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@@ -1,1699 +0,0 @@
-#LyX 1.5.2 created this file. For more info see http://www.lyx.org/
-\lyxformat 276
-\begin_document
-\begin_header
-\textclass article
-\language english
-\inputencoding auto
-\font_roman default
-\font_sans default
-\font_typewriter default
-\font_default_family default
-\font_sc false
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-\font_sf_scale 100
-\font_tt_scale 100
-\graphics default
-\paperfontsize default
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-\use_geometry false
-\use_amsmath 1
-\use_esint 1
-\cite_engine basic
-\use_bibtopic false
-\paperorientation portrait
-\secnumdepth 3
-\tocdepth 3
-\paragraph_separation indent
-\defskip medskip
-\quotes_language english
-\papercolumns 1
-\papersides 1
-\paperpagestyle default
-\tracking_changes false
-\output_changes false
-\author ""
-\author ""
-\end_header
-
-\begin_body
-
-\begin_layout Title
-Dynamic Macros for LyX
-\end_layout
-
-\begin_layout Author
-Stefan Schimanski
-\newline
-
-\begin_inset LatexCommand url
-target "sts@1stein.org"
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Date
-21.10.2007
-\end_layout
-
-\begin_layout Section
-The old system
-\end_layout
-
-\begin_layout Standard
-LyX has the concept of math macros for quite some time.
- In LyX 1.4 or 1.5 you can create one in your document by calling the
-\family typewriter
-math-macro
-\family default
- command in the mini buffer.
- Visually this results in something equivalent to a TeX macro:
-\begin_inset listings
-inline false
-status open
-
-\begin_layout Standard
-
-
-\backslash
-newcommand{
-\backslash
-foo}{
-\backslash
-frac{1}{2}}
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-After LyX processed this, the command is available in math environments
- in the same documents.
- But internally there is nothing more than
-\series bold
-one
-\series default
- global macro table.
- The position inside the document does not matter.
- The command is available even in front of the definition.
- But even worse, this global macro table is global for all opened documents.
- If two buffers use the same macro name with different definitions, you
- are in trouble.
- The behaviour is undefined.
- If you are lucky LyX will not crash.
- Nothing must be said about redefining a macro later in the document: the
- behaviour of LyX will not be what you expect.
-\end_layout
-
-\begin_layout Standard
-LyX 1.4 and 1.5 do not show the support for this kind of macro very prominently.
- In fact it is described in the
-\begin_inset Quotes eld
-\end_inset
-
-Extended Features
-\begin_inset Quotes erd
-\end_inset
-
- manual.
- But there is no menu item to create macros.
- Next to the mentioned method with the mini buffer you can use the
-\begin_inset Quotes eld
-\end_inset
-
-Ctrl-L
-\begin_inset Quotes erd
-\end_inset
-
- short cut to convert a raw
-\backslash
-newcommand into a LyX math macro.
- Hence the role of macro is more of a power user tool for users who know
- what they are doing.
-\end_layout
-
-\begin_layout Section
-A wish list for a new macro implementation
-\end_layout
-
-\begin_layout Standard
-In the following usecases are shown which can be wished to be supported
- if macros are reimplemented.
- Most of them are not possible in the old implemention, or at least very
- hard to do.
-
-\end_layout
-
-\begin_layout Enumerate
-Define a
-\series bold
-new macro
-\series default
- with a known arity ("arity" = number of arguments).
- Use instances later on in the document.
-\end_layout
-
-\begin_layout Enumerate
-
-\series bold
-Redefine
-\series default
- a macro to use the same macro name with different definitions in different
- areas of the document.
-\end_layout
-
-\begin_layout Enumerate
-Have
-\family typewriter
-
-\backslash
-newcommand
-\family default
- in the preamble (i.e.
- by importing tex code) or
-\series bold
-not accessible
-\series default
- as a LyX macro in another way, and then define the command as a native
- LyX math macro later.
- All the uses of the old command should then turn into instances of the
- LyX math macro.
-
-\end_layout
-
-\begin_layout Enumerate
-
-\series bold
-Rename
-\series default
- a macro and also adapt all the instance of the macro in the document.
-\end_layout
-
-\begin_layout Enumerate
-
-\series bold
-Change the arity
-\series default
- of a macro (normaly probably increase it), maybe with a default value used
- in instances of the macro (possibly empty).
-\end_layout
-
-\begin_layout Enumerate
-
-\series bold
-Removal
-\series default
- of a macro.
-\end_layout
-
-\begin_layout Enumerate
-Insertion of a macro via the
-\series bold
-menu
-\series default
- like "Insert->MathMacro".
-\end_layout
-
-\begin_layout Enumerate
-
-\series bold
-Moving
-\series default
- of a macro.
-\end_layout
-
-\begin_layout Enumerate
-
-\series bold
-\begin_inset LatexCommand label
-name "sub:listedit"
-
-\end_inset
-
-
-\series default
-Editing of a macro instance as a
-\series bold
-list
-\series default
- of #1: __, #2: __, i.e.
- it
-\series bold
-unfold
-\series default
-s when the cursor goes inside.
-\end_layout
-
-\begin_layout Enumerate
-Editing of macros
-\series bold
-inline
-\series default
- (the macro definition will be read-only, only the arguments as holes are
- editable).
-\end_layout
-
-\begin_layout Enumerate
-Changing of the
-\series bold
-editing behaviour
-\series default
- of
-\series bold
-
-\begin_inset LatexCommand ref
-reference "sub:listedit"
-
-\end_inset
-
-
-\series default
- for certain macros, not only globally.
-\end_layout
-
-\begin_layout Enumerate
-Defining dynamic
-\series bold
-macros inside of macros
-\series default
-.
-\end_layout
-
-\begin_layout Enumerate
-Using macros with the
-\series bold
-same name
-\series default
-, but different definitions in different open documents or parts of the
- same document.
-\end_layout
-
-\begin_layout Enumerate
-Using macros from the
-\series bold
-master document
-\series default
-.
-\end_layout
-
-\begin_layout Enumerate
-Using the same argument, e.g.
- #1, (
-\series bold
-non-linearly
-\series default
-) more than once in the definition, like
-\family typewriter
-
-\backslash
-newcommand{
-\backslash
-ntothen}[1]{#1^#1}
-\end_layout
-
-\begin_layout Enumerate
-
-\series bold
-Patterns
-\series default
- like
-\family typewriter
-
-\backslash
-def
-\backslash
-foo #1/#2{
-\backslash
-frac{#1}{#2}}
-\end_layout
-
-\begin_layout Enumerate
-
-\series bold
-Higher order
-\series default
- substitution (or call-by-name text substition) like
-\family typewriter
-
-\backslash
-def
-\backslash
-foo #1{#1 12}
-\family default
-, which is applicable like
-\family typewriter
-
-\backslash
-foo
-\backslash
-frac
-\family default
- to give
-\family typewriter
-1/2
-\end_layout
-
-\begin_layout Enumerate
-
-\series bold
-Optional
-\series default
- parameters like
-\family typewriter
-
-\backslash
-newcommand{
-\backslash
-foo}[2][x]{#2_#1}
-\end_layout
-
-\begin_layout Standard
-The old implementation supports the following:
-\series bold
-new macro
-\series default
-,
-\series bold
-moving
-\series default
-,
-\series bold
-list
-\series default
-,
-\series bold
-master document
-\series default
-,
-\series bold
-non-linear.
-
-\series default
-Though support of master documents is more or less an coincidence by the
- global table.
-\end_layout
-
-\begin_layout Standard
-The implementation described later (short: the new implementation) supports
- the following:
-\series bold
-new macro
-\series default
-,
-\series bold
-redefine
-\series default
-,
-\series bold
-not accesible
-\series default
-,
-\series bold
-change the arity
-\series default
-,
-\series bold
-removal
-\series default
-,
-\series bold
-menu
-\series default
-,
-\series bold
-moving
-\series default
-,
-\series bold
-unfolds
-\series default
-,
-\series bold
-inline
-\series default
-,
-\series bold
-same name
-\series default
-,
-\series bold
-master documents
-\series default
-,
-\series bold
-non-linearly
-\series default
-,
-\series bold
-optional
-\series default
-.
-\end_layout
-
-\begin_layout Standard
-Not supported are:
-\series bold
-patterns
-\series default
-,
-\series bold
-higher order
-\series default
-,
-\series bold
-macros inside of macros
-\series default
-,
-\series bold
- editing behaviour
-\series default
-,
-\series bold
- list
-\series default
-,
-\series bold
- rename
-\series default
-.
- The last 3 should be doable without much work, maybe also
-\series bold
-patterns
-\series default
-.
-\end_layout
-
-\begin_layout Subsection
-Main deficiencies of the old system
-\end_layout
-
-\begin_layout Standard
-The main problem of the old implementation is that it is not dynamic at
- all.
- A macro is resolved (i.e.
- the lookup in the global table takes place) when the internal object is
- created, e.g.
- while parsing of the
-\family typewriter
-.lyx
-\family default
- document or when typing
-\family typewriter
-
-\backslash
-foo
-\family default
-.
- If no macro definition of the right name exists at this time, an ERT is
- created.
-
-\end_layout
-
-\begin_layout Standard
-Moreover there is no position awareness of the definition, only during loading
- of a document there is something like that because macro definitions are
- put into the global table at the point in the document where it appears.
-
-\end_layout
-
-\begin_layout Section
-A new approach
-\end_layout
-
-\begin_layout Standard
-The goal of a new macro approach must be to support as many use cases subsection
- 1.2 as possible, or at least make an implementation possible of the remaining
- ones.
- Moreover a proper implementation better brings most of TeX's power of math
- command into LyX.
-\end_layout
-
-\begin_layout Standard
-In a few words the new approach could be described as follow:
-\end_layout
-
-\begin_layout Itemize
-A macro is a dynamic inset which can
-\begin_inset Quotes eld
-\end_inset
-
-eat up
-\begin_inset Quotes erd
-\end_inset
-
- or
-\begin_inset Quotes eld
-\end_inset
-
-spit out
-\begin_inset Quotes erd
-\end_inset
-
- insets which follow the macro, depending on the success to resolve it and
- the arity of the macro definition at the position in the document.
-\end_layout
-
-\begin_layout Itemize
-Macros are resolved again everytime it is redrawn on screen if the macro
- definition changed which is valid at the position.
-\end_layout
-
-\begin_layout Standard
-This
-\begin_inset Quotes eld
-\end_inset
-
-eat up
-\begin_inset Quotes erd
-\end_inset
-
- and
-\begin_inset Quotes eld
-\end_inset
-
-spit out
-\begin_inset Quotes erd
-\end_inset
-
- process is the key idea.
- Imagine a macro definition
-\family typewriter
-
-\backslash
-newcommand{
-\backslash
-foo}[2]{a#1b#2c}
-\family default
- which is valid when a macro
-\family typewriter
-
-\backslash
-foo
-\family default
-appears in the context
-\family typewriter
-
-\backslash
-foo ABCD
-\family default
-.
- When the macro is drawn the definition is checked and the arity is compared
- to the number of
-\begin_inset Quotes eld
-\end_inset
-
-eaten
-\begin_inset Quotes erd
-\end_inset
-
- insets.
- At the beginning the latter will be zero.
- Because the arity of
-\family typewriter
-
-\backslash
-foo
-\family default
- is 2, the macro inset will eat up 2 insets (the
-\family typewriter
-A
-\family default
- and the
-\family typewriter
-B
-\family default
-), hence internally the macro
-\family typewriter
-
-\backslash
-foo
-\family default
- is changed to arity 2 and
-\family typewriter
-A
-\family default
- and
-\family typewriter
-B
-\family default
- are moved into it.
- The visual representation of macro is that of the definition with the arguments
- replaced by the eaten insets.
- So eventually you will see
-\family typewriter
-aAbBcCD
-\family default
- on screen.
-\end_layout
-
-\begin_layout Standard
-When you change the macro definition at the position into a unary macro,
- e.g.
-
-\family typewriter
-
-\backslash
-newcommand{
-\backslash
-foo}[1]{a#1b}
-\family default
-, the macro inset will spit out the second eaten inset, here the
-\family typewriter
-B
-\family default
-.
- Hence you will eventually see
-\family typewriter
-aAbBCD
-\family default
-.
-\end_layout
-
-\begin_layout Standard
-This process is done automatically, transparent to the user and in a fast
- way everytime the macro is rendered and the definition has changed.
-\end_layout
-
-\begin_layout Standard
-If you look at the produced TeX code of the
-\family typewriter
-
-\backslash
-foo ABCD
-\family default
- you will notice that it didn't change during all this eating and spitting.
- This is what you expect from a macro in TeX.
- There the whole sense of command (i.e.
- macros) is that you keep the same TeX code, independently from the macro
- definition.
- This approach carries this over to the LyX world.
-\end_layout
-
-\begin_layout Subsection
-The implementation
-\end_layout
-
-\begin_layout Subsubsection
-MathData
-\end_layout
-
-\begin_layout Standard
-When a MathData object is drawn, more precisely when the metrics are computed,
- all math macros in the
-\family typewriter
-MathData
-\family default
- are processed in the way described in the previous section.
- If the arity of definition of a macro is changed the spitting/eating process
- takes place.
- This is implemented in
-\family typewriter
-MathData::updateMacros
-\family default
-, in a quite straight forward way.
-
-\end_layout
-
-\begin_layout Standard
-Some complexity comes into the game by the necessary updating of the current
- cursor.
- If the user unfolds a macro the arity practically changes to zero, hence
- the arguments are spit out.
- If the cursor was inside an argument before, it should be in the same argument
- after the unfolding.
- The same should be the case for folding.
-\end_layout
-
-\begin_layout Standard
-The metrics calculation is, by its typing, a const method, i.e.
- it shouldn't change the
-\family typewriter
-MathData
-\family default
- object.
- The macro updating though does changes of course.
- Technically this is true, semantically (taking the produced TeX code as
- semantics) it is not because nothing changes by eating/spitting or folding/unfo
-lding with the later output.
- To still allow these changes in
-\family typewriter
-MathData::metrics
-\family default
- a
-\family typewriter
-const_cast
-\family default
- is used.
- This is somewhat ugly and a cleaner solution should be found.
- Maybe one day the drawing and metrics will merge, then it would make sense
- to think about the
-\family typewriter
-const_cast
-\family default
- as well again.
-\end_layout
-
-\begin_layout Subsubsection
-Macro Table
-\end_layout
-
-\begin_layout Standard
-How does the
-\family typewriter
-MathData
-\family default
- know which macro definitions are known at its position in the buffer? During
- the metrics call a
-\family typewriter
-MacroContext
-\family default
- is passed around as an element of the
-\family typewriter
-MetricsInfo
-\family default
- class.
- This context can be asked to resolve a macro name.
-\end_layout
-
-\begin_layout Standard
-To make this possible it has to know about a position in the buffer.
- In fact it knows about the paragraph in the buffer, and in addition it
- has a
-\begin_inset Quotes eld
-\end_inset
-
-local
-\begin_inset Quotes erd
-\end_inset
-
-
-\family typewriter
-MacroTable
-\family default
-.
- The latter is used to also resolve macros correctly which are defined in
- the paragraph where the macro appears.
- The inset loop in the
-\family typewriter
-TextMetrics::redoParagraph
-\family default
- creates and updates the
-\family typewriter
-MacroContext
-\family default
- and the local macros in the expected way.
-
-\end_layout
-
-\begin_layout Standard
-All the other macros are resolved by the
-\family typewriter
-MacroContext
-\family default
- by asking the buffer directly.
- For this the
-\family typewriter
-MacroContext
-\family default
-, as written above, knows the paragraph it belongs to.
- It passes this information to the buffer (via
-\family typewriter
-Buffer::hasMacro(docstring name, Paragraph par)
-\family default
-) and the buffer then uses the
-\family typewriter
-par.macrocontextPosition()
-\family default
- information to lookup the defined macros at the position in the map
-\family typewriter
-Buffer::pimpl->macros
-\family default
-.
- This maps macro names and positions to the macro definitions.
- which are defined at the position or before.
-\end_layout
-
-\begin_layout Standard
-The missing bit is how the buffer creates this map.
- This is done in the same way as in the old macro implementation, namely
- by the Buffer::updateMacros method which iterates over the top-level inset
- of the buffer.
- It is called from
-\family typewriter
-BufferView::processUpdateFlags
-\family default
- very often.
- This sounds slow, but it turned out that it is not noticable in fact.
- In LyX 1.5 the same is done as well already.
- Maybe some optimisation could help though, but was not investigated.
-\end_layout
-
-\begin_layout Standard
-To support master documents there will a last lookup (if the previous lookup
- were not successfull) by asking the master buffer.
-\end_layout
-
-\begin_layout Subsection
-File Format
-\end_layout
-
-\begin_layout Standard
-The file format concerning macros in the old macro implementation is not
- well defined.
- As described above there is a big difference between the visual semantics
- (what the user sees inside LyX 1.5) and the latex semantics (what LaTeX
- will make out of the document) are not the same.
-\end_layout
-
-\begin_layout Standard
-The new approach changes this for most documents (if the user does not do
- any dirty tricks at least) to be the same.
- So from the file format point of view there probably should not be any
- conversion needed to a new file format.
-\end_layout
-
-\begin_layout Standard
-One exception of this comes from the support for optional arguments in the
- new implementation.
- Those were not available in the old format.
-\end_layout
-
-\begin_layout Subsubsection
-Simple Macros
-\end_layout
-
-\begin_layout Standard
-Macro definitions are stored in the following way:
-\begin_inset listings
-inline false
-status open
-
-\begin_layout Standard
-
-
-\backslash
-begin_inset FormulaMacro
-\end_layout
-
-\begin_layout Standard
-
-
-\backslash
-newcommand{
-\backslash
-abc}[1]{
-\backslash
-sin
-\backslash
-left(
-\backslash
-frac{-3}{#1}
-\backslash
-right)}
-\end_layout
-
-\begin_layout Standard
-
-
-\backslash
-end_inset
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-The resulting LaTeX code is as expected:
-\begin_inset listings
-inline false
-status open
-
-\begin_layout Standard
-
-
-\backslash
-newcommand{
-\backslash
-abc}[1]{
-\backslash
-sin
-\backslash
-left(
-\backslash
-frac{-3}{#1}
-\backslash
-right)}
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsubsection
-One Optional Argument
-\end_layout
-
-\begin_layout Standard
-With one optional argument the LyX code looks like this:
-\begin_inset listings
-inline false
-status open
-
-\begin_layout Standard
-
-
-\backslash
-begin_inset FormulaMacro
-\end_layout
-
-\begin_layout Standard
-
-
-\backslash
-newcommand{
-\backslash
-abc}[1][42]{
-\backslash
-sin
-\backslash
-left(
-\backslash
-frac{-3}{#1}
-\backslash
-right)}
-\end_layout
-
-\begin_layout Standard
-
-
-\backslash
-end_inset
-\end_layout
-
-\end_inset
-
- and the LaTeX code again is the same:
-\begin_inset listings
-inline false
-status open
-
-\begin_layout Standard
-
-
-\backslash
-newcommand{
-\backslash
-abc}[1][42]{
-\backslash
-sin
-\backslash
-left(
-\backslash
-frac{-3}{#1}
-\backslash
-right)}
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsubsection
-Multi Optional Argument Macro
-\end_layout
-
-\begin_layout Standard
-More than one optional argument is not supported by LaTeX.
- There are several solutions to allow them by defining some custom
-\family typewriter
-
-\backslash
-newcommand
-\family default
-, but this is not standarized.
- It might make sense for LyX to also support those when importing, but this
- is not implemented.
- Instead the new implementation will create valid standard LaTeX code by
- outputting what the user sees on screen in LyX:
-\begin_inset listings
-inline false
-status open
-
-\begin_layout Standard
-
-
-\backslash
-begin_inset FormulaMacro
-\end_layout
-
-\begin_layout Standard
-
-
-\backslash
-newcommand{
-\backslash
-xyz}[2][42][28]{
-\backslash
-sqrt{#1}+
-\backslash
-ln
-\backslash
-left(
-\backslash
-frac{#2}{82}
-\backslash
-right)}
-\end_layout
-
-\begin_layout Standard
-
-
-\backslash
-end_inset
-\end_layout
-
-\end_inset
-
- with the LaTeX code:
-\begin_inset listings
-inline false
-status open
-
-\begin_layout Standard
-
-
-\backslash
-newcommand{
-\backslash
-xyz}[2][42]{
-\backslash
-sqrt{#1}+
-\backslash
-ln
-\backslash
-left(
-\backslash
-frac{#2}{82}
-\backslash
-right)}
-\end_layout
-
-\end_inset
-
-When the user creates an instance of
-\backslash
-xyz without substituting the optional argument, e.g.
- by
-\begin_inset listings
-inline false
-status open
-
-\begin_layout Standard
-
-
-\backslash
-xyz
-\end_layout
-
-\end_inset
-
- LyX will create the following LaTeX code when exporting to LaTeX:
-\begin_inset listings
-inline false
-status open
-
-\begin_layout Standard
-
-
-\backslash
-xyz{28}
-\end_layout
-
-\end_inset
-
-So the optional argument is not optional anymore after export, but explicit.
-\end_layout
-
-\begin_layout Subsubsection
-
-\backslash
-def style
-\end_layout
-
-\begin_layout Standard
-Last but not least, as in the old implementation you can use
-\family typewriter
-
-\backslash
-def
-\family default
- macros, i.e.
- TeX style definitions.
- They don't support optional arguments.
- They don't support
-\begin_inset Quotes eld
-\end_inset
-
-patterns
-\begin_inset Quotes erd
-\end_inset
-
- of the shape
-\family typewriter
-
-\backslash
-def
-\backslash
-term #1+#2{#1+#2}
-\family default
- where you can use it as in
-\family typewriter
-
-\backslash
-term 43+12
-\family default
-.
-\end_layout
-
-\begin_layout Subsubsection
-Redefinition
-\end_layout
-
-\begin_layout Standard
-On export LyX will correctly use
-\family typewriter
-
-\backslash
-newcommand
-\family default
- and
-\family typewriter
-
-\backslash
-renewcommand
-\family default
- if needed.
- This is not visible in the LyX file format though.
-\end_layout
-
-\begin_layout Subsection
-How it looks to the user
-\end_layout
-
-\begin_layout Subsubsection
-Creation
-\end_layout
-
-\begin_layout Standard
-Macro definitions look more or less the same as in the old implementation.
- I.e.
- there is a macro definition inset showing the macro like
-\family typewriter
-
-\backslash
-foo{#1}:={a#1b}
-\family default
-.
- You can create i
-\family typewriter
-t
-\family default
- via the
-\begin_inset Quotes eld
-\end_inset
-
-math-macro foo 4
-\begin_inset Quotes erd
-\end_inset
-
- to create a macro
-\family typewriter
-
-\backslash
-foo
-\family default
- with 4 parameters.
-\end_layout
-
-\begin_layout Standard
-A second way to create them is to write down the LaTeX definition like
-\family typewriter
-
-\backslash
-newcommand
-\backslash
-foo{abc}
-\family default
- as plain text.
- Select it and press Ctrl-m.
-\end_layout
-
-\begin_layout Standard
-The last way, which is new with the new implementation, is to use the Insert/Mat
-h/Macro menu item.
-\end_layout
-
-\begin_layout Subsubsection
-Modification
-\end_layout
-
-\begin_layout Standard
-The are the following actions defined:
-\end_layout
-
-\begin_layout Standard
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Standard
-Action
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Standard
-Menu
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Standard
-math-macro-unfold
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Standard
-View/Unfold Math Macro
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Standard
-math-macro-fold
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Standard
-View/Fold Math Macro
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Standard
-math-macro-add-param
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Standard
-Edit/Math/Macro/Append Parameter
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Standard
-math-macro-remove-param
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Standard
-Edit/Math/Macro/Remove Last Parameter
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Standard
-math-macro-append-greedy-param
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Standard
-Edit/Math/Macro/Append Parameter Eating From the Right
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Standard
-math-macro-make-optional
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Standard
-Edit/Math/Macro/Make First Non-Optional into Optional Parameter
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Standard
-math-macro-remove-greedy-param
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Standard
-Edit/Math/Macro/Remove Last Parameter Spitting Out To The Right
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Standard
-math-macro-make-nonoptional
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Standard
-Edit/Math/Macro/Make Last Optional into Non-Optional Parameter
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Standard
-math-macro-add-optional-param
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Standard
-Edit/Math/Macro/Insert Optional Parameter
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Standard
-math-macro-remove-optional-param
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Standard
-Edit/Math/Macro/Remove Optional Parameter
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Standard
-math-macro-add-greedy-optional-param
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Standard
-Edit/Math/Macro/Append Optional Parameter Eating From the Right
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsubsection
-Greedy vs.
- Non-Greedy
-\end_layout
-
-\begin_layout Standard
-As described above the key idea is that macros and eat up and spit out parameter
-s, depending on their arity.
- This makes them very dynamic and powerful, but at the same time adds some
- complexity which must be understood by the user to effectively use the
- macros.
-\end_layout
-
-\begin_layout Standard
-Hence if the arity is increased (i.e.
- another parameter is added to a macro) there are two ways to do that: if
- this is done greedily the macro tries to eat up another inset from the
- right.
- This is the natural way if you import a document and then start to define
- a macros with LyX's math macros.
- Then you want that the macros take the (existing) paramenters from the
- right.
-\end_layout
-
-\begin_layout Standard
-The second case is the non-greedy use case.
- E.g.
- you want to change a macro to take another parameter because you just found
- out that your notation needs another index.
- Then you want to insert this non-greedily.
- All macro instances in your text should get another parameter without touching
- the surrouindings.
-\end_layout
-
-\begin_layout Standard
-The greedy variants of the actions have the word
-\begin_inset Quotes eld
-\end_inset
-
-greedy
-\begin_inset Quotes erd
-\end_inset
-
- in their name.
-\end_layout
-
-\begin_layout Standard
-Some of the actions also take a paramenter to define the position to act
- on in the parameter list.
- E.g.
- you can write
-\family typewriter
-math-macro-add-param 2
-\family default
- in the mini-buffer to add a parameter at position 2.
-\end_layout
-
-\begin_layout Subsubsection
-Folding/Unfolding
-\end_layout
-
-\begin_layout Standard
-Sometimes it is desireable to switch to the TeX code of a macro instance,
- i.e.
- without any substitution using the macro definition.
- This can be done with the fold/unfold actions.
- You can use the
-\family typewriter
-Ctrl-+
-\family default
- and
-\family typewriter
-Ctrl--
-\family default
- shortcuts for that.
-\end_layout
-
-\begin_layout Standard
-If you nest macro instances these actions will unfold from inside to the
- outside and the same for folding.
- This is supposed to replace the old list display when entering a macro.
-\end_layout
-
-\begin_layout Subsubsection
-Toolbar
-\end_layout
-
-\begin_layout Standard
-Currently there is no toolbar for math macros.
- Because the menu hierarchy is very deep a toolbar would make the life a
- lot easier.
- It shouldn't be hard to implement that.
-\end_layout
-
-\begin_layout Subsubsection
-More natural macro definition editing
-\end_layout
-
-\begin_layout Standard
-Instead of the described actions it would desirable to add another more
- natural way to edit macros.
- The vision is that the user can put the cursor everywhere inside of the
- macro definition inset which shows (already now!) the definition in the
- way
-\family typewriter
-
-\backslash
-name{#1}{#2}:={definition}
-\family default
-.
- The user should be able to use the backspace and the
-\family typewriter
-{
-\family default
- key to remove and add parameters when the cursor is in the parameter definition
- part.
- For a non-greedy macro-append one could put a small (+) button or a hungry
- packman
-\family typewriter
-(<
-\family default
- behind the
-\family typewriter
-{#2}
-\family default
- in front of the definition.
-\end_layout
-
-\begin_layout Standard
-For implementing this one has to customize the
-\family typewriter
-MathInsetNest
-\family default
- a lot to handle the keypresses correctly, because it's probably not directly
- doable with
-\family typewriter
-MathInsetNest
-\family default
- in a simple way with its children insets.
-\end_layout
-
-\begin_layout Subsubsection
-Keyboard navigation
-\end_layout
-
-\begin_layout Standard
-You can jump from
-\family typewriter
-#n
-\family default
- to
-\family typewriter
- #n+1
-\family default
- with the cursor key and conversely backwards.
- This navigation is not visual.
- I.e.
- the user can define macros like
-\family typewriter
-
-\backslash
-foo{#1}{#2}:={#2+#1}
-\family default
-.
- Then the cursor jumps first to the right and then to the left where the
- #1 is.
- This can be confusing.
- One could think about a visual movement mode by taking the position of
- the macro argument insets into account to find the next inset for the cursor
- keys.
- This should be doable.
-\end_layout
-
-\end_body
-\end_document
diff --git a/development/mathmacros/testcases_basic.lyx b/development/mathmacros/testcases_basic.lyx
deleted file mode 100644
index bd11a011eb..0000000000
--- a/development/mathmacros/testcases_basic.lyx
+++ /dev/null
@@ -1,260 +0,0 @@
-#LyX 1.6svn created this file. For more info see http://www.lyx.org/
-\lyxformat 317
-\begin_document
-\begin_header
-\textclass article
-\language english
-\inputencoding auto
-\font_roman default
-\font_sans default
-\font_typewriter default
-\font_default_family default
-\font_sc false
-\font_osf false
-\font_sf_scale 100
-\font_tt_scale 100
-\graphics default
-\paperfontsize default
-\use_hyperref false
-\papersize default
-\use_geometry false
-\use_amsmath 1
-\use_esint 1
-\cite_engine basic
-\use_bibtopic false
-\paperorientation portrait
-\secnumdepth 3
-\tocdepth 3
-\paragraph_separation indent
-\defskip medskip
-\quotes_language english
-\papercolumns 1
-\papersides 1
-\paperpagestyle default
-\tracking_changes false
-\output_changes false
-\author ""
-\author ""
-\end_header
-
-\begin_body
-
-\begin_layout Title
-Macro Testcases
-\end_layout
-
-\begin_layout Enumerate
-Simple macro definitions with position awareness:
-\begin_inset FormulaMacro
-\newcommand{\bla}{42}
-\end_inset
-
-
-\begin_inset Formula \[
-\bla\mbox{ should look like }42\]
-
-\end_inset
-
-now redined as
-\begin_inset FormulaMacro
-\renewcommand{\bla}{21}
-\end_inset
-
-, such that
-\begin_inset Formula \[
-\bla\mbox{ should look like }21.\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Enumerate
-Redefinitions of macros appearing in the definition of another macro:
-\begin_inset FormulaMacro
-\newcommand{\fooa}{x}
-\end_inset
-
-
-\begin_inset FormulaMacro
-\newcommand{\foob}[1]{(#1\fooa)}
-\end_inset
-
-
-\begin_inset FormulaMacro
-\renewcommand{\fooa}{y}
-\end_inset
-
- with the TeX code
-\begin_inset listings
-inline false
-status open
-
-\begin_layout PlainLayout
-
-\backslash
-newcommand{
-\backslash
-fooa}{x}
-\end_layout
-
-\begin_layout PlainLayout
-
-\backslash
-newcommand{
-\backslash
-foob}[1]{(#1
-\backslash
-fooa)}
-\end_layout
-
-\begin_layout PlainLayout
-
-\backslash
-renewcommand{
-\backslash
-fooa}{y}
-\end_layout
-
-\end_inset
-
-gives the following:
-\begin_inset Formula \[
-\foob{\fooa}\mbox{ should look like }(yy)\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Enumerate
-Arity change:
-\begin_inset FormulaMacro
-\newcommand{\foo}{-}
-\end_inset
-
-
-\begin_inset FormulaMacro
-\renewcommand{\foo}[2]{(#1,#2)}
-\end_inset
-
-
-\begin_inset Formula \[
-\foo{abc}d\mbox{ should look like }(abc,d)\mbox{ if the second foo is there, otherwise like }-{abc}d\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Enumerate
-Arity change with incomplete arguments at line end:
-\begin_inset FormulaMacro
-\renewcommand{\foo}{-}
-\end_inset
-
-
-\begin_inset FormulaMacro
-\renewcommand{\foo}[2]{(#1,#2)}
-\end_inset
-
-
-\begin_inset Formula \[
-\frac{\foo{abc}{}}{1}\mbox{ should be }\frac{(abc,\,)}{1}\mbox{ if the second foo is defined. Otherwise }\frac{-{abc}{}}{1}\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Enumerate
-Recursion:
-\begin_inset FormulaMacro
-\renewcommand{\foo}[1]{\foo #1{}}
-\end_inset
-
-.
- The inner foo should not we resolved as TeX would give a infinite recursion.
-\end_layout
-
-\begin_layout Enumerate
-Recursive usage:
-\begin_inset FormulaMacro
-\renewcommand{\foo}[3]{\frac{{\displaystyle #1}\,{\displaystyle #2}}{{\displaystyle #3}}}
-\end_inset
-
- can be used to create tree-like structures like this one:
-\begin_inset Formula \[
-\foo{\foo{42}{\foo{asdf}{asdf}{asdf}}{21}}{\foo{asdf}{asdf}{asdf}}{asdf}.\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Enumerate
-Folding/Unfolding:
-\begin_inset FormulaMacro
-\renewcommand{\foo}[2]{<#1|#2>}
-\end_inset
-
-.
- Start using Ctrl-+ and Ctrl-- when you are inside of the macro to fold
- and unfold, e.g.
- here:
-\begin_inset Formula \[
-\foo{\foo{42}{12}}{\foo{21}4}.\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Enumerate
-Scripts:
-\begin_inset FormulaMacro
-\renewcommand{\foo}[3][A][B]{(#1,#2)#3}
-\end_inset
-
-
-\begin_inset Formula \[
-\foo[a]{}^{4}[b]c_{1}\mbox{ should look like }(a,B)\sqcup^{4}[b]c_{1}\]
-
-\end_inset
-
-
-\begin_inset Formula \[
-\foo[a]c^{3}\mbox{ should look like }(a,B)c^{3}\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Enumerate
-Multiple optional parameters:
-\begin_inset FormulaMacro
-\renewcommand{\foo}[3][a][b][c]{(#1,#2,#3)}
-\end_inset
-
-
-\end_layout
-
-\begin_deeper
-\begin_layout Enumerate
-\begin_inset Formula $\foo[][B]123\mbox{ should be }(a,B,c)123$
-\end_inset
-
-
-\end_layout
-
-\begin_layout Enumerate
-\begin_inset Formula $\foo[][][C]123\mbox{ should be }(a,b,C)123$
-\end_inset
-
-
-\end_layout
-
-\end_deeper
-\end_body
-\end_document
diff --git a/development/mathmacros/testcases_environments.lyx b/development/mathmacros/testcases_environments.lyx
deleted file mode 100644
index 6586f8bc94..0000000000
--- a/development/mathmacros/testcases_environments.lyx
+++ /dev/null
@@ -1,1268 +0,0 @@
-#LyX 1.6svn created this file. For more info see http://www.lyx.org/
-\lyxformat 318
-\begin_document
-\begin_header
-\textclass amsart
-\begin_modules
-theorems-ams
-\end_modules
-\language english
-\inputencoding auto
-\font_roman default
-\font_sans default
-\font_typewriter default
-\font_default_family default
-\font_sc false
-\font_osf false
-\font_sf_scale 100
-\font_tt_scale 100
-\graphics default
-\paperfontsize default
-\spacing single
-\use_hyperref false
-\papersize default
-\use_geometry false
-\use_amsmath 1
-\use_esint 1
-\cite_engine basic
-\use_bibtopic false
-\paperorientation portrait
-\branch Branch1
-\selected 1
-\color #fa8a00
-\end_branch
-\branch Branch2
-\selected 0
-\color #00fabc
-\end_branch
-\secnumdepth 3
-\tocdepth 3
-\paragraph_separation indent
-\defskip medskip
-\quotes_language english
-\papercolumns 1
-\papersides 1
-\paperpagestyle default
-\tracking_changes false
-\output_changes false
-\author ""
-\author ""
-\extra_embedded_files ""
-\end_header
-
-\begin_body
-
-\begin_layout Title
-Macro Scopes
-\end_layout
-
-\begin_layout Section
-Simple
-\end_layout
-
-\begin_layout Standard
-\begin_inset Formula \[
-\backslash foo\mbox{ should be }\backslash foo\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-
-\family roman
-\series medium
-\shape up
-\size normal
-\emph off
-\bar no
-\noun off
-\color none
-\begin_inset FormulaMacro
-\newcommand{\foo}{A}
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset Formula \[
-\foo\mbox{ should be }A\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Section
-Redefinition
-\end_layout
-
-\begin_layout Standard
-
-\family roman
-\series medium
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-\noun off
-\color none
-\begin_inset FormulaMacro
-\renewcommand{\foo}{B}
-\end_inset
-
-
-\family default
-\series default
-\shape default
-\size default
-\emph default
-\bar default
-\noun default
-\color inherit
-
-\begin_inset Formula \[
-B\mbox{ should be }B\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Section
-In Paragraph Redefinition
-\end_layout
-
-\begin_layout Standard
-
-\family roman
-\series medium
-\shape up
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-\emph off
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-\noun off
-\color none
-\begin_inset FormulaMacro
-\renewcommand{\foo}{C}
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-
-
-\family default
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-\size default
-\emph default
-\bar default
-\noun default
-\color inherit
-
-\begin_inset Formula $\foo\mbox{ should be }C$
-\end_inset
-
-
-\family roman
-\series medium
-\shape up
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-
-\begin_inset FormulaMacro
-\renewcommand{\foo}{D}
-\end_inset
-
-
-\family default
-\series default
-\shape default
-\size default
-\emph default
-\bar default
-\noun default
-\color inherit
-
-\begin_inset Formula $\foo\mbox{ should be }D$
-\end_inset
-
-
-\end_layout
-
-\begin_layout Section
-Environment
-\end_layout
-
-\begin_layout Standard
-\begin_inset Note Note
-status open
-
-\begin_layout PlainLayout
-\begin_inset Formula $\foo\mbox{ should be }D$
-\end_inset
-
-
-\end_layout
-
-\begin_layout Section
-Environment local Definitions
-\end_layout
-
-\begin_layout PlainLayout
-
-\family roman
-\series medium
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-\color none
-\begin_inset FormulaMacro
-\renewcommand{\foo}{E}
-\end_inset
-
-
-\family default
-\series default
-\shape default
-\size default
-\emph default
-\bar default
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-
-\begin_inset Formula $\foo\mbox{ should be }E$
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-
-
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-
-\begin_inset FormulaMacro
-\renewcommand{\foo}{F}
-\end_inset
-
-
-\family default
-\series default
-\shape default
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-\color inherit
-
-\begin_inset Formula $\foo\mbox{ should be }F$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\begin_inset Formula $\foo\mbox{ should be }D$
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Section
-Definitions in Paragraph Style Environments
-\end_layout
-
-\begin_layout Abstract
-
-\family roman
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-\begin_inset FormulaMacro
-\renewcommand{\foo}{G}
-\end_inset
-
-
-\family default
-\series default
-\shape default
-\size default
-\emph default
-\bar default
-\noun default
-\color inherit
-
-\begin_inset Formula $\foo\mbox{ should be }G$
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset Formula $\foo\mbox{ should be }G$
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Itemize
-
-\family roman
-\series medium
-\shape up
-\size normal
-\emph off
-\bar no
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-\begin_inset FormulaMacro
-\renewcommand{\foo}{H}
-\end_inset
-
-
-\family default
-\series default
-\shape default
-\size default
-\emph default
-\bar default
-\noun default
-\color inherit
-
-\begin_inset Formula $\foo\mbox{ should be }H$
-\end_inset
-
-
-\end_layout
-
-\begin_layout Itemize
-\begin_inset Formula $H\mbox{ should be }H$
-\end_inset
-
-
-\family roman
-\series medium
-\shape up
-\size normal
-\emph off
-\bar no
-\noun off
-\color none
-
-\begin_inset FormulaMacro
-\renewcommand{\foo}{H2}
-\end_inset
-
-
-\family default
-\series default
-\shape default
-\size default
-\emph default
-\bar default
-\noun default
-\color inherit
-
-\begin_inset Formula $\foo\mbox{ should be }H2$
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset Formula $\foo\mbox{ should be }H2$
-\end_inset
-
-
-\end_layout
-
-\begin_layout Section
-Theorem and Proofs
-\end_layout
-
-\begin_layout Theorem
-\begin_inset Formula $1=0$
-\end_inset
-
-
-\family roman
-\series medium
-\shape up
-\size normal
-\emph off
-\bar no
-\noun off
-\color none
-
-\begin_inset FormulaMacro
-\renewcommand{\foo}{I}
-\end_inset
-
-
-\family default
-\series default
-\shape default
-\size default
-\emph default
-\bar default
-\noun default
-\color inherit
-
-\begin_inset Formula $\foo\mbox{ should be }I$
-\end_inset
-
-
-\end_layout
-
-\begin_layout Proof
-Because
-\begin_inset Formula $2=1$
-\end_inset
-
-.
-\begin_inset Formula $\foo\mbox{ should be }I$
-\end_inset
-
-
-\family roman
-\series medium
-\shape up
-\size normal
-\emph off
-\bar no
-\noun off
-\color none
-
-\begin_inset FormulaMacro
-\renewcommand{\foo}{J}
-\end_inset
-
-
-\family default
-\series default
-\shape default
-\size default
-\emph default
-\bar default
-\noun default
-\color inherit
-
-\begin_inset Formula $\foo\mbox{ should be }J$
-\end_inset
-
-.
-\family roman
-\series medium
-\shape up
-\size normal
-\emph off
-\bar no
-\noun off
-\color none
-
-\begin_inset FormulaMacro
-\renewcommand{\foo}{K}
-\end_inset
-
-
-\family default
-\series default
-\shape default
-\size default
-\emph default
-\bar default
-\noun default
-\color inherit
-
-\begin_inset Formula $\foo\mbox{ should be }K$
-\end_inset
-
-
-\end_layout
-
-\begin_layout Proof
-Blub
-\begin_inset Formula $\foo\mbox{ should be }K$
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-\begin_inset Formula $\foo\mbox{ should be }K$
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Section
-Tables
-\end_layout
-
-\begin_layout Standard
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout PlainLayout
-\begin_inset Formula $\foo\mbox{ should be }K$
-\end_inset
-
-
-\end_layout
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diff --git a/development/mathmacros/testcases_master_child.lyx b/development/mathmacros/testcases_master_child.lyx
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diff --git a/development/mathmacros/testcases_master_child.zip b/development/mathmacros/testcases_master_child.zip
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index a1e6d57d2b..0000000000
Binary files a/development/mathmacros/testcases_master_child.zip and /dev/null differ
diff --git a/development/mathmacros/testcases_speed.lyx b/development/mathmacros/testcases_speed.lyx
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-
-\begin_inset Formula \begin{align*}
-\xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
-\xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
-
-\end_inset
-
-
-\begin_inset Formula \begin{align*}
-\xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
-\xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
-
-\end_inset
-
-
-\begin_inset Formula \begin{align*}
-\xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
-\xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
-
-\end_inset
-
-
-\begin_inset Formula \begin{align*}
-\xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
-\xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
-
-\end_inset
-
-
-\begin_inset Formula \begin{align*}
-\xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
-\xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
-
-\end_inset
-
-
-\begin_inset Formula \begin{align*}
-\xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
-\xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
-
-\end_inset
-
-
-\begin_inset Formula \begin{align*}
-\xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
-\xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
-
-\end_inset
-
-
-\begin_inset Formula \begin{align*}
-\xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
-\xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
-
-\end_inset
-
-
-\begin_inset Formula \begin{align*}
-\xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
-\xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
-
-\end_inset
-
-
-\begin_inset Formula \begin{align*}
-\xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
-\xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
-
-\end_inset
-
-
-\begin_inset Formula \begin{align*}
-\xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
-\xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
-
-\end_inset
-
-
-\begin_inset Formula \begin{align*}
-\xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
-\xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
-
-\end_inset
-
-
-\begin_inset Formula \begin{align*}
-\xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
-\xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
-
-\end_inset
-
-
-\begin_inset Formula \begin{align*}
-\xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\\
-\xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]] & \xyz[1][\xyz[\xyz[\xyz[1][2]][2]][\xyz[1][2]]]\end{align*}
-
-\end_inset
-
-
-\end_layout
-
-\end_body
-\end_document