perfectcut (3nov14)

git-svn-id: svn://tug.org/texlive/trunk@35501 c570f23f-e606-0410-a88d-b1316a301751

1 files changed, 343 insertions, 272 deletions

diff --git a/Master/texmf-dist/tex/latex/perfectcut/perfectcut.sty b/Master/texmf-dist/tex/latex/perfectcut/perfectcut.sty
index 036750b09fd..87baaff7904 100644
--- a/Master/texmf-dist/tex/latex/perfectcut/perfectcut.sty
+++ b/Master/texmf-dist/tex/latex/perfectcut/perfectcut.sty
@@ -9,18 +9,20 @@
 %%% or (at your option) any later version. Refer to the README file.
 %%% 
 %%%
-\ProvidesPackage{perfectcut}[02/02/2014 Perfect Cut v1.9]
+\ProvidesPackage{perfectcut}[03/11/2014 Perfect Cut v2.0]
 %%% Option processing
 \newif\ifcut@mathstyle@
 \cut@mathstyle@true
 \newif\ifcut@realVert@
 \cut@realVert@false
+\newif\ifcut@fixxits@
+\cut@fixxits@false
 \DeclareOption{nomathstyle}{\cut@mathstyle@false}
 \let\cutstyle\textstyle
 \DeclareOption{realVert}{\cut@realVert@true}
+\DeclareOption{fixxits}{\cut@fixxits@true}
 \ProcessOptions*
 %%% End option processing
-\RequirePackage{amsmath}
 \RequirePackage{graphicx}
 \RequirePackage{calc}
 \newmuskip\cutangleskip
@@ -28,40 +30,57 @@
 \newmuskip\cutinterbarskip
 \newmuskip\cutangleouterskip
 \newif\ifcutdebug
-%%%
-\newcommand{\cutprimitive}[2]{\cut@{#1}{#2}}
-\newcommand{\cutbraprimitive}[1]{\cut@bra{#1}}
-\newcommand{\cutketprimitive}[1]{\cut@ket{#1}}
-\let\perfectcut\cutprimitive
-\let\perfectbra\cutbraprimitive
-\let\perfectket\cutketprimitive
-%%% The following variables can be redefined in your preamble
+%%% Exported commands
+%%See end of file for a more detailed description of the commands 
+\newcommand{\perfectcut}[2]{\cut@{#1}{#2}}%% displays <#1||#2>
+\newcommand{\perfectbra}[1]{\cut@bra{#1}}%% displays <#1|
+\newcommand{\perfectket}[1]{\cut@ket{#1}}%%  displays |#2>
+\let\cutprimitive\perfectcut%backward compat
+\let\cutbraprimitive\perfectbra%backward compat
+\let\cutketprimitive\perfectket%backward compat
+\newcommand{\perfectcase}[2]{\cut@case{#1}{#2}}%% displays [#1|#2]
+\newcommand{\perfectbrackets}[1]{\cut@brackets{#1}}%% displays [#1]
+\newcommand{\perfectparens}[1]{\cut@parens{#1}}%% displays (#1)
+\newcommand{\perfectunary}[4]{\cut@customUnary{#1}{#2}{#3}{#4}}%% displays
+  %% #2#3#4 where #2 and #4 are delimiters. The size of the delimiters is
+  %% computed according to #1 which must be one of IncreaseHeight,
+  %% CurrentHeight, or CurrentHeightPlusOne.
+\newcommand{\perfectbinary}[6]{\cut@customBinary{#1}{#2}{#3}{#4}{#5}{#6}}%%
+  %% displays #2#3#4#5#6 where #2, #4 and #6 are delimiters. The size of the
+  %% delimiters is computed according to #1 which must be one of IncreaseHeight,
+  %% CurrentHeight, or CurrentHeightPlusOne.
+%% The following variables can be redefined in your preamble
 \cutbarskip=5.0mu plus 8.0mu minus 2.0mu
 \cutangleskip=0.0mu plus 8mu minus 1.0mu
 \cutangleouterskip=0.0mu plus 8mu minus 0.0mu
-\cutinterbarskip=0.8mu plus 0mu minus 0mu
-\cutdebugfalse%print the size after each \rangle?
-%%%
-%%%\nthleft{4}\langle ==> fourth size of \langle; begins at 0
+\cutinterbarskip=1.4mu plus 0mu minus 0mu
+\cutdebugfalse%% print the size after each \rangle?
+%%% Various reimplementations of \left, \right and \middle.
+%% \nthleft{4}\langle ==> fourth size of \langle; begins at 0
 \newcommand{\nthleft}[2]{\cut@nthldelim{#1}{#2}}
-%%%same for right and middle
 \newcommand{\nthright}[2]{\cut@nthrdelim{#1}{#2}}
 \newcommand{\nthmiddle}[2]{\cut@nthmdelim{#1}{#2}}
-%%%\lenleft{3mm}\langle ===> \langle of size at least 3mm
-%%%in math mode it is preferable to use math units such as 10mu,...
-%%%however only regular units are implemented now.
+%% \matchleft{\big\langle}| ===> | of the same size as \big\langle obtained
+%% by resizing the closest glyph
+\newcommand{\matchleft}[2]{\cut@matchingldelim{#1}{#2}}
+\newcommand{\matchright}[2]{\cut@matchingrdelim{#1}{#2}}
+\newcommand{\matchmiddle}[2]{\cut@matchingmdelim{#1}{#2}}
+%% \lenleft{3mm}\langle ===> \langle of size at least 3mm
+%% (in math mode it is preferable to use math units such as 10mu,...
+%% however only regular units are implemented now.)
 \newcommand{\lenleft}[2]{\cut@lengthldelim{#1}#2}
-%%%same for right and middle
 \newcommand{\lenright}[2]{\cut@lengthrdelim{#1}#2}
 \newcommand{\lenmiddle}[2]{\cut@lengthmdelim{#1}#2}
-%%%\reallenleft{3mm}\langle ===> \langle of size 3mm by resizing the
-%%%closest glyph
+%% \reallenleft{3mm}\langle ===> \langle of size 3mm by resizing the
+%% closest glyph
 \newcommand{\reallenleft}[2]{\cut@reallengthldelim{#1}{#2}}
-%%%same for right and middle
 \newcommand{\reallenright}[2]{\cut@reallengthrdelim{#1}{#2}}
 \newcommand{\reallenmiddle}[2]{\cut@reallengthmdelim{#1}{#2}}
 
-% setting up mathstyle
+
+%%% Preliminary commands
+
+%% setting up mathstyle
 \ifcut@mathstyle@
   \RequirePackage{mathstyle}
   \def\currentcutstyle{\currentmathstyle}
@@ -69,13 +88,7 @@
   \def\currentcutstyle{\cutstyle}
 \fi
 
-%setting up realVert
-\ifcut@realVert@
-  \def\cut@bar{\cut@Vert}
-\else
-  \def\cut@bar{\cut@vert}
-\fi
-
+%% sets the behaviour of delimiters to always grow while evaluating #1
 \newcommand{\cut@setshortfall}[1]{%
   \skip0=\delimitershortfall%
   \global\delimitershortfall=-0.1pt%that's the trick to get perfect growth
@@ -86,186 +99,89 @@
   \global\delimiterfactor=\count0%
 }
 
-\newcommand{\cut@nextrdelim}[2]{%
-  \left.\hspace{-\nulldelimiterspace}\vphantom{#2}\right#1%
-}
-\newcommand{\cut@nextldelim}[2]{%
-  \left#1\vphantom{#2}\hspace{-\nulldelimiterspace}\right.%
-}
-\newcommand{\cut@nextmdelim}[2]{%
-  \left.\hspace{-\nulldelimiterspace}\middle#1\vphantom{#2}\hspace{-\nulldelimiterspace}\right.%
-}
-
-\newcommand{\cut@lengthldelim}[2]{\cut@setshortfall{\cut@nextldelim#2{\rule[-0.101pt]{0pt}{#1}}}}
-\newcommand{\cut@lengthrdelim}[2]{\cut@setshortfall{\cut@nextrdelim#2{\rule[-0.101pt]{0pt}{#1}}}}
-\newcommand{\cut@lengthmdelim}[2]{\cut@setshortfall{\cut@nextmdelim#2{\rule[-0.101pt]{0pt}{#1}}}}
-\newcommand{\cut@reallengthldelim}[2]{\cut@resizetoheight{#1}{\cut@lengthldelim{#1}{#2}}}
-\newcommand{\cut@reallengthrdelim}[2]{\cut@resizetoheight{#1}{\cut@lengthrdelim{#1}{#2}}}
-\newcommand{\cut@reallengthmdelim}[2]{\cut@resizetoheight{#1}{\cut@lengthmdelim{#1}{#2}}}
-
-%\newcommand{\cut@nextrangle}[1]{%
-%  \left.\hspace{-\nulldelimiterspace}\vphantom{#1}\right\rangle%
-%}
-\newcommand{\cut@nextrangle}[1]{\cut@nextrdelim{\rangle}{#1}}
-
-%\newcommand{\cut@nextlangle}[1]{%
-%  \left\langle\vphantom{#1}\hspace{-\nulldelimiterspace}\right.%
-%}
-\newcommand{\cut@nextlangle}[1]{\cut@nextldelim{\langle}{#1}}
-
-\newcommand{\cut@iter}[2]{%
-  \ifcase#1%
-    #2{\cdot}   % 0 = smallest. This dot is here to prevent a
-            % bug regarding vertical positioning.
-  \else%
-    \count0=#1%
-    \advance\count0 -1\relax%
-    \expandafter#2{\expandafter\cut@iter{\the\count0}#2}%
- \fi%
-}
-
-\newcommand{\cut@primitive}[2]{%
-  %resetting shortfall
-  \cut@setshortfall{\cut@iter#2#1}%
-}
-
-%%%\cut@nthdelim{n}{delim}{f}
-\newcommand{\cut@nthdelim}[3]{
-  \def\cut@tempnextdelim{#3{#2}}%
-  \cut@primitive\cut@tempnextdelim{#1}%
-}
-\newcommand{\cut@nthldelim}[2]{\cut@nthdelim{#1}{#2}{\cut@nextldelim}}
-\newcommand{\cut@nthrdelim}[2]{\cut@nthdelim{#1}{#2}{\cut@nextrdelim}}
-\newcommand{\cut@nthmdelim}[2]{\cut@nthdelim{#1}{#2}{\cut@nextmdelim}}
-
-\newcommand{\cut@langleprimitive}[1]{\cut@primitive\cut@nextlangle{#1}}
-\newcommand{\cut@rangleprimitive}[1]{\cut@primitive\cut@nextrangle{#1}}
-%\newcommand{\cut@langleprimitive}[1]{\cut@nthldelim{#1}{\langle}}
-%\newcommand{\cut@rangleprimitive}[1]{\cut@nthrdelim{#1}{\rangle}}
-
-\newcommand{\cut@vertprimitiveunscaled}[1]{\cut@nthmdelim{#1}\vert}%\hbox{$\m@th\mathord{|}$}
-
-\newcommand{\cut@Vertprimitiveunscaled}[1]{\cut@nthmdelim{#1}\Vert}
-
-\newsavebox\cut@boxi
-\newsavebox\cut@boxj
-
+%% scale #2 to size #1 (length)
 \newcommand{\cut@resizetoheight}[2]{%
   \resizebox{!}{#1}{\hbox{$\m@th\currentcutstyle#2$}}%
 }
 
+\newsavebox\cut@boxi
+\newsavebox\cut@boxj
+%% scale #2 to the size of #1. Assumes that #1 goes above and below the base line.
 \newcommand{\cut@resizetoheightof}[2]{%
   \sbox{\cut@boxi}{$\m@th\currentcutstyle#1$}%
   \sbox{\cut@boxj}{$\m@th\currentcutstyle#2$}%
   \raisebox{-\dp\cut@boxi}{%
-    \resizebox{\width}{\ht\cut@boxi+\dp\cut@boxi}{%
+    \resizebox{!}{\ht\cut@boxi+\dp\cut@boxi}{%
       \raisebox{\dp\cut@boxj}{\usebox{\cut@boxj}}%
     }%
-  }
-}
-
-\newcommand{\cut@vertprimitive}[1]{%
-\setbox0=\hbox{%
-  $\m@th\currentcutstyle%
-  \cut@resizetoheightof{\cut@langleprimitive{#1}}{\cut@vertprimitiveunscaled{#1}}%
-  $}%
-\dimen0=\wd0
-\def\cut@unspace{%removing the margins around the bar
-  \kern -.5\dimen0%
-  \mkern.75mu%
-}%
-\cut@unspace%
-\copy0%
-\cut@unspace%
-\mspace{\cutinterbarskip}%
-\penalty \the\binoppenalty\relax%
-\cut@unspace%
-\box0%
-\cut@unspace%
-}
-
-\newcommand{\cut@halfvertprimitive}[1]{%
-\cut@resizetoheightof{\cut@langleprimitive{#1}}{\cut@vertprimitiveunscaled{#1}}%
-}
-
-\newcommand{\cut@Vertprimitive}[1]{%
-\mkern-3.26mu%
-\cut@resizetoheightof{\cut@langleprimitive{#1}}{\cut@Vertprimitiveunscaled{#1}}%
-\mkern-3.26mu%
-}
-
-
-\newcommand{\cut@langle}[1]{%
-  \edef\cut@n{\expandafter\the#1}%
-  %yes, i'm turning the integer into tokens to do call-by-value
-  \cut@langleprimitive{\cut@n}%
-}
-
-\newcommand{\cut@rangle}[1]{%
-  \edef\cut@n{\expandafter\the#1}%
-  \cut@rangleprimitive{\cut@n}%
-    \ifcutdebug^\cut@n\else\fi%
-}
-
-\newcommand{\cut@vert}[1]{%
-  \edef\cut@n{\expandafter\the#1}%
-  \cut@vertprimitive{\cut@n}%
+  }%
 }
 
-\newcommand{\cut@halfvert}[1]{%
-  \edef\cut@n{\expandafter\the#1}%
-  \cut@halfvertprimitive{\cut@n}%
+%% gives the delimiter #1 which is immediately bigger than #2
+%% notice that \delimitershortfall is not modified so LaTeX can decide to give
+%% a smaller one.
+\newcommand{\cut@nextrdelim}[2]{\left.\hspace{-\nulldelimiterspace}\vphantom{#2}\right#1}
+\newcommand{\cut@nextldelim}[2]{\left#1\vphantom{#2}\hspace{-\nulldelimiterspace}\right.}
+\newcommand{\cut@nextmdelim}[2]{\left.\hspace{-\nulldelimiterspace}\middle#1\vphantom{#2}\hspace{-\nulldelimiterspace}\right.}
+
+%% like the previous one but resized to exactly match argument #1
+%% used in order to have vertical bars of the perfect size
+\newcommand{\cut@matchingldelim}[2]{\mathopen{\cut@resizetoheightof{#1}{\cut@nextldelim{#2}{#1}}}}
+\newcommand{\cut@matchingrdelim}[2]{\mathclose{\cut@resizetoheightof{#1}{\cut@nextrdelim{#2}{#1}}}}
+\newcommand{\cut@matchingmdelim}[2]{\mathrel{\cut@resizetoheightof{#1}{\cut@nextmdelim{#2}{#1}}}}
+
+%% gives the delimiter #2 which is immediately longer than #1 (length)
+\newcommand{\cut@lengthldelim}[2]{\mathopen{\cut@setshortfall{\cut@nextldelim#2{\rule[-0.101pt]{0pt}{#1}}}}}
+\newcommand{\cut@lengthrdelim}[2]{\mathclose{\cut@setshortfall{\cut@nextrdelim#2{\rule[-0.101pt]{0pt}{#1}}}}}
+\newcommand{\cut@lengthmdelim}[2]{\mathrel{\cut@setshortfall{\cut@nextmdelim#2{\rule[-0.101pt]{0pt}{#1}}}}}
+
+%% like the previous one but resized to exactly match #1 (length) 
+\newcommand{\cut@reallengthldelim}[2]{\mathopen{\cut@resizetoheight{#1}{\cut@nextldelim#2{\rule[-0.101pt]{0pt}{#1}}}}}
+\newcommand{\cut@reallengthrdelim}[2]{\mathclose{\cut@resizetoheight{#1}{\cut@nextrdelim#2{\rule[-0.101pt]{0pt}{#1}}}}}
+\newcommand{\cut@reallengthmdelim}[2]{\mathrel{\cut@resizetoheight{#1}{\cut@nextmdelim#2{\rule[-0.101pt]{0pt}{#1}}}}}
+
+%I don't get anything about this bug which affects the
+%alignment with respect to the math axis
+\ifcut@fixxits@
+  \def\bugfix{}
+\else
+  \def\bugfix{\cdot}
+\fi
+%% iterates #2 over itself #1 number of times
+\newcommand{\cut@iter}[2]{%
+  \ifcase#1%
+    #2{\bugfix} % 0 = smallest. This dot is here to prevent a
+                 % bug regarding vertical positioning.
+  \else%
+    \count0=#1%
+    \advance\count0 -1\relax%
+    \expandafter#2{\expandafter\cut@iter{\the\count0}#2}%
+ \fi%
 }
 
-\newcommand{\cut@Vert}[1]{%
-  \edef\cut@n{\expandafter\the#1}%
-  \cut@Vertprimitive{\cut@n}%
+%% \cut@nthdelim{n}{delim}{f} iterates f{delim} n time over itself after
+%% resetting delimiter shortfall
+\newcommand{\cut@nthdelim}[3]{
+  \def\cut@tempnextdelim{#3{#2}}%
+  \cut@setshortfall{\cut@iter{#1}\cut@tempnextdelim}%
 }
+%% \cut@nthxdelim gives the #1-th size of the delimiter #2  
+\newcommand{\cut@nthldelim}[2]{\mathopen{\cut@nthdelim{#1}{#2}{\cut@nextldelim}}}
+\newcommand{\cut@nthrdelim}[2]{\mathclose{\cut@nthdelim{#1}{#2}{\cut@nextrdelim}}}
+\newcommand{\cut@nthmdelim}[2]{\mathrel{\cut@nthdelim{#1}{#2}{\cut@nextmdelim}}}
 
-\newcommand{\cut@angles}[1]{\cut@langle{#1}\cut@vert{#1}\cut@rangle{#1}}
 
-%%% now the main algorithm
+%%%% now the main algorithm
 
 \newcounter{cut@depth}
 
-\newcommand{\cut@testangles}{%
-  \setcounter{cut@depth}{0}%
-  \def\cut@d{%
-    \cut@angles{\value{cut@depth}}%
-    \stepcounter{cut@depth}%
-  }
-  \cut@d\cut@d\cut@d\cut@d\cut@d\cut@d\cut@d
-}
-
-\newcommand{\cut@testssstyle}{\scriptscriptstyle{\cut@testangles}}
-\newcommand{\cut@testsstyle}{\scriptstyle{\cut@testangles}}
-\newcommand{\cut@testnormal}{\textstyle{\cut@testangles}}
-
-\newcommand{\cut@testsize}[1]{
-{#1 \[ \mathrm{\f@size\,pt:} \begin{array}{l}
-  \cut@testnormal{}\\
-  \cut@testsstyle{}\\
-  \cut@testssstyle{}
-  \end{array}\]}
-}
-
-\newcommand{\cut@test}{
-\cut@testsize{\Large}
-\cut@testsize{\large}
-\cut@testsize{}
-\cut@testsize{\small}
-\cut@testsize{\footnotesize}
-\cut@testsize{\scriptsize}
-\cut@testsize{\tiny}
-}
-
 % lengths with names of the form \cut@height{depth}
 \newcommand{\cut@localheight}{cut@height\thecut@depth}
 \newcommand{\cut@newlocalheightcounter}{%
   \@ifundefined{c@\cut@localheight}{\newcounter{\cut@localheight}}{}
 }
 
-% boxes with names of the form  \cut@savebox{num}@{depth}
+% boxes with names of the form \cut@savebox{num}@{depth}
 \newcommand{\cut@localsavebox}[1]{cut@savebox#1@\thecut@depth}
 \newcommand{\cut@newlocalsavebox}[1]{%
   \@ifundefined{\cut@localsavebox{#1}}{%
@@ -278,7 +194,11 @@
 \newsavebox\cut@boxleft
 \newsavebox\cut@boxright
 
-\newcommand{\cut@}[2]{%
+%%% Definition of Cut primitives
+
+%% Main loop. #1 determines how the height is incremented. #2 and #3 are saved
+%% in cut@boxleft and cut@boxright. Computed height is stored in cut@finalheight
+\newcommand{\cut@computeBinary@main}[3]{%
   \setcounter{cut@finalheight}{0}%
   {%
     \addtocounter{cut@depth}{1}%
@@ -289,10 +209,10 @@
     %computing recursively
     \setcounter{\cut@localheight}{-1}%
     \expandafter\sbox\csname\cut@localsavebox{0}\endcsname%
-      {$\m@th\currentcutstyle#1$}%
-    \expandafter\sbox\csname\cut@localsavebox{1}\endcsname%
       {$\m@th\currentcutstyle#2$}%
-    \addtocounter{\cut@localheight}{1}%
+    \expandafter\sbox\csname\cut@localsavebox{1}\endcsname%
+      {$\m@th\currentcutstyle#3$}%
+    \addtocounter{\cut@localheight}{#1}%
     %exporting values outside the local scope
     \setcounter{cut@finalheight}{\value{\cut@localheight}}%
     \global\sbox\cut@boxleft%
@@ -301,104 +221,255 @@
       {\expandafter\usebox\csname\cut@localsavebox{1}\endcsname}%
     \addtocounter{cut@depth}{-1}%
   }%
-  \@ifundefined{c@\cut@localheight}{}{%
+}
+
+%% Displays #1#2#3#4#5. Arguments #2 and #4 can contain other cut primitives.
+%% Calls to cut primitives inside #2 and #4 will have a smaller height.
+%% Arguments #1, #3 and #5 can access the current height in two different
+%% forms via \cut@n and \count0.
+\newcommand{\cut@computeBinary@IncreaseHeight}[5]{%
+  \cut@computeBinary@main{1}{#2}{#4}%
+  \@ifundefined{c@\cut@localheight}{}{% if #2 and #4 did not contain any cut primitive
     \ifnum\value{cut@finalheight}>\value{\cut@localheight}%
      \setcounter{\cut@localheight}{\value{cut@finalheight}}%
     \fi%
-    }%end @ifundefined
-  \mspace{\cutangleouterskip}%
-  {\cut@langle{\value{cut@finalheight}}}%
-  \mspace{\cutangleskip}%
+  }%end @ifundefined
+  \count0=\value{cut@finalheight}%
+  \edef\cut@n{\expandafter\the\count0}%
+  #1%
   \usebox{\cut@boxleft}%
-  \mspace{\cutbarskip}%
-  {\cut@bar{\value{cut@finalheight}}}%
-  \mspace{\cutbarskip}%
+  #3%
   \usebox{\cut@boxright}%
-  \mspace{\cutangleskip}%
-  {\cut@rangle{\value{cut@finalheight}}}%
-  \mspace{\cutangleouterskip}%
+  #5%
 }
 
-\newcommand{\cut@bra}[1]{%
-  \setcounter{cut@finalheight}{0}%
-  {%
-    \addtocounter{cut@depth}{1}%
-    %defining variables
-    \cut@newlocalheightcounter%
-    \cut@newlocalsavebox{0}%
-    %\cut@newlocalsavebox{1}%
-    %computing recursively
-    \setcounter{\cut@localheight}{-1}%
-    \expandafter\sbox\csname\cut@localsavebox{0}\endcsname%
-      {$\m@th\currentcutstyle#1$}%
-    %\expandafter\sbox\csname\cut@localsavebox{1}\endcsname%
-    %  {$\m@th\currentcutstyle#2$}%
-    \addtocounter{\cut@localheight}{1}%
-    %exporting values outside the local scope
-    \setcounter{cut@finalheight}{\value{\cut@localheight}}%
-    \global\sbox\cut@boxleft%
-      {\expandafter\usebox\csname\cut@localsavebox{0}\endcsname}%
-    %\global\sbox\cut@boxright%
-    %  {\expandafter\usebox\csname\cut@localsavebox{1}\endcsname}%
-    \addtocounter{cut@depth}{-1}%
-  }%
-  \@ifundefined{c@\cut@localheight}{}{%
+%% Displays #1#2#3#4#5. Arguments #2 and #4 can contain other cut primitives.
+%% Does not increase the current height computed by cut primitives inside #2
+%% and #4. 
+%% Arguments #1, #3 and #5 can access the current height in two different
+%% forms via \cut@n and \count0.
+\newcommand{\cut@computeBinary@CurrentHeight}[5]{%
+  \cut@computeBinary@main{0}{#2}{#4}%
+  \ifnum\value{cut@finalheight}<0%
+    \setcounter{cut@finalheight}{0}%
+  \fi%
+  \@ifundefined{c@\cut@localheight}{}{% if #2 and #4 did not contain any cut primitive
     \ifnum\value{cut@finalheight}>\value{\cut@localheight}%
      \setcounter{\cut@localheight}{\value{cut@finalheight}}%
     \fi%
-    }%end @ifundefined
-  \mspace{\cutangleouterskip}%
-  {\cut@langle{\value{cut@finalheight}}}%
-  \mspace{\cutangleskip}%
+  }%end @ifundefined
+  \count0=\value{cut@finalheight}%
+  \edef\cut@n{\expandafter\the\count0}%
+  #1%
   \usebox{\cut@boxleft}%
-  \mspace{\cutbarskip}%
-  \mkern-3.26mu%
-  {\cut@halfvert{\value{cut@finalheight}}}%
-  \mspace{\cutangleouterskip}%
-  %\mspace{\cutbarskip}%
-  %\usebox{\cut@boxright}%
-  %\mspace{\cutangleskip}%
-  %\cut@rangle{\value{cut@finalheight}}%
+  #3%
+  \usebox{\cut@boxright}%
+  #5%
 }
 
-\newcommand{\cut@ket}[1]{%
-  \setcounter{cut@finalheight}{0}%
-  {%
-    \addtocounter{cut@depth}{1}%
-    %defining variables
-    \cut@newlocalheightcounter%
-    \cut@newlocalsavebox{0}%
-    %\cut@newlocalsavebox{1}%
-    %computing recursively
-    \setcounter{\cut@localheight}{-1}%
-    \expandafter\sbox\csname\cut@localsavebox{0}\endcsname%
-      {$\m@th\currentcutstyle#1$}%
-    %\expandafter\sbox\csname\cut@localsavebox{1}\endcsname%
-    %  {$\m@th\currentcutstyle#2$}%
-    \addtocounter{\cut@localheight}{1}%
-    %exporting values outside the local scope
-    \setcounter{cut@finalheight}{\value{\cut@localheight}}%
-    \global\sbox\cut@boxleft%
-      {\expandafter\usebox\csname\cut@localsavebox{0}\endcsname}%
-    %\global\sbox\cut@boxright%
-    %  {\expandafter\usebox\csname\cut@localsavebox{1}\endcsname}%
-    \addtocounter{cut@depth}{-1}%
-  }%
-  \@ifundefined{c@\cut@localheight}{}{%
+%% Displays #1#2#3#4#5. Arguments #2 and #4 can contain other cut primitives.
+%% Does not increase the current height computed by cut primitives inside #2
+%% and #4 but the height to display is increased by 1. 
+%% Arguments #1, #3 and #5 can access the height height in two different
+%% forms via \cut@n and \count0.
+\newcommand{\cut@computeBinary@CurrentHeightPlusOne}[5]{%
+  \cut@computeBinary@main{0}{#2}{#4}
+  \@ifundefined{c@\cut@localheight}{}{% if #2 and #4 did not contain any cut primitive
     \ifnum\value{cut@finalheight}>\value{\cut@localheight}%
      \setcounter{\cut@localheight}{\value{cut@finalheight}}%
     \fi%
-    }%end @ifundefined
-  %\cut@langle{\value{cut@finalheight}}%
-  %\mspace{\cutangleskip}%
-  %\usebox{\cut@boxleft}%
-  %\mspace{\cutbarskip}%
-  \mspace{\cutangleouterskip}%
-  {\cut@halfvert{\value{cut@finalheight}}}%
-  \mkern-3.26mu%
-  \mspace{\cutbarskip}%
-  \usebox{\cut@boxleft}%right}%
-  \mspace{\cutangleskip}%
-  {\cut@rangle{\value{cut@finalheight}}}%
-  \mspace{\cutangleouterskip}%
+  }%end @ifundefined
+  \count0=\value{cut@finalheight}%
+  \advance\count0 1%
+  \edef\cut@n{\expandafter\the\count0}%
+  #1%
+  \usebox{\cut@boxleft}%
+  #3%
+  \usebox{\cut@boxright}%
+  #5%
 }
+
+%%% Implementation of the particular delimiters
+
+%% special vertical bars
+%% \vert adjusted to #1
+\newcommand{\cut@matchvert}[1]{%
+  \setbox0=\hbox{$\matchmiddle{#1}\vert$}%
+  \mkern.6mu%
+  \kern -.5\wd0%
+  \copy0%
+  \kern -.5\wd0%
+  \mkern.6mu%
+}
+
+%% special double vertical bars
+\newcommand{\cut@doublevert}[1]{%
+  \cut@matchvert{\nthleft{#1}\langle}
+  \mskip\cutinterbarskip%
+  \penalty \the\binoppenalty\relax%
+  \cut@matchvert{\nthleft{#1}\langle}
+}
+
+%% special double vertical bars (alternate)
+\newcommand{\cut@Vert}[1]{%
+  \setbox0=\hbox{$\matchmiddle{\nthleft{#1}\langle}\Vert$}%
+  \mkern.8mu%
+  \kern -.3\wd0%
+  \copy0%
+  \kern -.3\wd0%
+  \mkern.8mu%
+%\mkern-3.26mu%
+%\matchmiddle{\nthleft{#1}\langle}\Vert%
+%\mkern-3.26mu%
+}
+
+%% setting up realVert
+\ifcut@realVert@
+  \let\cut@bars\cut@Vert
+\else
+  \let\cut@bars\cut@doublevert
+\fi
+
+%% \perfectcut
+%% <#1||#2>, increases height, inserts skips
+\newcommand{\cut@}[2]{%
+  \cut@computeBinary@IncreaseHeight%
+    {\mskip\cutangleouterskip%
+     \nthleft{\cut@n}{\langle}%
+     \mskip\cutangleskip}%
+    {#1}%
+    {\mskip\cutbarskip%
+     \cut@bars{\cut@n}%
+     \mskip\cutbarskip}%
+    {#2}%
+    {\mskip\cutangleskip%
+     \nthright{\cut@n}{\rangle}%
+     \mskip\cutangleouterskip}%
+}
+
+%% \perfectbra
+%% <#1|, increases height, inserts skips
+\newcommand{\cut@bra}[1]{%
+  \cut@computeBinary@IncreaseHeight%
+    {\mskip\cutangleouterskip%
+     \nthleft{\cut@n}{\langle}%
+     \mskip\cutangleskip}%
+    {#1}%
+    {\mskip\cutbarskip%
+     \cut@matchvert{\nthleft{\cut@n}\langle}%
+     \mskip\cutangleouterskip}%
+    {}{}%only one argument
+}
+
+%% \perfectket
+%% |#1>, increases height, inserts skips
+\newcommand{\cut@ket}[1]{%
+  \cut@computeBinary@IncreaseHeight%
+    {\mskip\cutangleouterskip%
+     \cut@matchvert{\nthleft{\cut@n}\langle}%
+     \mskip\cutbarskip}%
+    {#1}%
+    {\mskip\cutangleskip%
+     \nthright{\cut@n}{\rangle}%
+     \mskip\cutangleouterskip}%
+    {}{}%only one argument
+}
+
+%% \perfectcase
+%% [#1|#2], height is current height plus one, inserts skips
+\newcommand{\cut@case}[2]{%
+  \cut@computeBinary@CurrentHeightPlusOne%
+    {\nthleft{\cut@n}[%
+     \mskip\cutangleskip}%
+    {#1}%
+    {\mskip\cutbarskip%
+     \cut@matchvert{\nthleft{\cut@n}[}%
+     \mskip\cutbarskip}%
+    {#2}%
+    {\mskip\cutangleskip%
+     \nthright{\cut@n}]}%
+}
+
+%% \perfectbrackets
+%% [#1], height is current height plus one, inserts skips only inside
+\newcommand{\cut@brackets}[1]{%
+  \cut@computeBinary@CurrentHeightPlusOne%
+    {\nthleft{\cut@n}[%
+     \mskip\cutangleskip}%
+    {#1}%
+    {\mskip\cutangleskip%
+     \nthright{\cut@n}]}%
+    {}{}%only one argument
+}
+
+%% \perfectparens
+%% (#1), height is current height, inserts skips only inside
+\newcommand{\cut@parens}[1]{%
+  \cut@computeBinary@CurrentHeight%
+    {\nthleft{\cut@n}(%
+     \mskip\cutangleskip}%
+    {#1}%
+    {\mskip\cutangleskip%
+     \nthright{\cut@n})}%
+    {}{}%only one argument
+}
+
+%% \perfectunary
+%% #2#4#3 where #2 and #3 are delimiters. The size of the delimiters is computed
+%% according to #1 which must be one of IncreaseHeight, CurrentHeight,
+%% or CurrentHeightPlusOne.
+\newcommand{\cut@customUnary}[4]{%
+  \csname cut@computeBinary@#1\endcsname%
+    {\nthleft{\cut@n}#2}%
+    {#4}%
+    {\nthright{\cut@n}#3}%
+    {}{}%
+}%
+
+%% \perfectbinary
+%% #2#5#3#6#4 where #2, #3 and #4 are delimiters. The size of the delimiters is
+%% computed according to #1 which must be one of IncreaseHeight, CurrentHeight,
+%% or CurrentHeightPlusOne.
+\newcommand{\cut@customBinary}[6]{%
+   \csname cut@computeBinary@#1\endcsname%
+    {\nthleft{\cut@n}#2}%
+    {#5}%
+    {\matchmiddle{\nthleft{\cut@n}#2}#3}%{{\nthmiddle{\cut@n}#4}}%
+    {#6}%
+    {\nthright{\cut@n}#4}%
+}%
+%% Example: The following displays a set {#1|#2} with delimiters of the
+%% appropriate size if there are \perfectcommands inside #1 and #2.
+%% \def\Set#1#2{\perfectbinary{IncreaseHeight}\{|\}{#1\mathrel{}}{\mathrel{}#2}}
+
+
+
+%%% for testing purposes
+\newcommand{\cut@testsize}[2]{
+{#1 \[ \mathrm{\f@size\,pt:} \begin{array}{l}
+  \scriptscriptstyle{#2}\\
+  \scriptstyle{#2}\\
+  \textstyle{#2}
+  \end{array}\]}
+}
+\newcommand{\cut@test}[1]{%
+\cut@testsize{\Large}{#1}%
+\cut@testsize{\large}{#1}%
+\cut@testsize{}{#1}%
+\cut@testsize{\small}{#1}%
+\cut@testsize{\footnotesize}{#1}%
+\cut@testsize{\scriptsize}{#1}%
+\cut@testsize{\tiny}{#1}%
+}
+\newcommand{\cut@testangles}{\cut@test{%
+  \cut@{\cut@{\cut@{\cut@{\cut@{a}{b}}{c}}{d}}{e}}{f}}%
+}%
+\newcommand{\cut@testverts}{
+ \def\line{\rule[-3ex]{0.5em}{3ex}}%
+ \def\v##1{\cut@doublevert{##1}\line}
+ \def\V##1{\cut@Vert{##1}\line}
+ \cut@test{%
+ \line\vert\line\v{0}\v{1}\v{2}\v{3}\v{4}\v{5}
+ \line\Vert\line\V{0}\V{1}\V{2}\V{3}\V{4}\V{5}
+}}%
+