\Omega) H^{\mathrm{div}}(\Omega) + \Hdiv0 ==> H_0(\mathrm{div};\Omega) H^{\mathrm{div}}_0(\Omega) + \Hdiv[\Gamma_D] ==> H_{\Gamma_D}(\mathrm{div};\Omega) H^{\mathrm{div}}_{\Gamma_D}(\Omega) ++ +
+The \L command is used to generate the symbol of Lebesgue-measurable +functions. +It has one argument which is the exponent of the L-space. +Again, if this argument is a digit (or a single symbol, +like ``\infty'') the surrounding braces are optional. +Like for the \H command, the output of \DefaultSet +is appended. + +
+Here are some examples: +
+ \L2 ==> L^2(\Omega) + \L10 ==> L^{10}(\Omega) + \L ==> L^\infty(\Omega) ++ +
+The \W command is completly analogous, except that it prints a ``W'' +insted af an ``L'' and that it has two argument, both printed as a supercript, +separated by a comma. +It is used for the generalized Sobolev spaces. + +
+Here is an example of how it is used: +
+ \W{k}{p} ==> W^{k,p}(\Omega) + \W1 ==> W^{1,\infty}(\Omega) ++ +
+The \D command is used in the theory of distributions: +it prints the space of distributions over the \DefaultSet if +followed by a prime symbol, or its dual space, otherwise. +
+ \D ==> \mathcal{D}(\Omega) + \D' ==> \mathcal{D}'(\Omega) ++ +
+The \Norm command has a mandatory and an optional argument; +it generates the norm of the mandatory argument, with the optional argument, +if present, as a whole subscript, to denote the space within which the norm +is taken. + +
+Some examples: +
+ \Normf(x) ==> \left\Vert f(x)\right\Vert + \Normg[L^2] ==> \left\Vert g\right\Vert _{L^2} ++ +
+The \SemiNorm command is completly analoguos, but generates the +semi-norm instead of the norm. + +
+Some examples: +
+ \SemiNorm{f(x)} ==> \left\Vert f(x)\right\Vert + \SemiNormg[H^1] ==> \left\vert g\right\vert _{H^1} ++ +
+The \Scalar command has two arguments; a third optional argument +(which is used as a whole subscript) may follow inside square brackets. +The output consists of the two arguments separated by a comma and enclosed +in a pair of adjustable-size brackets, with the optional argument placed as +a subscript (to denote the space inside which the scalr product is taken). + +
+Some examples: +
+ \Scalar{f}{g} ==> \left(f,g\right) + \Scalar{u}{v}[L^2] ==> left(u,v\right)_{L^2} ++ +
+The \Crochet command has two arguments; a third optional argument +(which is used as a whole subscript) may follow inside square brackets. +The output consists of the two arguments separated by a comma and enclosed +in a pair of adjustable-size angular-parenthesys, with the optional argument +placed as a subscript (to denote the space inside which the duality is taken). + +
+Some examples: +
+ \Crochet{f}{g} ==> \left\langle f,g\right\rangle + \Crochet{u}{v}[D] ==> \left\langle u,v\right\rangle_D ++ +