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authorKarl Berry <karl@freefriends.org>2019-07-08 21:26:49 +0000
committerKarl Berry <karl@freefriends.org>2019-07-08 21:26:49 +0000
commitc4d25ba0abc929fb7d75595e5687bc7b362eeab2 (patch)
treec04f8d83a6b46302b6f41b05912840352f5ac943
parent8dd544702d71b30ddfdae8363aa9db69195c526d (diff)
logix (8jul19)
git-svn-id: svn://tug.org/texlive/trunk@51581 c570f23f-e606-0410-a88d-b1316a301751
-rw-r--r--Master/texmf-dist/doc/fonts/logix/CHANGELOG13
-rw-r--r--Master/texmf-dist/doc/fonts/logix/README22
-rw-r--r--Master/texmf-dist/doc/fonts/logix/logix.eotbin375806 -> 375967 bytes
-rw-r--r--Master/texmf-dist/doc/fonts/logix/logix.pdfbin414596 -> 419723 bytes
-rw-r--r--Master/texmf-dist/doc/fonts/logix/logix.tex275
-rw-r--r--Master/texmf-dist/doc/fonts/logix/logix.vfcbin3540997 -> 3544723 bytes
-rw-r--r--Master/texmf-dist/fonts/opentype/public/logix/logix.otfbin428624 -> 429200 bytes
-rw-r--r--Master/texmf-dist/fonts/opentype/public/logix/logix.woffbin458796 -> 459280 bytes
-rw-r--r--Master/texmf-dist/fonts/opentype/public/logix/logix.woff2bin278056 -> 278444 bytes
-rw-r--r--Master/texmf-dist/fonts/truetype/public/logix/logix.ttfbin1050320 -> 1051392 bytes
-rw-r--r--Master/texmf-dist/tex/latex/logix/logix.sty51
11 files changed, 292 insertions, 69 deletions
diff --git a/Master/texmf-dist/doc/fonts/logix/CHANGELOG b/Master/texmf-dist/doc/fonts/logix/CHANGELOG
index bd4f67ee98a..83660b46a52 100644
--- a/Master/texmf-dist/doc/fonts/logix/CHANGELOG
+++ b/Master/texmf-dist/doc/fonts/logix/CHANGELOG
@@ -1,3 +1,16 @@
+2019-07-07 v1.01
+
+ 1. Minor additions and corrections to README file, documentation and
+ logix.sty comments.
+
+ 2. Corrected widths and macro names for several \Knt symbols.
+
+ 3. Added \KntlgX macros for changing the height of \Knt symbols.
+
+ 4. Added a dozen half width or height symbols to facilitate drawing knot bridges.
+
+ 5. Additional examples added to the documentation for using the \Knt symbols.
+
2019-07-01 v1.00
Initial release.
diff --git a/Master/texmf-dist/doc/fonts/logix/README b/Master/texmf-dist/doc/fonts/logix/README
index 6f25adafbd8..22cd554e5be 100644
--- a/Master/texmf-dist/doc/fonts/logix/README
+++ b/Master/texmf-dist/doc/fonts/logix/README
@@ -1,6 +1,6 @@
The logix package.
-This is the README for the logix package, version 2019-07-01 v1.00.
+This is the README for the logix package, version 2019-07-07 v1.01.
This package provides supplemental symbols for use in logic and mathematics
which are largely not present in Unicode. Some symbols are in Unicode but
@@ -9,7 +9,9 @@ applications. Logic tends not to have the complex layouts that is common for
more general mathematics, but has different requirements for readability.
This font is intended to complement, but not replace the AMS STIX2 fonts.
However, it may used with any mathematical font since it does not replace or
-redefine any symbols.
+redefine any symbols. This package also provides an environment for drawing
+knots using the \Knt drawing symbols and three environments for Hilbert style
+logic definitions and theorems.
This is an OpenType font where all of the symbols (more than 4,000) other than
the ASCII codepage are in the private use area. As such, the package requires
@@ -89,4 +91,20 @@ For example:
\setmainfont{STIX Two Text} % AMS STIX2 used for main font.
\setmathfont{STIX Two Math} % AMS STIX2 used for math font.
+This distribution also contains logix.vfc, which is the master font file used to
+derive the actual font files. It is not needed for LaTeX usage, but is provided
+should I become unable to maintain the package, and it is picked up by another
+maintainer. This is a FontLab source file.
+
+As briefly mentioned above, the various web font files (.eot, .ttf, .woff and
+.woff2) are provided so that any user who wishes to use the font on a web page
+does not need to convert font files.
+
+Users can report bugs or request support at
+
+ ctan@metachaos.net
+
+which is an email address devoted exclusively to my interaction with CTAN.
+There are no web pages, URLs, repositories etc. that the user can access.
+
% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
diff --git a/Master/texmf-dist/doc/fonts/logix/logix.eot b/Master/texmf-dist/doc/fonts/logix/logix.eot
index 56fc790dc86..286fb9f4d42 100644
--- a/Master/texmf-dist/doc/fonts/logix/logix.eot
+++ b/Master/texmf-dist/doc/fonts/logix/logix.eot
Binary files differ
diff --git a/Master/texmf-dist/doc/fonts/logix/logix.pdf b/Master/texmf-dist/doc/fonts/logix/logix.pdf
index 2bda220cfdb..a9a4bae76a4 100644
--- a/Master/texmf-dist/doc/fonts/logix/logix.pdf
+++ b/Master/texmf-dist/doc/fonts/logix/logix.pdf
Binary files differ
diff --git a/Master/texmf-dist/doc/fonts/logix/logix.tex b/Master/texmf-dist/doc/fonts/logix/logix.tex
index 53c1831daf1..020410ad4d9 100644
--- a/Master/texmf-dist/doc/fonts/logix/logix.tex
+++ b/Master/texmf-dist/doc/fonts/logix/logix.tex
@@ -31,7 +31,7 @@
{%
\renewcommand{\arraystretch}{1.50}
\flushleft%
- \begin{tabular}{ | L{25.00em} | L{20.00em} | >{$} L{4.00em} <{$} | @{} }%
+ \begin{tabular}{ | L{26.00em} | L{20.00em} | >{$} L{4.00em} <{$} | @{} }%
\hline%
}%
{ \end{tabular}%
@@ -83,16 +83,15 @@
\begin{document}
- \newgeometry{left=1.7in,right=1.7in,bottom=0.75in,top=0.75in}
+ \newgeometry{left=1.5in,right=1.5in,bottom=1.00in,top=0.75in}
- \section{Introduction}
+ \section{Introduction: logix 2019-07-07 v1.01}
The logix package provides the logix Unicode font and, at this time, must be used either
with \LuaLaTeX\ or \XeLaTeX. There are no available options. The logix font contains
supplemental symbols for logic and mathematics, most of which are not found in Unicode.
- All of the symbols \textemdash\ other than those in the ASCII code space \textemdash\
- are in Unicode's Private Use Area. This package does not replace either the text font
- or the math font.
+ All of the symbols, with the exception of those in the ASCII code space, are in Unicode's
+ Private Use Area. This package does not replace either the text font or the math font.
The logix package includes, in turn, the ifxetex, ifluatex, unicode-math and arydshln
packages. The unicode-math package includes the fontspec package. If the array package
@@ -135,13 +134,13 @@
the Unicode codepoint (or even font file) for any symbol in the font. Those may change
with updates to this package. Use the provided macro names and not the Unicode codepoints.
- The international organizations that maintain Unicode (and its 32-bit counterpart, ISO 10646)
+ The international organizations that maintain Unicode and ISO 10646
live in time frames more appropriate to watching trees grow than users' time frames.
This font allows a more rapid response, permitting new symbols to be added simply
because someone wants to try one out. That is entirely how this font came into
existence, the author found that Unicode simply did not have enough arrows for use in
logic and what was there was poorly designed for the purpose and inconsistent to boot.
- Many of the non-exported symbols are variants on arrows or ordering operators.
+ Many non-exported symbols are variants on arrows or ordering operators.
Formal logic expressions differ from mathematical expressions in several ways. First,
layout is typically linear rather than the more complex two-dimensional layout more
@@ -166,9 +165,9 @@
since there is no real consensus for their use \textemdash\ although some are most
frequently associated with classical logic. Various flavors of turnstiles (and their
negations) are also provided. There is more of a consensus for their usage although the
- author has only seen two publications with the sequent ({\textbackslash}Seq) symbol.
- Additional arrows are provided as an alternative to the slash typically used for replacement
- in quantification and arrows are provided for shift operators.
+ author has only seen two publications with the very useful sequent ({\textbackslash}Seq)
+ symbol. Additional arrows are provided as an alternative to the slash typically used for
+ replacement in quantification and arrows are provided for shift operators.
Many basic logic symbols are provided (including some experimental) along with a small
collection of punctuation symbols. Operators for choice, least and greatest fixed points
@@ -183,7 +182,7 @@
\section{Scripts}
Often in logic, it is desirable to distinguish different types using script variants.
- Unicode is lacking in this area \textemdash it does not always provide either all
+ Unicode is lacking in this area \textemdash\ it does not always provide either all
symbols for a script (e.g. missing digits) or all variants for a script (e.g. normal,
oblique, bold and bold oblique). Slab serif scripts are not provided by Unicode at
all. To alleviate this, 20 supplemental scripts are provided. None of these scripts
@@ -268,33 +267,35 @@
have the same height as all other knot symbols in the same row and same width as all other
knot symbols in the same column. The KnotGrid environment has no options and is used as follows
(this example has three rows and five columns):
- \vspace{-0.75em}
+ \vspace{-0.50em}
\begin{verbatim}
\begin{KnotGrid}
- \KntLFC \KntTSN \KntHXSOSU \KntTSFN \KntTRSC \\
- \KntNF \KntHXSUSO \KntNN \KntRQC \KntNQ \KntRSN \\
- \KntLFC \KntBSN \KntHXSOSU \KntBSFN \KntRBSC \\
- \end{KnotGrid}
+ \KntLFC \KntTSN \KntHXSOSU \KntTSFN \KntTRSC \\
+ \KntNF \KntHXSUSO \KntNN \KntRQC \KntNQ \KntRSN \\
+ \KntLFC \KntBSN \KntHXSOSU \KntBSFN \KntRBSC \\
+ \end{KnotGrid}
\end{verbatim}
- \vspace{-1.50em}
+ \vspace{-0.75em}
- \begin{flushleft}
- which produces the following knot diagram for the Trefoil knot.
- \vspace{0.50em}
+ \noindent which produces the following knot diagram for the Trefoil knot.
+ \vspace{-0.25em}
+ \begin{flushleft}
\begin{addmargin}[0.25in]{0.em}
\begin{KnotGrid}
\KntLFC \KntTSN \KntHXSOSU \KntTSFN \KntTRSC \\
\KntNF \KntHXSUSO \KntNN \KntRQC \KntNQ \KntRSN \\
\KntLFC \KntBSN \KntHXSOSU \KntBSFN \KntRBSC \\
\end{KnotGrid}
- \vspace{0.50em}
\end{addmargin}
+ \end{flushleft}
+ \vspace{-0.25em}
- A more complex example is the Square Knot using the Knt script for line labeling.
- \vspace{0.50em}
+ \noindent This example is the Square Knot using the Knt script for line labeling.
+ \vspace{-0.25em}
+ \begin{flushleft}
\begin{addmargin}[0.25in]{0.em}
\begin{KnotGrid}
\KntLFC \KntTSN \KntHXSOSU \KntTSFN \KntTSQN \KntTDN \Kntone \KntTDN \KntTSQN \KntTSFN \KntHXSUSO \KntTSN \KntRFC \\
@@ -304,17 +305,161 @@
\end{KnotGrid}
\end{addmargin}
\end{flushleft}
- \vspace{-1.25em}
+
+ \newpage
+ This example is a braid for a double of the left-handed Trefoil.
+ The left and right columns are half width and the top and bottom rows
+ are half height to achieve a slightly better appearance.
+ \vspace{-0.75em}
+
+\begin{verbatim}
+\begin{KnotGrid}
+ \KntBSFNF \KntBSNF \KntBSNF \KntBSNF \KntBSNF \KntBSFNF \\
+ \KntRSFNF \KntRSFN \KntRSFN \KntRSFN \KntRSFN \KntFF \\
+ \KntNF \KntVXSUSO \KntNN \KntVXSOSU \KntRSN \KntNF \\
+ \KntRSNF \KntNN \KntVXSOSU \KntRSN \KntRSN \KntNF \\
+ \KntRSNF \KntNN \KntVXSOSU \KntRSN \KntRSN \KntNF \\
+ \KntNF \KntVXSOSU \KntNN \KntVXSUSO \KntRSN \KntNF \\
+ \KntRSNF \KntNN \KntVXSUSO \KntNN \KntVXSOSU \KntNF \\
+ \KntRSNF \KntRSN \KntNN \KntVXSOSU \KntRSN \KntNF \\
+ \KntRSNF \KntNN \KntVXSOSU \KntNN \KntVXSUSO \KntNF \\
+ \KntNF \KntVXSUSO \KntRSN \KntRSN \KntRSN \KntNF \\
+ \KntRSNF \KntNN \KntVXSOSU \KntRSN \KntRSN \KntNF \\
+ \KntNF \KntVXSOSU \KntRSN \KntRSN \KntRSN \KntNF \\
+ \KntRSNF \KntNN \KntVXSUSO \KntRSN \KntRSN \KntNF \\
+ \KntRSNF \KntRSN \KntNN \KntVXSOSU \KntRSN \KntNF \\
+ \KntRSNF \KntNN \KntVXSOSU \KntRSN \KntRSN \KntNF \\
+ \KntRSNF \KntRSN \KntNN \KntVXSUSO \KntRSN \KntNF \\
+ \KntRSNF \KntRSN \KntRSN \KntNN \KntVXSOSU \KntNF \\
+ \KntRSNF \KntRSN \KntNN \KntVXSOSU \KntRSN \KntNF \\
+ \KntRSFNF \KntRSFN \KntRSFN \KntRSFN \KntRSFN \KntFF \\
+ \KntTSFNF \KntTSNF \KntTSNF \KntTSNF \KntTSNF \KntTSFNF \\
+ \end{KnotGrid}
+\end{verbatim}
+ \vspace{-0.75em}
+
+ \noindent Which is typeset as below.
+ \vspace{-1.50em}
+
+ \begin{flushleft}
+ \begin{addmargin}[0.25in]{0.em}
+ \begin{KnotGrid}
+ \KntBSFNF \KntBSNF \KntBSNF \KntBSNF \KntBSNF \KntBSFNF \\
+ \KntRSFNF \KntRSFN \KntRSFN \KntRSFN \KntRSFN \KntFF \\
+ \KntNF \KntVXSUSO \KntNN \KntVXSOSU \KntRSN \KntNF \\
+ \KntRSNF \KntNN \KntVXSOSU \KntRSN \KntRSN \KntNF \\
+ \KntRSNF \KntNN \KntVXSOSU \KntRSN \KntRSN \KntNF \\
+ \KntNF \KntVXSOSU \KntNN \KntVXSUSO \KntRSN \KntNF \\
+ \KntRSNF \KntNN \KntVXSUSO \KntNN \KntVXSOSU \KntNF \\
+ \KntRSNF \KntRSN \KntNN \KntVXSOSU \KntRSN \KntNF \\
+ \KntRSNF \KntNN \KntVXSOSU \KntNN \KntVXSUSO \KntNF \\
+ \KntNF \KntVXSUSO \KntRSN \KntRSN \KntRSN \KntNF \\
+ \KntRSNF \KntNN \KntVXSOSU \KntRSN \KntRSN \KntNF \\
+ \KntNF \KntVXSOSU \KntRSN \KntRSN \KntRSN \KntNF \\
+ \KntRSNF \KntNN \KntVXSUSO \KntRSN \KntRSN \KntNF \\
+ \KntRSNF \KntRSN \KntNN \KntVXSOSU \KntRSN \KntNF \\
+ \KntRSNF \KntNN \KntVXSOSU \KntRSN \KntRSN \KntNF \\
+ \KntRSNF \KntRSN \KntNN \KntVXSUSO \KntRSN \KntNF \\
+ \KntRSNF \KntRSN \KntRSN \KntNN \KntVXSOSU \KntNF \\
+ \KntRSNF \KntRSN \KntNN \KntVXSOSU \KntRSN \KntNF \\
+ \KntRSFNF \KntRSFN \KntRSFN \KntRSFN \KntRSFN \KntFF \\
+ \KntTSFNF \KntTSNF \KntTSNF \KntTSNF \KntTSNF \KntTSFNF \\
+ \end{KnotGrid}
+ \end{addmargin}
+ \end{flushleft}
+ \vspace{-1.25em}
+
+ A horizontal version of the above braid is shown below.
+ \vspace{-0.25em}
+
+ \begin{flushleft}
+ \begin{addmargin}[0.25in]{0.em}
+ \begin{KnotGrid}
+ \KntRSFNF \KntBSFNF \KntBSNF \KntBSNF \KntBSNF \KntBSNF \KntBSNF \KntBSNF \KntFN \KntBSNF \KntFN \KntBSNF \KntBSNF \KntBSNF \KntFN \KntBSNF \KntBSNF \KntFN \KntBSFNF \KntLSFNF \\
+ \KntRSNF \KntBSFN \KntBSN \KntBSN \KntBSN \KntNN \KntBSN \KntNN \KntHXSOSU \KntNN \KntHXSUSO \KntNN \KntBSN \KntNN \KntHXSOSU \KntNN \KntNN \KntHXSUSO \KntBSFN \KntLSNF \\
+ \KntRSNF \KntBSFN \KntNN \KntBSN \KntNN \KntHXSOSU \KntNN \KntHXSUSO \KntBSN \KntHXSOSU \KntBSN \KntHXSOSU \KntNN \KntHXSUSO \KntNN \KntHXSOSU \KntHXSOSU \KntNN \KntBSFN \KntLSNF \\
+ \KntRSNF \KntBSFN \KntHXSOSU \KntNN \KntHXSUSO \KntBSN \KntHXSOSU \KntBSN \KntBSN \KntBSN \KntBSN \KntNN \KntHXSOSU \KntNN \KntHXSUSO \KntBSN \KntBSN \KntHXSOSU \KntBSFN \KntLSNF \\
+ \KntRSNF \KntBSFN \KntBSN \KntHXSOSU \KntBSN \KntBSN \KntBSN \KntBSN \KntBSN \KntBSN \KntBSN \KntHXSUSO \KntBSN \KntHXSOSU \KntBSN \KntBSN \KntBSN \KntBSN \KntBSFN \KntLSNF \\
+ \KntRSFNF \KntFF \KntFN \KntFN \KntFN \KntFN \KntFN \KntFN \KntFN \KntFN \KntFN \KntFN \KntFN \KntFN \KntFN \KntFN \KntFN \KntFN \KntFF \KntLSFNF \\
+ \end{KnotGrid}
+ \end{addmargin}
+ \end{flushleft}
\newpage
+ \noindent This example is the $9_6 (L)$ knot.
+ \vspace{-0.75em}
+
+\begin{verbatim}
+\begin{KnotGrid}
+ \KntNN \KntNN \KntLTSC \KntTSN \KntTRSC \KntNN \KntNN \\
+ \KntNN \KntRSN \KntNN \KntTCS \KntNN \KntLSN \KntNN \\
+ \KntNN \KntNN \KntVXSUSO \KntNN \KntVXSUSO \KntNN \KntNN \\
+ \KntNN \KntRBSC \KntNN \KntVXSOSU \KntNN \KntBLSC \KntNN \\
+ \KntLTSC \KntNN \KntNN \KntVXSOSU \KntNN \KntNN \KntTRSC \\
+ \KntLSN \KntNN \KntRBSC \KntNN \KntBLSC \KntNN \KntRSN \\
+ \KntLSN \KntLTSC \KntNN \KntNN \KntNN \KntTRSC \KntRSN \\
+ \KntVXSUSO \KntNN \KntNN \KntNN \KntNN \KntNN \KntVXSUSO\\
+ \KntLSN \KntBLSC \KntNN \KntNN \KntNN \KntRBSC \KntRSN \\
+ \KntBLSC \KntBSN \KntHXSUSO \KntHXSUSO \KntHXSUSO \KntBSN \KntRBSC \\
+ \end{KnotGrid}
+\end{verbatim}
+ \vspace{-0.50em}
+
+ \noindent Which is typeset as below.
+ \vspace{-0.50em}
+
+ \begin{flushleft}
+ \begin{addmargin}[0.25in]{0.em}
+ \begin{KnotGrid}
+ \KntNN \KntNN \KntLTSC \KntTSN \KntTRSC \KntNN \KntNN \\
+ \KntNN \KntRSN \KntNN \KntTCS \KntNN \KntLSN \KntNN \\
+ \KntNN \KntNN \KntVXSUSO \KntNN \KntVXSUSO \KntNN \KntNN \\
+ \KntNN \KntRBSC \KntNN \KntVXSOSU \KntNN \KntBLSC \KntNN \\
+ \KntLTSC \KntNN \KntNN \KntVXSOSU \KntNN \KntNN \KntTRSC \\
+ \KntLSN \KntNN \KntRBSC \KntNN \KntBLSC \KntNN \KntRSN \\
+ \KntLSN \KntLTSC \KntNN \KntNN \KntNN \KntTRSC \KntRSN \\
+ \KntVXSUSO \KntNN \KntNN \KntNN \KntNN \KntNN \KntVXSUSO \\
+ \KntLSN \KntBLSC \KntNN \KntNN \KntNN \KntRBSC \KntRSN \\
+ \KntBLSC \KntBSN \KntHXSUSO \KntHXSUSO \KntHXSUSO \KntBSN \KntRBSC \\
+ \end{KnotGrid}
+ \end{addmargin}
+ \end{flushleft}
+
+ \noindent This final example, is the rational link corresponding to the rational number $4117\, /\, 17426$.
+ \vspace{-0.50em}
+
+ \begin{flushleft}
+ \begin{addmargin}[0.25in]{0.em}
+ \begin{KnotGrid}
+ \KntLCD \KntTDLA \KntTDN \KntTDN \KntHXDUSO \KntHXSUDO \KntTDN \KntTDLA \KntTDN \KntHXDUDO \KntHXDUDO \KntHXDUDO \KntTDN \KntHXDUSO \KntHXSUDO \KntTDN \KntTDRA \KntTDN \KntHXDUDO \KntHXDUDO \KntHXDUDO \KntHXDUDO \KntTDN \KntTDN \KntTDN \KntTDRA \KntRCD \\
+ \KntNN \KntHXDOSU \KntHXSODU \KntHXDOSU \KntNN \KntNN \KntHXSODU \KntHXDOSU \KntHXSODU \KntNN \KntNN \KntNN \KntHXDOSU \KntNN \KntNN \KntHXSODU \KntHXDOSU \KntHXSODU \KntNN \KntNN \KntNN \KntNN \KntHXDOSU \KntHXSODU \KntHXDOSU \KntHXSODU \KntNN \\
+ \KntLCS \KntBSLA \KntBSN \KntBSN \KntTDNBSN \KntTDRABSN \KntBSN \KntBSN \KntBSN \KntTSNBSN \KntTSRABSN \KntTSNBSN \KntBSN \KntTDNBSN \KntTDLABSN \KntBSN \KntBSN \KntBSN \KntTSNBSN \KntTSNBSN \KntTSRABSN \KntTSNBSN \KntBSN \KntBSN \KntBSN \KntBSLA \KntRCS \\
+ \end{KnotGrid}
+ \end{addmargin}
+ \end{flushleft}
+ \vspace{-0.50em}
+
+ \noindent With its Seifert circle decomposition.
+ \vspace{-0.50em}
+
+ \begin{flushleft}
+ \begin{addmargin}[0.25in]{0.em}
+ \begin{KnotGrid}
+ \KntLCS \KntTSLA \KntTSN \KntTSN \KntHVMSLSR \KntHVMSLSR \KntTSN \KntTSLA \KntTSN \KntHVMSLSR \KntHVMSLSR \KntHVMSLSR \KntTSN \KntHHMSTSB \KntHHMSTSB \KntTSN \KntTSRA \KntTSN \KntHVMSLSR \KntHVMSLSR \KntHVMSLSR \KntHVMSLSR \KntTSN \KntTSN \KntTSN \KntTSRA \KntRCS \\
+ \KntNN \KntHHMSTSB \KntHHMSTSB \KntHHMSTSB \KntNN \KntNN \KntHHMSTSB \KntHHMSTSB \KntHHMSTSB \KntNN \KntNN \KntNN \KntHVMSLSR \KntNN \KntNN \KntHVMSLSR \KntHVMSLSR \KntHVMSLSR \KntNN \KntNN \KntNN \KntNN \KntHVMSLSR \KntHVMSLSR \KntHVMSLSR \KntHVMSLSR \KntNN \\
+ \KntLCS \KntBSLA \KntBSN \KntBSN \KntTSNBSN \KntTSRABSN \KntBSN \KntBSN \KntBSN \KntTSNBSN \KntTSRABSN \KntTSNBSN \KntBSN \KntTSNBSN \KntTSLABSN \KntBSN \KntBSN \KntBSN \KntTSNBSN \KntTSNBSN \KntTSRABSN \KntTSNBSN \KntBSN \KntBSN \KntBSN \KntBSLA \KntRCS \\
+ \end{KnotGrid}
+ \end{addmargin}
+ \end{flushleft}
+
Where a grid cell would otherwise be empty or where padding is required to
satisfy the size requirements for a cell, 25 KntXY (X is height, Y width, both
are one of: N, E, F, Q, Z) space or strut symbols are provided which are exactly
sized both horizontally and vertically to assist. The knot symbols are typeset
in math mode so that spaces are ignored. This allows the grid structure to be
- explicit, making readability and maintenance easier. In the first example above,
- the fourth grid column is 0.5em wide, but in the second row an 0.25em width symbol
- is used, which must then be padded with an 0.25em space.
+ explicit, making readability and maintenance easier. In the first example above
+ (the Trefoil knot), the fourth grid column is 0.5em wide, but in the second row
+ an 0.25em width symbol is used, which must then be padded with an 0.25em space.
\noindent In order to keep names shortish, the following abbreviations are used for
Knt symbols
@@ -332,6 +477,7 @@
M & sMoothed & Z & Zero \\
\end{tabular}
+ \newpage
\section{Logic Proofs}
\LaTeX\ has more than adequate support for traditional mathematical proofs.
@@ -380,9 +526,8 @@
\end{LogixDefn}
\end{verbatim}
- \newpage
\begin{flushleft}
- which would be typeset as shown below.
+ which is typeset as shown below.
\vspace{0.25em}
\begin{addmargin}[0.25in]{0.em}
@@ -399,7 +544,7 @@
\end{flushleft}
\vspace{-0.50em}
- None of the environments defined in this package affects the indentation level.
+ Environments defined in this package do not affect the indentation level.
The LogixDefn environment would also be used to state axioms or theorems without
associated proofs. In this document, the addmargin environment provided by the
scrextend package is used to provide indentation.
@@ -412,10 +557,12 @@
by a comment when the length argument is present. The other three arguments are the
name (and any associated number) of the theorem, a possibly empty set of postulates
which are assumed only for the purpose of the proof (e.g. assuming the Axiom of
- Choice (AC) for a specific theorem when working in ZF instead of ZFC). Thus, postulates
- are distinguished from axioms which are assumed to hold for all theorems in a system
- whereas a postulate holds only for a specific proof. The third parameter is the
- statement (the theorem's expression) of the proof.
+ Choice (AC) for a specific theorem when working in ZF instead of ZFC).
+
+ \newpage
+ Thus, postulates are distinguished from axioms which are assumed to hold for all
+ theorems in a system whereas a postulate holds only for a specific proof. The third
+ parameter is the statement (the theorem's expression) of the proof.
The LogixProof environment defines the Dash and Line nested macros. These are
identical except that the Dash macro is followed by a dashed line separator and
@@ -452,7 +599,6 @@
\end{LogixProof}
\end{verbatim}
- \newpage
\begin{verbatim}
\begin{LogixProof}[5em] {Th 46} {} {\prop{p} \Nd \prop{q}}
\Line {1} {Th 41} {} {\prop{p} \Impl \prop{q}} {First comment}
@@ -471,7 +617,7 @@
\vspace{-1.50em}
\begin{flushleft}
- which would be typeset as shown below.
+ which is typeset as shown below.
\vspace{0.25em}
\begin{addmargin}[0.25in]{0.em}
@@ -492,8 +638,8 @@
\end{LogixProof}
\end{addmargin}
\end{flushleft}
- \vspace{-1.50em}
+ \newpage
\begin{flushleft}
A more realistic example of using the LogixProof environment is shown below
(note the use of different implication arrow lengths to indicate depth of
@@ -545,9 +691,8 @@
\end{verbatim}
\vspace{-1.50em}
- \newpage
\begin{flushleft}
- which would be typeset as shown below.
+ which is typeset as shown below.
\vspace{0.25em}
\begin{addmargin}[0.25in]{0.em}
@@ -582,8 +727,8 @@
\end{LogixSeqnt}
\end{addmargin}
\end{flushleft}
- \vspace{-0.25em}
+ \newpage
\section{Symbols}
The remainder of this document is the list of symbols. Each symbol has a name
@@ -617,6 +762,15 @@
is no spam filter on this email account. Under normal circumstances,
this email account is checked at least daily.
+ This distribution also contains logix.vfc, which is the master font file used to
+ derive the actual font files. It is not needed for \LaTeX usage, but is provided
+ should I become unable to maintain the package, and it is picked up by another
+ maintainer. This is a FontLab source file.
+
+ In addition, and also not required for \LaTeX\ usage, the various web font files
+ (.eot, .ttf, .woff and .woff2) are included in the distribution so that users who
+ wish to use the font in a web page do not need to convert font files.
+
\restoregeometry
\newpage
@@ -1312,7 +1466,7 @@
Vert flow, Vertical smoothing; solid left, dashed right & {\textbackslash}KntVVMSLDR & \scalebox{1.50}{\KntVVMSLDR} \\ \hline
Horz flow, Horizontal smoothing; solid top, dashed bottom & {\textbackslash}KntHHMSTDB & \scalebox{1.50}{\KntHHMSTDB} \\ \hline
Vert flow, Vertical smoothing; dashed left, solid right & {\textbackslash}KntVVMDLSR & \scalebox{1.50}{\KntVVMDLSR} \\ \hline
- Horz flow, Horizontal smoothing; dashed top, dashed btm & {\textbackslash}KntHHMDTDB & \scalebox{1.50}{\KntHHMDTDB} \\ \hline
+ Horz flow, Horizontal smoothing; dashed top, dashed bottom & {\textbackslash}KntHHMDTDB & \scalebox{1.50}{\KntHHMDTDB} \\ \hline
Vert flow, Vertical smoothing; dashed left, dashed right & {\textbackslash}KntVVMDLDR & \scalebox{1.50}{\KntVVMDLDR} \\ \hline
Horz flow, Vertical smoothing, solid left, solid right & {\textbackslash}KntHVMSLSR & \scalebox{1.50}{\KntHVMSLSR} \\ \hline
Vert flow, Horizontal smoothing, solid top, solid bottom & {\textbackslash}KntVHMSTSB & \scalebox{1.50}{\KntVHMSTSB} \\ \hline
@@ -1504,7 +1658,7 @@
Top solid line, bottom solid left arrow & {\textbackslash}KntTSNBSLA & \scalebox{1.50}{\KntTSNBSLA} \\ \hline
Left solid up arrow, right solid line & {\textbackslash}KntLSUARSN & \scalebox{1.50}{\KntLSUARSN} \\ \hline
Top solid right arrow, bottom solid line & {\textbackslash}KntTSRABSN & \scalebox{1.50}{\KntTSRABSN} \\ \hline
- Left solid line, right solid down arrow & {\textbackslash}KntRSNRSDA & \scalebox{1.50}{\KntRSNRSDA} \\ \hline
+ Left solid line, right solid down arrow & {\textbackslash}KntLSNRSDA & \scalebox{1.50}{\KntLSNRSDA} \\ \hline
Top solid line, bottom solid right arrow & {\textbackslash}KntTSNBSRA & \scalebox{1.50}{\KntTSNBSRA} \\ \hline
Left solid down arrow, right solid line & {\textbackslash}KntLSDARSN & \scalebox{1.50}{\KntLSDARSN} \\ \hline
Top solid left arrow, bottom solid line & {\textbackslash}KntTSLABSN & \scalebox{1.50}{\KntTSLABSN} \\ \hline
@@ -1512,10 +1666,10 @@
Top dashed line, bottom solid left arrow & {\textbackslash}KntTDNBSLA & \scalebox{1.50}{\KntTDNBSLA} \\ \hline
Left solid up arrow, right dashed line & {\textbackslash}KntLSUARDN & \scalebox{1.50}{\KntLSUARDN} \\ \hline
Top solid right arrow, bottom dashed line & {\textbackslash}KntTSRABDN & \scalebox{1.50}{\KntTSRABDN} \\ \hline
- Left dashed line, right solid down arrow & {\textbackslash}KntRDNRSDA & \scalebox{1.50}{\KntRDNRSDA} \\ \hline
- Top dashed line, bottom solid right arrow & {\textbackslash}KntTDNBSRA & \scalebox{1.50}{\KntTDNBSRA} \\ \hline
- Left dashed line, right solid up arrow & {\textbackslash}KntLDNRSUA & \scalebox{1.50}{\KntLDNRSUA} \\ \hline
+ Left dashed line, right solid down arrow & {\textbackslash}KntLDNRSDA & \scalebox{1.50}{\KntLDNRSDA} \\ \hline
Top solid left arrow, bottom dashed line & {\textbackslash}KntTSLABDN & \scalebox{1.50}{\KntTSLABDN} \\ \hline
+ Left dashed line, right solid up arrow & {\textbackslash}KntLDNRSUA & \scalebox{1.50}{\KntLDNRSUA} \\ \hline
+ Top dashed line, bottom solid right arrow & {\textbackslash}KntTDNBSRA & \scalebox{1.50}{\KntTDNBSRA} \\ \hline
Left solid down arrow, right dashed line & {\textbackslash}KntLSDARDN & \scalebox{1.50}{\KntLSDARDN} \\ \hline
\end{symbolListA}
@@ -1524,21 +1678,36 @@
Top solid line, bottom dashed left arrow & {\textbackslash}KntTSNBDLA & \scalebox{1.50}{\KntTSNBDLA} \\ \hline
Left dashed up arrow, right solid line & {\textbackslash}KntLDUARSN & \scalebox{1.50}{\KntLDUARSN} \\ \hline
Top dashed right arrow, bottom solid line & {\textbackslash}KntTDRABSN & \scalebox{1.50}{\KntTDRABSN} \\ \hline
- Left solid line, right dashed down arrow & {\textbackslash}KntRSNRDDA & \scalebox{1.50}{\KntRSNRDDA} \\ \hline
- Top solid line, bottom dashed right arrow & {\textbackslash}KntTSNBDRA & \scalebox{1.50}{\KntTSNBDRA} \\ \hline
- Left solid line, right dashed up arrow & {\textbackslash}KntLSNRDUA & \scalebox{1.50}{\KntLSNRDUA} \\ \hline
+ Left solid line, right dashed down arrow & {\textbackslash}KntLSNRDDA & \scalebox{1.50}{\KntLSNRDDA} \\ \hline
Top dashed left arrow, bottom solid line & {\textbackslash}KntTDLABSN & \scalebox{1.50}{\KntTDLABSN} \\ \hline
+ Left solid line, right dashed up arrow & {\textbackslash}KntLSNRDUA & \scalebox{1.50}{\KntLSNRDUA} \\ \hline
+ Top solid line, bottom dashed right arrow & {\textbackslash}KntTSNBDRA & \scalebox{1.50}{\KntTSNBDRA} \\ \hline
Left dashed down arrow, right solid line & {\textbackslash}KntLDDARSN & \scalebox{1.50}{\KntLDDARSN} \\ \hline
Top dashed line, bottom dashed left arrow & {\textbackslash}KntTDNBDLA & \scalebox{1.50}{\KntTDNBDLA} \\ \hline
Left dashed up arrow, right dashed line & {\textbackslash}KntLDUARDN & \scalebox{1.50}{\KntLDUARDN} \\ \hline
Top dashed right arrow, bottom dashed line & {\textbackslash}KntTDRABDN & \scalebox{1.50}{\KntTDRABDN} \\ \hline
- Left dashed line, right dashed down arrow & {\textbackslash}KntRDNRDDA & \scalebox{1.50}{\KntRDNRDDA} \\ \hline
- Top dashed line, bottom dashed right arrow & {\textbackslash}KntTDNBDRA & \scalebox{1.50}{\KntTDNBDRA} \\ \hline
- Left dashed line, right dashed up arrow & {\textbackslash}KntLDNRDUA & \scalebox{1.50}{\KntLDNRDUA} \\ \hline
+ Left dashed line, right dashed down arrow & {\textbackslash}KntLDNRDDA & \scalebox{1.50}{\KntLDNRDDA} \\ \hline
Top dashed left arrow, bottom dashed line & {\textbackslash}KntTDLABDN & \scalebox{1.50}{\KntTDLABDN} \\ \hline
+ Left dashed line, right dashed up arrow & {\textbackslash}KntLDNRDUA & \scalebox{1.50}{\KntLDNRDUA} \\ \hline
+ Top dashed line, bottom dashed right arrow & {\textbackslash}KntTDNBDRA & \scalebox{1.50}{\KntTDNBDRA} \\ \hline
Left dashed down arrow, right dashed line & {\textbackslash}KntLDDARDN & \scalebox{1.50}{\KntLDDARDN} \\ \hline
\end{symbolListA}
+ \begin{symbolListA}
+ Top solid line, half height & {\textbackslash}KntTSNF & \scalebox{1.50}{\KntTSNF} \\ \hline
+ Right solid line, half width & {\textbackslash}KntRSNF & \scalebox{1.50}{\KntRSNF} \\ \hline
+ Bottom solid line, half height & {\textbackslash}KntBSNF & \scalebox{1.50}{\KntBSNF} \\ \hline
+ Left solid line, half width & {\textbackslash}KntLSNF & \scalebox{1.50}{\KntLSNF} \\ \hline
+ Top solid half line, half height & {\textbackslash}KntTSFNF & \scalebox{1.50}{\KntTSFNF} \\ \hline
+ Right solid half line, half width & {\textbackslash}KntRSFNF & \scalebox{1.50}{\KntRSFNF} \\ \hline
+ Bottom solid half line, half height & {\textbackslash}KntBSFNF & \scalebox{1.50}{\KntBSFNF} \\ \hline
+ Left solid half line, half width & {\textbackslash}KntLSFNF & \scalebox{1.50}{\KntLSFNF} \\ \hline
+ Top solid forth line, half height & {\textbackslash}KntTSQNF & \scalebox{1.50}{\KntTSQNF} \\ \hline
+ Right solid forth line, half width & {\textbackslash}KntRSQNF & \scalebox{1.50}{\KntRSQNF} \\ \hline
+ Bottom solid forth line, half height & {\textbackslash}KntBSQNF & \scalebox{1.50}{\KntBSQNF} \\ \hline
+ Left solid forth line, half width & {\textbackslash}KntLSQNF & \scalebox{1.50}{\KntLSQNF} \\ \hline
+ \end{symbolListA}
+
\newpage
\begin{symbolListX}
Black square & {\textbackslash}BlackSquare & \scalebox{1.50}{\BlackSquare} \\ \hline
@@ -2484,7 +2653,7 @@
\newpage
\begin{flushleft}
- Map Variable: {\textbackslash}syscli\{<alphanum>\} -- calligraphic script
+ Map Variable: {\textbackslash}symcli\{<alphanum>\} -- calligraphic script
\end{flushleft}
\vspace{-0.15em}
diff --git a/Master/texmf-dist/doc/fonts/logix/logix.vfc b/Master/texmf-dist/doc/fonts/logix/logix.vfc
index 302280925f9..8124b8653b1 100644
--- a/Master/texmf-dist/doc/fonts/logix/logix.vfc
+++ b/Master/texmf-dist/doc/fonts/logix/logix.vfc
Binary files differ
diff --git a/Master/texmf-dist/fonts/opentype/public/logix/logix.otf b/Master/texmf-dist/fonts/opentype/public/logix/logix.otf
index e29c33e639a..713364713b9 100644
--- a/Master/texmf-dist/fonts/opentype/public/logix/logix.otf
+++ b/Master/texmf-dist/fonts/opentype/public/logix/logix.otf
Binary files differ
diff --git a/Master/texmf-dist/fonts/opentype/public/logix/logix.woff b/Master/texmf-dist/fonts/opentype/public/logix/logix.woff
index a613a11ce7b..d267a8b110b 100644
--- a/Master/texmf-dist/fonts/opentype/public/logix/logix.woff
+++ b/Master/texmf-dist/fonts/opentype/public/logix/logix.woff
Binary files differ
diff --git a/Master/texmf-dist/fonts/opentype/public/logix/logix.woff2 b/Master/texmf-dist/fonts/opentype/public/logix/logix.woff2
index d420790e5c5..3b18627a63b 100644
--- a/Master/texmf-dist/fonts/opentype/public/logix/logix.woff2
+++ b/Master/texmf-dist/fonts/opentype/public/logix/logix.woff2
Binary files differ
diff --git a/Master/texmf-dist/fonts/truetype/public/logix/logix.ttf b/Master/texmf-dist/fonts/truetype/public/logix/logix.ttf
index bd220f632e1..0eb95a3651a 100644
--- a/Master/texmf-dist/fonts/truetype/public/logix/logix.ttf
+++ b/Master/texmf-dist/fonts/truetype/public/logix/logix.ttf
Binary files differ
diff --git a/Master/texmf-dist/tex/latex/logix/logix.sty b/Master/texmf-dist/tex/latex/logix/logix.sty
index bd6984eeb03..3c99c23f853 100644
--- a/Master/texmf-dist/tex/latex/logix/logix.sty
+++ b/Master/texmf-dist/tex/latex/logix/logix.sty
@@ -1,6 +1,7 @@
-% logix.sty
% Copyright (c) 2001..2019 by Michael Lee Finney.
%
+% logix.sty - 2019-07-07 v1.01
+%
% This work may be distributed and/or modified under the conditions of the
% LaTeX Project Public License, either version 1.3 of this license or (at your
% option) any later version. The latest version of this license is in
@@ -67,9 +68,9 @@
% columns):
%
% \begin{KnotGrid}
-% \KntLFC \KntTSN \KntHXSOSU \KntTSFN \KntTRSC \\
-% \KntNFSpace \KntHXSUSO \KntNNSpace \KntRQC \KntNQSpace \KntRSN \\
-% \KntLFC \KntBSN \KntHXSOSU \KntBSFN \KntRBSC
+% \KntLFC \KntTSN \KntHXSOSU \KntTSFN \KntTRSC \\
+% \KntNF \KntHXSUSO \KntNN \KntRQC \KntNQ \KntRSN \\
+% \KntLFC \KntBSN \KntHXSOSU \KntBSFN \KntRBSC
% \end{KnotGrid}
%
% where a grid cell would otheriwse be empty or where padding is required to satisfy
@@ -1180,6 +1181,9 @@
% be used for empty cells matching the the width and height of the current row
% and column and for padding a symbol.
%
+% The \KntlgX macros (where X is one of k, e, f, q or v) may be used to force
+% a specific height for a symbol.
+%
\newcommand \lgk[1] {\protect\raisebox{0.0000em}[0.7620em][0.2380em]{\ensuremath{\Umathchar "0 \symLogix "#1}}}
\newcommand \lge[1] {\protect\raisebox{0.0000em}[0.5120em][0.2380em]{\ensuremath{\Umathchar "0 \symLogix "#1}}}
@@ -1187,6 +1191,12 @@
\newcommand \lgq[1] {\protect\raisebox{0.0000em}[0.0120em][0.2380em]{\ensuremath{\Umathchar "0 \symLogix "#1}}}
\newcommand \lgv[1] {\protect\raisebox{0.4330em}[0.7620em][0.2380em]{\ensuremath{\Umathchar "0 \symLogix "#1}}}
+ \newcommand \Kntlgk[1] {\protect\raisebox{0.0000em}[0.7620em][0.2380em]{#1}}
+ \newcommand \Kntlge[1] {\protect\raisebox{0.0000em}[0.5120em][0.2380em]{#1}}
+ \newcommand \Kntlgf[1] {\protect\raisebox{0.0000em}[0.2620em][0.2380em]{#1}}
+ \newcommand \Kntlgq[1] {\protect\raisebox{0.0000em}[0.0120em][0.2380em]{#1}}
+ \newcommand \Kntlgv[1] {\protect\raisebox{0.4330em}[0.7620em][0.2380em]{#1}}
+
\newcommand \KntNN {\lgk{E210}} % Full height, full width space.
\newcommand \KntNE {\lgk{E211}} % Full height, three quarter width space.
\newcommand \KntNF {\lgk{E212}} % Full height, half width space.
@@ -1407,7 +1417,7 @@
\newcommand \KntTSNBSLA {\lgk{E1F0}} % Top solid line, bottom solid left arrow
\newcommand \KntLSUARSN {\lgk{E1F1}} % Left solid up arrow, right solid line
\newcommand \KntTSRABSN {\lgk{E1F2}} % Top solid right arrow, bottom solid line
- \newcommand \KntRSNRSDA {\lgk{E1F3}} % Left solid line, right solid down arrow
+ \newcommand \KntLSNRSDA {\lgk{E1F3}} % Left solid line, right solid down arrow
\newcommand \KntTSNBSRA {\lgk{E1F4}} % Top solid line, bottom solid right arrow
\newcommand \KntLSDARSN {\lgk{E1F5}} % Left solid down arrow, right solid line
\newcommand \KntTSLABSN {\lgk{E1F6}} % Top solid left arrow, bottom solid line
@@ -1415,29 +1425,42 @@
\newcommand \KntTDNBSLA {\lgk{E1F8}} % Top dashed line, bottom solid left arrow
\newcommand \KntLSUARDN {\lgk{E1F9}} % Left solid up arrow, right dashed line
\newcommand \KntTSRABDN {\lgk{E1FA}} % Top solid right arrow, bottom dashed line
- \newcommand \KntRDNRSDA {\lgk{E1FB}} % Left dashed line, right solid down arrow
- \newcommand \KntTDNBSRA {\lgk{E1FC}} % Top dashed line, bottom solid right arrow
+ \newcommand \KntLDNRSDA {\lgk{E1FB}} % Left dashed line, right solid down arrow
+ \newcommand \KntTSLABDN {\lgk{E1FC}} % Top solid left arrow, bottom dashed line
\newcommand \KntLDNRSUA {\lgk{E1FD}} % Left dashed line, right solid up arrow
- \newcommand \KntTSLABDN {\lgk{E1FE}} % Top solid left arrow, bottom dashed line
+ \newcommand \KntTDNBSRA {\lgk{E1FE}} % Top dashed line, bottom solid right arrow
\newcommand \KntLSDARDN {\lgk{E1FF}} % Left solid down arrow, right dashed line
\newcommand \KntTSNBDLA {\lgk{E200}} % Top solid line, bottom dashed left arrow
\newcommand \KntLDUARSN {\lgk{E201}} % Left dashed up arrow, right solid line
\newcommand \KntTDRABSN {\lgk{E202}} % Top dashed right arrow, bottom solid line
- \newcommand \KntRSNRDDA {\lgk{E203}} % Left solid line, right dashed down arrow
- \newcommand \KntTSNBDRA {\lgk{E204}} % Top solid line, bottom dashed right arrow
+ \newcommand \KntLSNRDDA {\lgk{E203}} % Left solid line, right dashed down arrow
+ \newcommand \KntTDLABSN {\lgk{E204}} % Top dashed left arrow, bottom solid line
\newcommand \KntLSNRDUA {\lgk{E205}} % Left solid line, right dashed up arrow
- \newcommand \KntTDLABSN {\lgk{E206}} % Top dashed left arrow, bottom solid line
+ \newcommand \KntTSNBDRA {\lgk{E206}} % Top solid line, bottom dashed right arrow
\newcommand \KntLDDARSN {\lgk{E207}} % Left dashed down arrow, right solid line
\newcommand \KntTDNBDLA {\lgk{E208}} % Top dashed line, bottom dashed left arrow
\newcommand \KntLDUARDN {\lgk{E209}} % Left dashed up arrow, right dashed line
\newcommand \KntTDRABDN {\lgk{E20A}} % Top dashed right arrow, bottom dashed line
- \newcommand \KntRDNRDDA {\lgk{E20B}} % Left dashed line, right dashed down arrow
- \newcommand \KntTDNBDRA {\lgk{E20C}} % Top dashed line, bottom dashed right arrow
+ \newcommand \KntLDNRDDA {\lgk{E20B}} % Left dashed line, right dashed down arrow
+ \newcommand \KntTDLABDN {\lgk{E20C}} % Top dashed left arrow, bottom dashed line
\newcommand \KntLDNRDUA {\lgk{E20D}} % Left dashed line, right dashed up arrow
- \newcommand \KntTDLABDN {\lgk{E20E}} % Top dashed left arrow, bottom dashed line
+ \newcommand \KntTDNBDRA {\lgk{E20E}} % Top dashed line, bottom dashed right arrow
\newcommand \KntLDDARDN {\lgk{E20F}} % Left dashed down arrow, right dashed line
+ \newcommand \KntTSNF {\lgf{E214}} % Top solid line, half height
+ \newcommand \KntRSNF {\lgk{E215}} % Right solid line, half width
+ \newcommand \KntBSNF {\lgf{E216}} % Bottom solid line, half height
+ \newcommand \KntLSNF {\lgk{E217}} % Left solid line, half width
+ \newcommand \KntTSFNF {\lgf{E218}} % Top solid half line, half height
+ \newcommand \KntRSFNF {\lgf{E219}} % Right solid half line, half width
+ \newcommand \KntBSFNF {\lgf{E21A}} % Bottom solid half line, half height
+ \newcommand \KntLSFNF {\lgf{E21B}} % Left solid half line, half width
+ \newcommand \KntTSQNF {\lgf{E21C}} % Top solid forth line, half height
+ \newcommand \KntRSQNF {\lgq{E21D}} % Right solid forth line, half width
+ \newcommand \KntBSQNF {\lgf{E21E}} % Bottom solid forth line, half height
+ \newcommand \KntLSQNF {\lgq{E21F}} % Left solid forth line, half width
+
\newcommand \Kntzero {\lgv{EFB0}} % Monospace raised italic, serif font: digit 0
\newcommand \Kntone {\lgv{EFB1}} % Monospace raised italic, serif font: digit 1
\newcommand \Knttwo {\lgv{EFB2}} % Monospace raised italic, serif font: digit 2