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Diffstat (limited to 'Master/texmf-dist/tex/generic/xypic/xyknot.tex')
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diff --git a/Master/texmf-dist/tex/generic/xypic/xyknot.tex b/Master/texmf-dist/tex/generic/xypic/xyknot.tex new file mode 100644 index 00000000000..dfe7d5006be --- /dev/null +++ b/Master/texmf-dist/tex/generic/xypic/xyknot.tex @@ -0,0 +1,902 @@ +%% xyknot.tex from $Id: xyknot.doc,v 3.4 1997/05/18 01:13:24 ross Exp $ +%% +%% Xy-pic ``Knots and Links'' feature. +%% Copyright (c) 1994-1996 Ross Moore <ross@mpce.mq.edu.au> +%% +%% This file is part of the Xy-pic package for graphs and diagrams in TeX. +%% See the companion README and INSTALL files for further information. +%% Copyright (c) 1991-1996 Kristoffer H. Rose <krisrose@brics.dk> +%% +%% The Xy-pic package is free software; you can redistribute it and/or modify +%% it under the terms of the GNU General Public License as published by the +%% Free Software Foundation; either version 2 of the License, or (at your +%% option) any later version. +%% +%% The Xy-pic package is distributed in the hope that it will be useful, but +%% WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY +%% or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +%% for more details. +%% +%% You should have received a copy of the GNU General Public License along +%% with this macro package; if not, write to the Free Software Foundation, +%% Inc., 675 Mass Ave, Cambridge, MA 02139, USA. +%% +\ifx\xyloaded\undefined \input xy \fi +\xyprovide{knot}{Knots and Links feature}{\stripRCS$Revision: 3.4 $}% + {Ross Moore}{ross@mpce.mq.edu.au}% + {Mathematics Department, Macquarie University, NSW~2109, Australia} +\message{knots and links,} +\xyrequire{arrow}\xycatcodes +\xydef@\xykparsecross@{% + \def\xykSCALE@@{}\edef\xyknotPLACE{\xykmidPLACE@}% + \let\xykparser@=\xykparsecross@@ + \def\xykdefaultbreak@{\let\xykbreak@=\xykforetemp@ + \def\xyknotPLACE{(.5)}\appendtoholder@}% + \xyFN@\xykparsescale@ } +{\xyuncatcodes \catcode`@=11 +\gdef\next{% + \ifx\space@\next \expandafter\DN@\space{\xyFN@\xykparsecross@@}% + \else\addLT@\ifx\next \addLT@\DN@{\xyprecross@}% + \else\addGT@\ifx\next \addGT@\DN@{\xypostcross@}% + \else\addEQ@\ifx\next \addEQ@\DN@{\xyFN@\xykparsetips@@}% + \else\ifx|\next\DN@|{\xymidcross@}% + \else\addAT@\ifx\next \addAT@\DN@(##1){% + \xyadjustBREAK@i##1@@\xyFN@\xykparsecross@@}% + \else\DN@{\afterknot@}% + \fi\fi\fi\fi\fi\fi \next@ }} +\xylet@\xykparsecross@@=\next +\xydef@\xyprecross@{% + \def\xykholder@{\xykprebreak@@}% + \edef\xyknotPLACE{\xykprePLACE@}% + \xyFN@\xykparsebreak@} +\xydef@\xypostcross@{% + \def\xykholder@{\xykpostbreak@@}% + \edef\xyknotPLACE{\xykpostPLACE@}% + \xyFN@\xykparsebreak@} +\xydef@\xymidcross@{% + \def\xykholder@{\xykmidbreak@@}% + \edef\xyknotPLACE{\xykmidPLACE@}% + \xyFN@\xykparsebreak@} +\xydef@\xykcross@#1{\xykcheckTIPS@ + \expandafter\toks@\expandafter{\expandafter#1\knotSTYLE}} +\xydef@\xykoverstring@{\addtotoks@{{}}\xykmidbreak@ \xyknottips@} +\xydef@\xykunderstring@{\xykprebreak@ \xykpostbreak@ \xyknottips@} +\xydef@\vcross{\begingroup\def\afterknot@{\xyvcross}% + \def\xykprePLACE@{(.1)}\def\xykpostPLACE@{(.9)}% + \def\xykmidPLACE@{(.9)}\def\xykpostbreak@@{|\knothole}% + \xyFN@\xykparsecross@ }% +\xydef@\hcross{\begingroup\def\afterknot@{\xyhcross}% + \def\xykprePLACE@{(.1)}\def\xykpostPLACE@{(.9)}% + \def\xykmidPLACE@{(.9)}\def\xykpostbreak@@{|\knothole}% + \xyFN@\xykparsecross@ }% +\xydef@\vcrossneg{\begingroup\def\afterknot@{\xyvcrossneg}% + \def\xykprePLACE@{(.1)}\def\xykpostPLACE@{(.9)}% + \def\xykmidPLACE@{(.9)}\def\xykpostbreak@@{|\knothole}% + \xyFN@\xykparsecross@ }% +\xydef@\hcrossneg{\begingroup\def\afterknot@{\xyhcrossneg}% + \def\xykprePLACE@{(.1)}\def\xykpostPLACE@{(.9)}% + \def\xykmidPLACE@{(.9)}\def\xykpostbreak@@{|\knothole}% + \xyFN@\xykparsecross@ }% +\xydef@\vuncross{\begingroup\def\afterknot@{\xyvuncross}% + \def\xykprePLACE@{(.1)}\def\xykpostPLACE@{(.9)}% + \def\xykmidPLACE@{(.9)}\def\xykpostbreak@@{}% + \xyFN@\xykparsecross@ }% +\xydef@\huncross{\begingroup\def\afterknot@{\xyhuncross}% + \def\xykprePLACE@{(.1)}\def\xykpostPLACE@{(.9)}% + \def\xykmidPLACE@{(.9)}\def\xykpostbreak@@{}% + \xyFN@\xykparsecross@ }% +\xydef@\xyvcross{\xykcross@\xykcrossv + \xykoverstring@ \xykunderstring@ \xykhvobject@{+(0,-1)}} +\xydef@\xyhcross{\xykcross@\xykcrossh + \xykoverstring@ \xykunderstring@ \xykhvobject@{+(1,0)}} +\xydef@\xyvcrossneg{\xykcross@\xykcrossv + \xykunderstring@ \xykoverstring@ \xykhvobject@{+(0,-1)}} +\xydef@\xyhcrossneg{\xykcross@\xykcrossh + \xykunderstring@ \xykoverstring@ \xykhvobject@{+(1,0)}} +\xydef@\xyvuncross{\xykcross@\xykuncrossv + \xykoverstring@ \xykunderstring@ \xykhvobject@{+(0,-1)}} +\xydef@\xyhuncross{\xykcross@\xykuncrossh + \xykoverstring@ \xykunderstring@ \xykhvobject@{+(1,0)}} +{\xyuncatcodes \gdef\next#1#2#3#4#5#6#7#8#9{\save, + "^<",{\xykz_\ar #1@'{"_<"**{}?(.25)@+,?+(.375,0)@+, + "_>";"^>"**{}?-(.375,0)@+,?(.25)@+}"_>"#3#4#5}, + "_<",{\xykz^\ar #2@'{"^<"**{}?(.25)@+,?+(.375,0)@+, + "^>";"_>"**{}?-(.375,0)@+,?(.25)@+}"^>"#6#7#8} + \restore\POS #9}} +\xylet@\xykcrossv=\next +{\xyuncatcodes \gdef\next#1#2#3#4#5#6#7#8#9{\save, + "_<",{\xykz_\ar #1@'{"_>"**{}?(.25)@+,?+(0,.375)@+, + "^>";"^<"**{}?-(0,.375)@+,?(.25)@+}"^>"#3#4#5}, + "_>",{\xykz^\ar #2@'{"_<"**{}?(.25)@+,?+(0,.375)@+, + "^<";"^>"**{}?-(0,.375)@+,?(.25)@+}"^<"#6#7#8} + \restore\POS #9}} +\xylet@\xykcrossh=\next +{\xyuncatcodes \gdef\next#1#2#3#4#5#6#7#8#9{\save, + "^<",{\xykz^\ar #1@'{"_<"**{}?(.25)@+,?(.375)+(.375,0)@+, + "^>";"_>"**{}?(.375)-(.375,0)@+,?(.25)@+}"^>"#3#4#5}, + "_<",{\xykz^\ar #2@'{"^<"**{}?(.25)@+,?(.375)+(.375,0)@+, + "_>";"^>"**{}?(.375)-(.375,0)@+,?(.25)@+}"_>"#6#7#8} + \restore\POS #9}} +\xylet@\xykuncrossv=\next +{\xyuncatcodes \gdef\next#1#2#3#4#5#6#7#8#9{\save, + "_<",{\xykz^\ar #1@'{"_>"**{}?(.25)@+,?(.375)+(0,.375)@+, + "^<";"^>"**{}?(.375)-(0,.375)@+,?(.25)@+}"^<"#3#4#5}, + "_>",{\xykz^\ar #2@'{"_<"**{}?(.25)@+,?(.375)+(0,.375)@+, + "^>";"^<"**{}?(.375)-(0,.375)@+,?(.25)@+}"^>"#6#7#8} + \restore\POS #9}} +\xylet@\xykuncrossh=\next +\xydef@\vover{\begingroup\def\afterknot@{\xyvover}% + \def\xykprePLACE@{(.2)}\def\xykpostPLACE@{(.9)}% + \def\xykmidPLACE@{(.8)}\def\xykpostbreak@@{|(.725)\knothole}% + \xyFN@\xykparsecross@ }% +\xydef@\hover{\begingroup\def\afterknot@{\xyhover}% + \def\xykprePLACE@{(.2)}\def\xykpostPLACE@{(.9)}% + \def\xykmidPLACE@{(.8)}\def\xykpostbreak@@{|(.725)\knothole}% + \xyFN@\xykparsecross@ }% +\xydef@\vunder{\begingroup\def\afterknot@{\xyvunder}% + \def\xykprePLACE@{(.1)}\def\xykpostPLACE@{(.8)}% + \def\xykmidPLACE@{(.2)}\def\xykpostbreak@@{|(.275)\knothole}% + \xyFN@\xykparsecross@ }% +\xydef@\hunder{\begingroup\def\afterknot@{\xyhunder}% + \def\xykprePLACE@{(.1)}\def\xykpostPLACE@{(.8)}% + \def\xykmidPLACE@{(.2)}\def\xykpostbreak@@{|(.275)\knothole}% + \xyFN@\xykparsecross@ }% +\xydef@\vunover{\begingroup\def\afterknot@{\xyvunover}% + \def\xykprePLACE@{(.1)}\def\xykpostPLACE@{(.9)}% + \def\xykmidPLACE@{(.8)}\def\xykpostbreak@@{}% + \xyFN@\xykparsecross@ }% +\xydef@\hunover{\begingroup\def\afterknot@{\xyhunover}% + \def\xykprePLACE@{(.1)}\def\xykpostPLACE@{(.9)}% + \def\xykmidPLACE@{(.8)}\def\xykpostbreak@@{}% + \xyFN@\xykparsecross@ }% +\xydef@\xoverv{\begingroup\def\afterknot@{\xyxoverv}% + \def\xykprePLACE@{(.15)}\def\xykpostPLACE@{(.85)}% + \def\xykmidPLACE@{(.15)}\def\xykpostbreak@@{|\knothole}% + \xyFN@\xykparsecross@ }% +\xydef@\xunderv{\begingroup\def\afterknot@{\xyxunderv}% + \def\xykprePLACE@{(.15)}\def\xykpostPLACE@{(.85)}% + \def\xykmidPLACE@{(.15)}\def\xykpostbreak@@{|\knothole}% + \xyFN@\xykparsecross@ }% +\xydef@\xoverh{\begingroup\def\afterknot@{\xyxoverh}% + \def\xykprePLACE@{(.15)}\def\xykpostPLACE@{(.85)}% + \def\xykmidPLACE@{(.15)}\def\xykpostbreak@@{|\knothole}% + \xyFN@\xykparsecross@ }% +\xydef@\xunderh{\begingroup\def\afterknot@{\xyxunderh}% + \def\xykprePLACE@{(.15)}\def\xykpostPLACE@{(.85)}% + \def\xykmidPLACE@{(.85)}\def\xykpostbreak@@{|\knothole}% + \xyFN@\xykparsecross@ }% +\xydef@\xunover{\begingroup\def\afterknot@{\xyxunover}% + \def\xykprePLACE@{(.15)}\def\xykpostPLACE@{(.85)}% + \def\xykmidPLACE@{(.15)}\def\xykpostbreak@@{}% + \xyFN@\xykparsecross@ }% +\xydef@\xunoverv{\begingroup\def\afterknot@{\xyxunoverv}% + \def\xykprePLACE@{(.2)}\def\xykpostPLACE@{(.8)}% + \def\xykmidPLACE@{(.2)}\def\xykpostbreak@@{}% + \xyFN@\xykparsecross@ }% +\xydef@\xunoverh{\begingroup\def\afterknot@{\xyxunoverh}% + \def\xykprePLACE@{(.2)}\def\xykpostPLACE@{(.8)}% + \def\xykmidPLACE@{(.8)}\def\xykpostbreak@@{}% + \xyFN@\xykparsecross@ }% +\xydef@\xyvover{\xykcross@\xykoverv + \xykoverstring@ \xykunderstring@ \xykhvobject@{+(0,-1)}} +\xydef@\xyhover{\xykcross@\xykoverh + \xykoverstring@ \xykunderstring@ \xykhvobject@{+(1,0)}} +\xydef@\xyvunder{\xykcross@\xykoverv + \xykunderstring@ \xykoverstring@ \xykhvobject@{+(0,-1)}} +\xydef@\xyhunder{\xykcross@\xykoverh + \xykunderstring@ \xykoverstring@ \xykhvobject@{+(1,0)}} +\xydef@\xyvunover{\xykcross@\xykunoverv + \xykoverstring@ \xykunderstring@ \xykhvobject@{+(0,-1)}} +\xydef@\xyhunover{\xykcross@\xykunoverh + \xykoverstring@ \xykunderstring@ \xykhvobject@{+(1,0)}} +\xydef@\xyxoverv{\xykcross@\xykxoverv + \xykoverstring@ \xykunderstring@ \xykhvobject@{+(0,-1)}} +\xydef@\xyxunderv{\xykcross@\xykxoverv + \xykunderstring@ \xykoverstring@ \xykhvobject@{+(0,-1)}} +\xydef@\xyxoverh{\xykcross@\xykxoverh + \xykoverstring@ \xykunderstring@ \xykhvobject@{+(1,0)}} +\xydef@\xyxunderh{\xykcross@\xykxoverh + \xykunderstring@ \xykoverstring@ \xykhvobject@{+(1,0)}} +\xydef@\xyxunover{\xykcross@\xykxoverv + \xykoverstring@ \xykunderstring@ \xykhvobject@{+(1,0)}} +\xydef@\xyxunoverv{\xykcross@\xykxunoverv + \xykoverstring@ \xykunderstring@ \xykhvobject@{+(0,-1)}} +\xydef@\xyxunoverh{\xykcross@\xykxunoverh + \xykoverstring@ \xykunderstring@ \xykhvobject@{+(1,0)}} +{\xyuncatcodes \gdef\next#1#2#3#4#5#6#7#8#9{\save, + "^<",{\xykz^\ar #1@'{"^>"**{}?(.25)@+,?(.625)+(0,-.125)@+, + "_>";"^>"**{}?(.625)-(.125,0)@+,?(.25)@+}"_>"#3#4#5}, + "_<",{\xykz^\ar #2@'{"^<"**{}?(.25)@+,?(.625)+(.125,0)@+, + "^>";"^<"**{}?(.625)-(0,.125)@+,?(.25)@+}"^>"#6#7#8},\restore\POS#9}} +\xylet@\xykoverv=\next +{\xyuncatcodes \gdef\next#1#2#3#4#5#6#7#8#9{\save, + "_<",{\xykz^\ar #1@'{"^<"**{}?(.25)@+,?(.625)+(.125,0)@+, + "^>";"^<"**{}?(.625)-(0,.125)@+,?(.25)@+}"^>"#3#4#5}, + "_>",{\xykz^\ar #2@'{"_<"**{}?(.25)@+,?(.625)+(0,.125)@+, + "^<";"_<"**{}?(.625)+(.125,0)@+,?(.25)@+}"^<"#6#7#8},\restore\POS#9}} +\xylet@\xykoverh=\next +{\xyuncatcodes \gdef\next#1#2#3#4#5#6#7#8#9{\save, + "^<",{\xykz^\ar #1@'{"^>"**{}?(.25)@+,?-(0,.175)@+,?(.75)@+} + "^>"#3#4#5}, + "_<",{\xykz^\ar #2@'{"^<"**{}?(.25)@+,?+(.125,0)@+, + "_>"**{}?+(0,.7)@+,"_>";"^>"**{}?-(.125,0)@+,?(.25)@+} + "_>"#6#7#8},\restore\POS#9}} +\xylet@\xykunoverv=\next +{\xyuncatcodes \gdef\next#1#2#3#4#5#6#7#8#9{\save, + "_<",{\xykz^\ar #1@'{"^<"**{}?(.25)@+,?+(.175,0)@+,?(.75)@+} + "^<"#3#4#5}, + "_>",{\xykz^\ar #2@'{"_<"**{}?(.25)@+,?+(0,.125)@+, + "^>"**{}?-(.7,0)@+,"^>";"^<"**{}?-(0,.125)@+,?(.25)@+} + "^>"#6#7#8},\restore\POS#9}} +\xylet@\xykunoverh=\next +{\xyuncatcodes \gdef\next#1#2#3#4#5#6#7#8#9{\save, + "^<";"^>"**{}?="^_","_<";"_>"**{}?;"^_",**{}?="^_", + "^>",{\xykz^\ar #1@'{"^_"@+}"_<"#3#4#5}, + "^<",{\xykz_\ar #2@'{"^_"@+}"_>"#6#7#8},\restore\POS#9}} +\xylet@\xykxoverv=\next +{\xyuncatcodes \gdef\next#1#2#3#4#5#6#7#8#9{\save, + "^<";"_<"**{}?="^_","^>";"_>"**{}?;"^_",**{}?="^_", + "^<",{\xykz_\ar #1@'{"^_"@+}"_>"#3#4#5}, + "_<",{\xykz_\ar #2@'{"^_"@+}"^>"#6#7#8},\restore\POS#9}} +\xylet@\xykxoverh=\next +{\xyuncatcodes \gdef\next#1#2#3#4#5#6#7#8#9{\save, + "^<";"^>"**{}?="^_","_<";"_>"**{}?;"^_",**{}?="^_", + "^>",{\xykz^\ar #1@'{"^_"@+}"_>"#3#4#5}, + "^<",{\xykz^\ar #2@'{"^_"@+}"_<"#6#7#8},\restore\POS#9}} +\xylet@\xykxunoverv=\next +{\xyuncatcodes \gdef\next#1#2#3#4#5#6#7#8#9{\save, + "^<";"_<"**{}?="^_","^>";"_>"**{}?;"^_",**{}?="^_", + "^<",{\xykz^\ar #1@'{"^_"@+}"^>"#3#4#5}, + "_<",{\xykz^\ar #2@'{"^_"@+}"_>"#6#7#8}, + \restore\POS#9}} +\xylet@\xykxunoverh=\next +\xydef@\vtwist{\begingroup\def\afterknot@{\xyvtwist}% + \def\xykprePLACE@{(.1)}\def\xykpostPLACE@{(.9)}% + \def\xykmidPLACE@{(.9)}\def\xykpostbreak@@{|\knothole}% + \xyFN@\xykparsecross@ }% +\xydef@\htwist{\begingroup\def\afterknot@{\xyhtwist}% + \def\xykprePLACE@{(.1)}\def\xykpostPLACE@{(.9)}% + \def\xykmidPLACE@{(.9)}\def\xykpostbreak@@{|\knothole}% + \xyFN@\xykparsecross@ }% +\xydef@\vtwistneg{\begingroup\def\afterknot@{\xyvtwistneg}% + \def\xykprePLACE@{(.1)}\def\xykpostPLACE@{(.9)}% + \def\xykmidPLACE@{(.9)}\def\xykpostbreak@@{|\knothole}% + \xyFN@\xykparsecross@ }% +\xydef@\htwistneg{\begingroup\def\afterknot@{\xyhtwistneg}% + \def\xykprePLACE@{(.1)}\def\xykpostPLACE@{(.9)}% + \def\xykmidPLACE@{(.9)}\def\xykpostbreak@@{|\knothole}% + \xyFN@\xykparsecross@ }% +\xydef@\vuntwist{\begingroup\def\afterknot@{\xyvuntwist}% + \def\xykprePLACE@{(.15)}\def\xykpostPLACE@{(.85)}% + \def\xykmidPLACE@{(.85)}\def\xykpostbreak@@{}% + \xyFN@\xykparsecross@ }% +\xydef@\huntwist{\begingroup\def\afterknot@{\xyhuntwist}% + \def\xykprePLACE@{(.15)}\def\xykpostPLACE@{(.85)}% + \def\xykmidPLACE@{(.85)}\def\xykpostbreak@@{}% + \xyFN@\xykparsecross@ }% +\xydef@\xyvtwist{\xykcross@\xyktwistv + \xykoverstring@ \xykunderstring@ \xykhvobject@{+(0,-1)}} +\xydef@\xyvtwistneg{\xykcross@\xyktwistv + \xykunderstring@ \xykoverstring@ \xykhvobject@{+(0,-1)}} +\xydef@\xyvuntwist{\xykcross@\xykuntwistv + \xykoverstring@ \xykunderstring@ \xykhvobject@{+(0,-1)}} +\xydef@\xyhtwist{\xykcross@\xyktwisth + \xykoverstring@ \xykunderstring@ \xykhvobject@{+(1,0)}} +\xydef@\xyhuntwist{\xykcross@\xykuntwisth + \xykoverstring@ \xykunderstring@ \xykhvobject@{+(1,0)}} +\xydef@\xyhtwistneg{\xykcross@\xyktwisth + \xykunderstring@ \xykoverstring@ \xykhvobject@{+(1,0)}} +{\xyuncatcodes \gdef\next#1#2#3#4#5#6#7#8#9{\save, + "^>",{\xykz_\ar #1@'{"_>"**{}?(.25)@+,?-(.375,0)@+, + "_<";"^<"**{}?+(.375,0)@+,?(.25)@+}"_<"#3#4#5}, + "^<",{\xykz^\ar #2@'{"_<"**{}?(.25)@+,?+(.375,0)@+, + "_>";"^>"**{}?+(-.375,0)@+,?(.25)@+}"_>"#6#7#8} + \restore\POS #9}} +\xylet@\xyktwistv=\next +{\xyuncatcodes \gdef\next#1#2#3#4#5#6#7#8#9{\save, + "^>",{\xykz^\ar #1@'{"_>"**{}?(.125)@+,?(.375)-(.25,0)@+, + ?(.625)-(.25,0)@+,?(.875)@+}"_>"#3#4#5}, + "^<",{\xykz^\ar #2@'{"_<"**{}?(.125)@+,?(.375)+(.25,0)@+, + ?(.625)+(.25,0)@+,?(.875)@+}"_<"#6#7#8} + \restore\POS #9}} +\xylet@\xykuntwistv=\next +{\xyuncatcodes \gdef\next#1#2#3#4#5#6#7#8#9{\save, + "^<",{\xykz_\ar #1@'{"^>"**{}?(.25)@+,?+(0,-.375)@+, + "_>";"_<"**{}?+(0,.375)@+,?(.25)@+}"_>"#3#4#5}, + "_<",{\xykz^\ar #2@'{"_>"**{}?(.25)@+,?+(0,.375)@+, + "^>";"^<"**{}?-(0,.375)@+,?(.25)@+}"^>"#6#7#8} + \restore\POS #9}} +\xylet@\xyktwisth=\next +{\xyuncatcodes \gdef\next#1#2#3#4#5#6#7#8#9{\save, + "^<",{\xykz^\ar #1@'{"^>",**{}?(.125)@+,?(.375)+(0,-.25)@+, + ?(.625)+(0,-.25)@+,?(.875)@+}"^>"#3#4#5}, + "_<",{\xykz^\ar #2@'{"_>",**{}?(.125)@+,?(.375)+(0,.25)@+, + ?(.625)+(0,.25)@+,?(.875)@+}"_>"#6#7#8},\restore\POS #9}} +\xylet@\xykuntwisth=\next +\xydef@\xykparsescale@{% + \ifx\space@\next \expandafter\DN@\space{\xyFN@\xykparsescale@}% + \else\addDASH@\ifx\next \addDASH@\DN@{\def\xykSCALE@@{-1}% + \xyFN@\xykparser@}% + \else\ifx[\next \DN@[##1]{\dimen@=##1\p@ + \ifdim\dimen@=\z@\xywarning@{\xykscaleerror@}% + \else\edef\xykSCALE@@{\expandafter\removePT@\the\dimen@}\fi + \xyFN@\xykparser@}% + \else\ifx~\next \DN@~##1##2##3##4{% + \def\xykSCALE@@{@{##1}{##2}{##3}{##4}}\xyFN@\xykparser@}% + \else\DN@{\xyFN@\xykparser@}% + \fi\fi\fi\fi \next@} +\xydef@\xykscaleerror@{Ignoring zero scale factor} +\xydef@\xykhobject@{\aftergroup\xykhadjust@ + \ifx\xykSCALE@@\empty\DN@{\xykkeepscale@}% + \else \DN@{\xyksavescale@{}}% + \fi \next@ } +\xydef@\xykvobject@{\aftergroup\xykvadjust@ + \ifx\xykSCALE@@\empty\DN@{\xykkeepscale@}% + \else \DN@{\xyksavescale@{}}% + \fi \next@ } +\xydef@\xykhvobject@{\aftergroup\xykhvadjust@ + \ifx\xykSCALE@@\empty\DN@{\xykkeepscale@}% + \else \DN@{\xyksavescale@{}}% + \fi \next@ } +\xydef@\xykhuobject@{\aftergroup\xykhuadjust@ + \ifx\xykSCALE@@\empty\DN@{\xykkeepscale@}% + \else \DN@{\xyksavescale@{}}% + \fi \next@ } +\xydef@\xyksavescale@#1#2{% + \expandafter\ifx\the\Edge@c\zeroEdge\relax \def\xyksaveEdgec{}% + \else + \edef\xyksaveEdgec{\noexpand\Edge@c={\expandafter\noexpand\the\Edge@c}% + \L@c=\the\L@c \R@c=\the\R@c \D@c=\the\D@c \U@c=\the\U@c}% + \fi + \edef\next@##1##2{\endgroup + \def\noexpand\xyksaveEdgec{}% + \def\noexpand\xykSCALE@@\noexpand{##1}% + \def\noexpand\xykjoincontrol\noexpand{\xykjoincontrol}% + \noexpand\toks@\noexpand{##2}% + \noexpand\xy@@{\def\noexpand\xyksaveEdgec{}% + \def\noexpand\xykSCALE@@{##1}% + \def\noexpand\xykjoincontrol{\xykjoincontrol}}}% + \expandafter\expandafter\expandafter\next@ + \expandafter\expandafter\expandafter{\expandafter\xykSCALE@@\expandafter}% + \expandafter{\the\toks@}% + \xykrescale@ #1\the\toks@\restore\POS#2} +\xydef@\xykkeepscale@{% + \edef\next@##1{\endgroup \noexpand\toks@={##1}% + \def\noexpand\xykjoincontrol{\xykjoincontrol}}% + \expandafter\next@\expandafter{\the\toks@}% + \def\xykSCALE@@{}\def\xyksaveEdgec{}% + \xy@@{\def\xykSCALE@@{}\def\xyksaveEdgec{}}% + \edef\next@{\def\noexpand\xykjoincontrol{\xykjoincontrol}}% + \expandafter\xy@@\expandafter{\next@}% + \xyknoflexscale@ \the\toks@} +\xydef@\xykrescale@{\expandafter\xykcheckscale@\xykSCALE@@ !}% +\xydef@\xykcheckscale@#1#2!{% + \expandafter\DN@\expandafter{\codeof{#1}}% + \expandafter\DNii@\expandafter{\codeof{@}}% + \ifx\next@\nextii@\relax\DN@{\xykflexiscale@#2% + \xy@@{\divide\X@xbase2\divide\X@ybase2\divide\Y@xbase2\divide\Y@ybase2% + \def\xykSCALE@@{}}\def\xykSCALE@@{}% + \expandafter\toks@\expandafter{\afterFLEX@}}% + \else\DN@{\save \xykrescale@@}\fi \next@ } +\xydef@\xykflexiscale@{% + \expandafter\def\expandafter\afterFLEX@\expandafter{\the\toks@}% + \xykflexiscale@@ } +\xydef@\xykrescale@@{% + \edef\next@{\X@xbase=\xykSCALE@@\X@xbase \X@ybase=\xykSCALE@@\X@ybase + \Y@xbase=\xykSCALE@@\Y@xbase \Y@ybase=\xykSCALE@@\Y@ybase}% + \expandafter\xy@@\expandafter{\next@}% + \ifdim\xykSCALE@@\p@<\z@\relax \DN@{\xyknegflexscale@}% + \else\DN@{\xyknoflexscale@}\fi \next@ } +{\xyuncatcodes \gdef\next#1#2#3#4{\save="@", + #1,="^<",\POS"@",#2,="^>",\POS"@",#3,="_<",\POS"@",#4,="_>", + (0,0);"^>"-"^<"+"_>"-"_<":"^<"-"_<"+"^>"-"_>"::}} +\xylet@\xykflexiscale@@=\next +{\xyuncatcodes \gdef\next{\save ="^<", + +(1,0)="^>",-(1,1)="_<",+(1,0)="_>"\restore }} +\xylet@\xyknoflexscale@@=\next +\xylet@\xyknoflexscale@=\next +{\xyuncatcodes \gdef\next{\save ="_>", + +(-1,1)="^<",+(1,0)="^>",-(1,1)="_<"\restore }} +\xylet@\xyknegflexscale@@=\next +\xylet@\xyknegflexscale@=\next +{\xyuncatcodes \gdef\next{\save ="_<", + +(1,0)="_>",+(-1,1)="^<",+(1,0)="^>"\restore }} +\xylet@\xykhscale@@=\next +{\xyuncatcodes \gdef\next{\save ="^>", + -(1,0)="^<",+(1,-1)="_>",-(1,0)="_<"\restore }} +\xylet@\xykvscale@@=\next +\xydef@\xykhadjust@{% + \let\xyknoflexscale@=\xykhscale@@ + \let\xyknegflexscale@=\xyknegflexscale@@ } +\xydef@\xykvadjust@{% + \let\xyknoflexscale@=\xyknoflexscale@@ + \let\xyknegflexscale@=\xykhscale@@ } +\xydef@\xykhvadjust@{% + \let\xyknoflexscale@=\xyknoflexscale@@ + \let\xyknegflexscale@=\xyknegflexscale@@ } +\xydef@\xykhuadjust@{% + \let\xyknoflexscale@=\xykhscale@@ + \let\xyknegflexscale@=\xykvscale@@ } +\xydef@\xykprebreak@{% + \ifx\xykprebreak@@\empty\addtotoks@{{}}\else + \expandafter\addtotoks@\expandafter{\expandafter{\xykprebreak@@}}\fi} +\xydef@\xykpostbreak@{% + \ifx\xykpostbreak@@\empty\addtotoks@{{}}\else + \expandafter\addtotoks@\expandafter{\expandafter{\xykpostbreak@@}}\fi} +\xydef@\xykmidbreak@{% + \ifx\xykmidbreak@@\empty\addtotoks@{{}}\else + \expandafter\addtotoks@\expandafter{\expandafter{\xykmidbreak@@}}\fi} +\xydef@\xykparsebreak@{% + \ifx\space@\next \expandafter\DN@\space{\xyFN@\xykparsebreak@}% + \else \addLT@\ifx\next + \expandafter\appendtoholder@\xykbacktemp@\next@ + \addLT@\DN@{\xyFN@\xykparser@}% + \else \addGT@\ifx\next + \expandafter\appendtoholder@\xykforetemp@\next@ + \addGT@\DN@{\xyFN@\xykparser@}% + \else \ifx|\next + \expandafter\appendtoholer@\xyknulltemp@\next@ + \DN@|{\xyFN@\xykparser@}% + \else \ifx\next \bgroup\DN@##1{\checkgroupbreak@##1@}% + \else \ifx (\next\DN@(##1){\xyadjustknotPLACE@i##1@@% + \xyFN@\xykparsebreak@}% + \else \ifx\next \knothole@\DN@##1{\expandafter\appendtoholder@@ + \expandafter{\expandafter|\xyknotPLACE\knothole}\next@ + \xyFN@\xykparser@}% + \else + \expandafter\xykdefaultbreak@\xykbreak@\next@ + \DN@{\xyFN@\xykparser@}% + \fi\fi\fi\fi\fi\fi\fi \next@ } +{\xyuncatcodes \gdef\next{^>*\dir{>}}} +\xylet@\xykforetips@=\next +{\xyuncatcodes \gdef\next{^<*\dir{<}}} +\xylet@\xykbacktips@=\next +{\xyuncatcodes \gdef\next{*!/-1pt/=0\dir{>}}} +\xylet@\xykforetemp@=\next +{\xyuncatcodes \gdef\next{*!/1pt/=0\dir{<}}} +\xylet@\xykbacktemp@=\next +{\xyuncatcodes \gdef\next{*=<\xykholesize>[o]{}}} +\xylet@\xykholetemp@=\next +\xydef@\knothole@{\hbox to\xykholesize{% + \dimen@=\xykholesize \divide\dimen@\tw@ + \hfill \vrule height\dimen@ depth\dimen@ width\z@ }} +\xylet@\knothole=\knothole@ +\xylet@\khole=\knothole@ +{\xyuncatcodes \gdef\next{*=<0pt>{}}} +\xylet@\xyknulltemp@=\next +\xylet@\xykbreak@=\xyknulltemp@ +\xydef@\checkgroupbreak@#1#2@{% + \ifx|#1\DN@{\appendtoholder@@#1#2\next@ \xyFN@\xykparser@}% + \else \ifx_#1\DN@{\appendtoholder@@_#2\next@ \xyFN@\xykparser@}% + \else \ifx^#1\DN@{\appendtoholder@@^#2\next@ \xyFN@\xykparser@}% + \else + \def\next##1\next{\expandafter\DNii@\expandafter{\xyk@@##1}}% + \expandafter\next\xyknotPLACE\next + \ifx*#1% + \expandafter\DN@\expandafter{% + \expandafter\appendtoholder@@\nextii@#1#2\next@ \xyFN@\xykparser@}% + \else + \expandafter\DN@\expandafter{% + \expandafter\appendtoholder@@\nextii@{#1#2}\next@ \xyFN@\xykparser@}% + \fi\fi\fi\fi \next@ } +{\xyuncatcodes \gdef\next{% + \expandafter{\expandafter^\xyknotPLACE##1}}}% + \DN@{\xydef@\xykholder@@##1}\DNii@{\expandafter\toks@}% + \expandafter\expandafter\expandafter\next@ + \expandafter\expandafter\expandafter{\expandafter\nextii@\next} +\xydef@\appendtoholder@#1\next@{\xykholder@@{#1}% + \DN@##1{\expandafter\DN@\expandafter{\xykholder@##1}}% + \expandafter\next@\expandafter{\the\toks@}\appendtoholder@@@ } +\xydef@\appendtoholder@@#1\next@{% + \DN@##1\next@{\expandafter\DN@\expandafter{\xykholder@##1}}% + \next@#1\next@ \appendtoholder@@@}% +\xydef@\appendtoholder@@@{% + \expandafter\expandafter\expandafter\DN@ + \expandafter\expandafter\expandafter{\next@}% + \DNii@{\expandafter\def\xykholder@}% + \expandafter\nextii@\expandafter{\next@}} +{\xyuncatcodes \gdef\next{% + \expandafter{\expandafter|\xyknotPLACE##1}}}% +\DN@{\xydef@\xykholer@@##1}\DNii@{\expandafter\toks@}% + \expandafter\expandafter\expandafter\next@ + \expandafter\expandafter\expandafter{\expandafter\nextii@\next} +\xydef@\appendtoholer@#1\next@{\xykholer@@{#1}% + \DN@##1{\expandafter\DN@\expandafter{\xykholder@##1}}% + \expandafter\next@\expandafter{\the\toks@}\appendtoholder@@@ } +\xydef@\xykz#1{\let\xyk@@=#1\xy@@{\let\xyk@@=#1}} +{\xyuncatcodes \global\let\next=_} +\xylet@\xyk@@=\next +\xydef@\xyadjustknotPLACE@i{% + \ifx\xyknotPLACE\empty\DN@{\dimen@=.5\p@}% + \else\DN@{\expandafter\xygetknotPLACE@@\xyknotPLACE}% + \fi \next@ \relax \let\xywhichknotPLACE@@=\xysetknotPLACE@@ + \xyFN@\xyadjustknotPLACE@} +\xydef@\xyadjustknotPLACE@{\expandafter\ifx\space@\next + \expandafter\DN@\space{\xyFN@\xyadjustknotPLACE@}% + \else\addDASH@\ifx\next\DN@{\xyadjustknotPLACE@@}% + \else\addPLUS@\ifx\next\DN@{\xyadjustknotPLACE@@}% + \else\addEQ@\ifx\next\addEQ@\DN@{\dimen@=\z@ \xyadjustknotPLACE@@}% + \else \DN@{\dimen@=\z@ \xyadjustknotPLACE@@}% + \fi\fi\fi\fi \next@} +\xydef@\xyadjustknotPLACE@@#1@@{\advance\dimen@#1\p@ + \expandafter\xysetknotPLACE@\expandafter{\the\dimen@}} +\xydef@\xysetknotPLACE@#1{% + \expandafter\xywhichknotPLACE@@\expandafter{\removePT@#1}} +{\xyuncatcodes\gdef\next#1{\def\xyknotPLACE{(#1)}}}% +\xylet@\xysetknotPLACE@@=\next +{\xyuncatcodes \catcode`@=11 + \gdef\next(#1){\DN@\next@{#1}\ifx\next@\empty + \dimen@=\z@\else\dimen@=#1\p@ \fi}}% +\xylet@\xygetknotPLACE@@=\next +\xydef@\xyadjustJOIN@i{% + \ifx\xykjoincontrol\empty\DN@{\dimen@=.75\p@}% + \else\DN@{\expandafter\xygetknotPLACE@@\expandafter(\xykjoincontrol)}% + \fi \next@ \relax \let\xywhichknotPLACE@@=\xysetjoincontrol@ + \xyFN@\xyadjustknotPLACE@} +\xydef@\xyadjustBREAK@i{% + \ifx\xykpostbreak@@\empty\DN@{\dimen@=.5\p@}% + \else\DN@{\expandafter\xygetpostBREAK@\xykpostbreak@@}% + \fi \next@ \relax \let\xywhichknotPLACE@@=\xysetpostbreak@ + \xyFN@\xyadjustknotPLACE@} +\xydef@\xygetpostBREAK@|#1\knothole{\DN@{#1}% + \ifx\next@\empty\dimen@=.5\p@\else \xygetknotPLACE@@#1\fi} +\xydef@\xysetpostbreak@#1{\def\xykpostbreak@@{|(#1)\knothole}} +\xydef@\xysetjoincontrol@#1{\edef\xykjoincontrol{#1}} +\xydef@\xykparsetips@{% + \def\xyknotTIPS@@{}\def\xyknotPLACE{}% + \let\xykparser@=\xykparsetips@@ + \xyFN@\xykparser@ } +\xydef@\xykparsetips@@{% + \ifx\space@\next \expandafter\DN@\space{\xyFN@\xykparsetips@@}% + \else\addLT@\ifx\next + \ifx\xyknotTIPS@@\empty \def\xyknotTIPS@@{TF}% + \else\DN@{FF}\ifx\next@\xyknotTIPS@@ \def\xyknotTIPS@@{TF}% + \else\DN@{FT}\ifx\next@\xyknotTIPS@@ \def\xyknotTIPS@@{TT}% + \fi\fi\fi + \addLT@\DN@{\xyFN@\xykparser@}% + \else\addGT@\ifx\next + \ifx\xyknotTIPS@@\empty \def\xyknotTIPS@@{FT}% + \else\DN@{FF}\ifx\next@\xyknotTIPS@@ \def\xyknotTIPS@@{FT}% + \else\DN@{TF}\ifx\next@\xyknotTIPS@@ \def\xyknotTIPS@@{TT}% + \fi\fi\fi + \addGT@\DN@{\xyFN@\xykparser@}% + \else\addEQ@\ifx\next \def\xyknotTIPS@@{TT}% + \addEQ@\DN@{\xyFN@\xykparser@}% + \else \ifx!\next \def\xyknotTIPS@@{FF}\DN@!{\xyFN@\xykparser@}% + \else\DN@{\xyFN@\xykparser@}% + \fi\fi\fi\fi\fi \next@ } +\xydef@\xykcheckTIPS@{% + \ifx\xyknotTIPS@@\empty \edef\xyknotTIPS@@{\xyknotTIPS@}\fi + \DN@{FF}\ifx\next@\xyknotTIPS@@\def\tmp@{}% + \else\DN@{FT}\ifx\next@\xyknotTIPS@@ + \expandafter\def\expandafter\tmp@\expandafter{\xykforetips@}% + \else\DN@{TF}\ifx\next@\xyknotTIPS@@ + \expandafter\def\expandafter\tmp@\expandafter{\xykbacktips@}% + \else + \DN@##1\next@{\DN@{\xykforetips@##1}}% + \expandafter\next@\xykbacktips@\next@ + \DNii@{\expandafter\def\expandafter\tmp@\expandafter}% + \expandafter\nextii@\expandafter{\next@}% + \fi\fi\fi \def\xyknotTIPS@@{}} +\xydef@\xyknottips@{% + \ifx\tmp@\empty\addtotoks@{{}}\else + \expandafter\addtotoks@\expandafter{\expandafter{\tmp@}}\fi} +\xydef@\xykparsejoin@{% + \def\xykSCALE@@{}% + \edef\xyknotPLACE{\xykmidPLACE@}% + \let\xykparser@=\xykparsejoin@@ + \def\xykdefaultbreak@{\let\xykbreak@=\xykforetemp@ + \def\xyknotPLACE{(.5)}\appendtoholder@}% + \xyFN@\xykparsescale@ } +{\xyuncatcodes \catcode`@=11 +\gdef\next{% + \ifx\space@\next \expandafter\DN@\space{\xyFN@\xykparsejoin@@}% + \else\addLT@\ifx\next \let\xykbreak@=\xykbacktemp@ + \def\xykdefaultbreak@{\def\xyknotPLACE{(.5)}% + \appendtoholder@}\addLT@\DN@{\xyprecross@}% + \else\addGT@\ifx\next \let\xykbreak@=\xykforetemp@ + \def\xykdefaultbreak@{\def\xyknotPLACE{(.5)}% + \appendtoholder@}\addGT@\DN@{\xypostcross@}% + \else\ifx|\next \let\xykbreak@=\xyknulltemp@ + \def\xykdefaultbreak@{\def\xyknotPLACE{(.5)}% + \appendtoholer@}\DN@|{\xymidcross@}% + \else\addEQ@\ifx\next \addEQ@\DN@{\xyFN@\xykparsetips@@}% + \else\addAT@\ifx\next \addAT@\DN@(##1){% + \xyadjustJOIN@i##1@@\xyFN@\xykparsejoin@@}% + \else\DN@{\afterknot@}% + \fi\fi\fi\fi\fi\fi \next@ }} +\xylet@\xykparsejoin@@=\next +\xydef@\xykjoincontrol@@{.75}% +\xydef@\xyk@joincontrol@#1{\DN@{#1}% + \ifx\next@\empty\edef\xykjoincontrol@@{.75}% + \else\dimen@=#1\p@ + \edef\xykjoincontrol@@{\expandafter\removePT@\the\dimen@}\fi} +\xylet@\xykjoincontrol\empty +\xydef@\xykjoincontrol@(#1){\DN@{#1}% + \ifx\next@\empty\edef\xykjoincontrol{\xykjoincontrol@@}% + \else\dimen@=#1\p@ + \edef\xykjoincontrol{\expandafter\removePT@\the\dimen@}% + \fi \xyFN@\xykparsejoin@@ } +\xydef@\xykjoincontrol@i#1{\DN@{#1}% + \ifx\next@\empty\edef\xykjoincontrol{\xykjoincontrol@@}% + \else\dimen@=#1\p@ + \edef\xykjoincontrol{\expandafter\removePT@\the\dimen@}\fi} +\xydef@\xykjoin@#1{% + \expandafter\toks@\expandafter{\expandafter#1\knotSTYLE}} +\xydef@\xyksetjoin@{\xykcheckTIPS@ + \xykprebreak@ \xykmidbreak@ \xykpostbreak@ \xyknottips@ } +\xydef@\hcap{\begingroup\def\afterknot@{\xyhcap}% + \def\xykprePLACE@{(.385)}\def\xykpostPLACE@{(.615)}% + \def\xykmidPLACE@{(.5)}\edef\xykjoincontrol{.25}% + \xyFN@\xykparsejoin@ }% +\xydef@\vcap{\begingroup\def\afterknot@{\xyvcap}% + \def\xykprePLACE@{(.385)}\def\xykpostPLACE@{(.615)}% + \def\xykmidPLACE@{(.5)}\edef\xykjoincontrol{.25}% + \xyFN@\xykparsejoin@ }% +\xydef@\xcapv{\begingroup\def\afterknot@{\xyxcapv}% + \def\xykprePLACE@{(.2)}\def\xykpostPLACE@{(.8)}% + \def\xykmidPLACE@{(.5)}\edef\xykjoincontrol{.5}% + \xyFN@\xykparsejoin@ }% +\xydef@\xcaph{\begingroup\def\afterknot@{\xyxcaph}% + \def\xykprePLACE@{(.2)}\def\xykpostPLACE@{(.8)}% + \def\xykmidPLACE@{(.5)}\edef\xykjoincontrol{.5}% + \xyFN@\xykparsejoin@ }% +\xydef@\xyvcap{\xykjoin@\xykcapv \xyksetjoin@ \xykhobject@{}} +\xydef@\xyhcap{\xykjoin@\xykcaph \xyksetjoin@ \xykvobject@{}} +\xydef@\xyxcapv{\xykjoin@\xykxcapv \xyksetjoin@ \xykvobject@{+(0,-1)}} +\xydef@\xyxcaph{\xykjoin@\xykxcaph \xyksetjoin@ \xykhobject@{+(1,0)}} +{\xyuncatcodes \gdef\next#1#2#3#4#5#6#7{\save, + "_>",{\xyksaveEdgec},{\xykz_\ar #1@'{"^>"**{}?(\xykjoincontrol)@+ + ,?-(.25,0)@+,"_<";"^<"**{}?+(.25,0)@+,?(\xykjoincontrol)@+} + "_<"#3#4#5#6},\restore \POS#7}} +\xylet@\xykcapv=\next +{\xyuncatcodes \gdef\next#1#2#3#4#5#6#7{\save, + "_<",{\xyksaveEdgec},{\xykz_\ar #1@'{"_>"**{}?(\xykjoincontrol)@+, + ?+(0,.25)@+,"^<";"^>"**{}?-(0,.25)@+,?(\xykjoincontrol)@+} + "^<"#3#4#5#6} + \restore \POS#7}} +\xylet@\xykcaph=\next +{\xyuncatcodes \gdef\next#1#2#3#4#5#6#7{\save, + "^>";"_>"**{}?="^_","^<";"_<"**{}?;"^_",**{}?(\xykjoincontrol)="^_", + "_<",{\xyksaveEdgec},{\xykz_\ar #1@'{"^_"@+} + "^<"#3#4#5#6},\restore \POS#7}} +\xylet@\xykxcapv=\next +{\xyuncatcodes \gdef\next#1#2#3#4#5#6#7{\save, + "^<";"^>"**{}?="^_","_<";"_>"**{}?;"^_",**{}?(\xykjoincontrol)="^_", + "_>",{\xyksaveEdgec},{\xykz_\ar #1@'{"^_"@+} + "_<"#3#4#5#6},\restore \POS#7}} +\xylet@\xykxcaph=\next +\xydef@\hloop{\begingroup\def\afterknot@{\xyhloop}% + \def\xykprePLACE@{(.07)}\def\xykpostPLACE@{(.93)}% + \def\xykmidPLACE@{(.5)}\edef\xykjoincontrol{.75}% + \xyFN@\xykparsejoin@ }% +\xydef@\vloop{\begingroup\def\afterknot@{\xyvloop}% + \def\xykprePLACE@{(.07)}\def\xykpostPLACE@{(.93)}% + \def\xykmidPLACE@{(.5)}\edef\xykjoincontrol{.75}% + \xyFN@\xykparsejoin@ }% +\xydef@\xyvloop{\xykjoin@\xykloopv \xyksetjoin@ \xykhobject@{}} +\xydef@\xyhloop{\xykjoin@\xyklooph \xyksetjoin@ \xykvobject@{}} +{\xyuncatcodes \gdef\next#1#2#3#4#5#6#7{\save, + "_>",{\xykz_\ar #1@'{"^>"**{}?(\xykjoincontrol)@+,?(1.25)-(.25,0)@+, + "_<";"^<"**{}?(1.25)+(.25,0)@+,?(\xykjoincontrol)@+}"_<"#3#4#5#6} + \restore \POS#7}} +\xylet@\xykloopv=\next +{\xyuncatcodes \gdef\next#1#2#3#4#5#6#7{\save, + "_<",{\xykz_\ar #1@'{"_>"**{}?(\xykjoincontrol)@+,?(1.25)+(0,.25)@+, + "^<";"^>"**{}?(1.25)+(0,-.25)@+,?(\xykjoincontrol)@+}"^<"#3#4#5#6} + \restore \POS#7}} +\xylet@\xyklooph=\next +\xydef@\zbendh{\begingroup\def\afterknot@{\xyzbendh}% + \def\xykprePLACE@{(.25)}\def\xykpostPLACE@{(.75)}% + \def\xykmidPLACE@{(.5)}\edef\xykjoincontrol{\xykjoincontrol@@}% + \xyFN@\xykparsejoin@ }% +\xydef@\sbendv{\begingroup\def\afterknot@{\xysbendv}% + \def\xykprePLACE@{(.25)}\def\xykpostPLACE@{(.75)}% + \def\xykmidPLACE@{(.5)}\edef\xykjoincontrol{\xykjoincontrol@@}% + \xyFN@\xykparsejoin@ }% +\xydef@\sbendh{\begingroup\def\afterknot@{\xysbendh}% + \def\xykprePLACE@{(.25)}\def\xykpostPLACE@{(.75)}% + \def\xykmidPLACE@{(.5)}\edef\xykjoincontrol{\xykjoincontrol@@}% + \xyFN@\xykparsejoin@ }% +\xydef@\zbendv{\begingroup\def\afterknot@{\xyzbendv}% + \def\xykprePLACE@{(.25)}\def\xykpostPLACE@{(.75)}% + \def\xykmidPLACE@{(.5)}\edef\xykjoincontrol{\xykjoincontrol@@}% + \xyFN@\xykparsejoin@ }% +\xydef@\xbendr{\begingroup\def\afterknot@{\xyxbendr}% + \def\xykprePLACE@{(.15)}\def\xykpostPLACE@{(.75)}% + \def\xykmidPLACE@{(.5)}\edef\xykjoincontrol{.5}% + \xyFN@\xykparsejoin@ }% +\xydef@\xbendl{\begingroup\def\afterknot@{\xyxbendl}% + \def\xykprePLACE@{(.15)}\def\xykpostPLACE@{(.75)}% + \def\xykmidPLACE@{(.5)}\edef\xykjoincontrol{.5}% + \xyFN@\xykparsejoin@ }% +\xydef@\xbendu{\begingroup\def\afterknot@{\xyxbendu}% + \def\xykprePLACE@{(.15)}\def\xykpostPLACE@{(.75)}% + \def\xykmidPLACE@{(.5)}\edef\xykjoincontrol{.5}% + \xyFN@\xykparsejoin@ }% +\xydef@\xbendd{\begingroup\def\afterknot@{\xyxbendd}% + \def\xykprePLACE@{(.15)}\def\xykpostPLACE@{(.75)}% + \def\xykmidPLACE@{(.5)}\edef\xykjoincontrol{.5}% + \xyFN@\xykparsejoin@ }% +\xydef@\xyzbendh{\xykjoin@\xykzbendh \xyksetjoin@ \xykhvobject@{+(1,-1)}} +\xydef@\xysbendv{\xykjoin@\xyksbendv \xyksetjoin@ \xykhvobject@{+(1,-1)}} +\xydef@\xysbendh{\xykjoin@\xyksbendh \xyksetjoin@ \xykhuobject@{+(1,1)}} +\xydef@\xyzbendv{\xykjoin@\xykzbendv \xyksetjoin@ \xykhuobject@{+(1,1)}} +\xydef@\xyxbendr{\xykjoin@\xykxbendr \xyksetjoin@ \xykhvobject@{+(1,-1)}} +\xydef@\xyxbendl{\xykjoin@\xykxbendl \xyksetjoin@ \xykhvobject@{+(0,-1)}} +\xydef@\xyxbendu{\xykjoin@\xykxbendu \xyksetjoin@ \xykhvobject@{+(1,0)}} +\xydef@\xyxbendd{\xykjoin@\xykxbendd \xyksetjoin@ \xykhvobject@{+(1,-1)}} +{\xyuncatcodes \gdef\next#1#2#3#4#5#6#7{\save, + "^<",{\xyksaveEdgec}, + {\xykz^\ar #1@'{"^>"**{}?(\xykjoincontrol)@+, + "_>";"_<"**{}?(\xykjoincontrol)@+}"_>"#3#4#5#6}% + \restore \POS#7}} +\xylet@\xykzbendh=\next +{\xyuncatcodes \gdef\next#1#2#3#4#5#6#7{\save, + "^<",{\xyksaveEdgec}, + {\xykz_\ar #1@'{"_<"**{}?(\xykjoincontrol)@+, + "_>";"^>"**{}?(\xykjoincontrol)@+}"_>"#3#4#5#6}% + \restore \POS#7}} +\xylet@\xyksbendv=\next +{\xyuncatcodes \gdef\next#1#2#3#4#5#6#7{\save, + "_<",{\xyksaveEdgec}, + {\xykz_\ar #1@'{"_>"**{}?(\xykjoincontrol)@+, + "^>";"^<"**{}?(\xykjoincontrol)@+}"^>"#3#4#5#6}% + \restore \POS#7}} +\xylet@\xyksbendh=\next +{\xyuncatcodes \gdef\next#1#2#3#4#5#6#7{\save, + "_<",{\xyksaveEdgec}, + {\xykz^\ar #1@'{"^<"**{}?(\xykjoincontrol)@+, + "^>";"_>"**{}?(\xykjoincontrol)@+}"^>"#3#4#5#6}% + \restore \POS#7}} +\xylet@\xykzbendv=\next +{\xyuncatcodes \gdef\next#1#2#3#4#5#6#7{\save, + "^<"-(0,.5),{\xyksaveEdgec}, + {\xykz_\ar #1@'{"_<";"_>"**{}?(\xykjoincontrol)@+,}"_>"#3#4#5#6}% + \restore \POS#7}} +\xylet@\xykxbendr=\next +{\xyuncatcodes \gdef\next#1#2#3#4#5#6#7{\save, + "^>"-(0,.5),{\xyksaveEdgec}, + {\xykz^\ar #1@'{"_>";"_<"**{}?(\xykjoincontrol)@+,}"_<"#3#4#5#6}% + \restore \POS#7}} +\xylet@\xykxbendl=\next +{\xyuncatcodes \gdef\next#1#2#3#4#5#6#7{\save, + "_<"+(.5,0),{\xyksaveEdgec}, + {\xykz_\ar #1@'{"_>";"^>"**{}?(\xykjoincontrol)@+,}"^>"#3#4#5#6}% + \restore \POS#7}} +\xylet@\xykxbendu=\next +{\xyuncatcodes \gdef\next#1#2#3#4#5#6#7{\save, + "^<"+(.5,0),{\xyksaveEdgec}, + {\xykz^\ar #1@'{"^>";"_>"**{}?(\xykjoincontrol)@+,}"_>"#3#4#5#6}% + \restore \POS#7}} +\xylet@\xykxbendd=\next +{\xyuncatcodes \gdef\next{{@{-}}{@{-}}}} +\xylet@\knotSTYLE=\next +{\xyuncatcodes \gdef\next#1{\def\knotSTYLE{{@{#1}}{@{#1}}}}} +\xylet@\knotstyle=\next +{\xyuncatcodes \gdef\next#1#2{\def\knotSTYLE{{@{#1}}{@{#2}}}}} +\xylet@\knotstyles=\next +{\xyuncatcodes \gdef\next#1{\def\knotSTYLE{#1}}} +\xylet@\KNOTstyle=\next +\xydef@\knotholesize@#1{\def\xykholesize{#1}} +\xydef@\xykholesize{5pt} +\xylet@\knotholesize=\knotholesize@ +\xylet@\holesize=\knotholesize@ +\xydef@\knottips#1{\def\xyknotTIPS@{#1}} +\xydef@\xyknotTIPS@{FF} +\xydef@\xyknotTIPS@@{} +\xydef@\xykSCALE@@{} +\xydef@\xykprebreak@@{}% +\xydef@\xykpostbreak@@{}% +\xydef@\xykmidbreak@@{}% +\xydef@\xykprePLACE@{(.25)}% +\xydef@\xykpostPLACE@{(.75)}% +\xydef@\xykmidPLACE@{}% +\xylet@\xykPLACE@=\xykmidPLACE@ +{\gdef\next#1#2#3#4{% + \save(0,0);"#2"-"#1"+"#4"-"#3":(.5,0): + "#3"-"#1"+"#4"-"#2"::(0,.5)::}} +\xylet@\xykflexbase@=\next +\xylet@\xykflexbase=\xykflexbase@ +{\xyuncatcodes \gdef\next#1#2#3#4#5#6#7#8{\xykflexbase{#1}{#2}{#3}{#4}% + "#1",{\ar @{#5}@'{"#1"+(0,.125)@++(.1875,.125)@+, + "#4"-(.1875,.25)@++(.1875,.125)@+}"#4" #6}, + "#2",{\ar @{#5}@'{"#2"+(0,.125)@++(-.1875,.125)@+, + "#3"+(.1875,-.25)@++(-.1875,.125)@+}"#3" #7}% +\restore \POS#8}} +\xylet@\Xtwist=\next +{\xyuncatcodes \gdef\next#1#2#3#4#5#6#7#8{\xykflexbase{#1}{#2}{#3}{#4}% + "#1",{\ar @{#5}@'{"#1"+(0,.0625)@++(.1875,.0625)@+, + "#3"+(.1875,-.125)@++(-.1875,.0625)@+}"#3" #6}, + "#2",{\ar @{#5}@'{"#2"+(0,.0625)@++(-.1875,.0625)@+, + "#4"-(.1875,.125)@++(.1875,.0625)@+}"#4" #7}% +\restore \POS#8}} +\xylet@\Xuntwist=\next +{\xyuncatcodes \gdef\next#1#2#3#4#5#6#7#8#9{\xykflexbase{#1}{#2}{#3}{#4}% + "#1",{\ar @{#5}@'{"#1"+(.1875,.0625)@++(.1875,.1875)@+, + "#4"+(-#9,-.125)@+}"#4" #6}, + "#2",{\ar @{#5}@'{"#2"+(-.1875,.0625)@++(-.1875,.1875)@+, + "#3"+(#9,-.125)@+}"#3" #7}% +\restore \POS#8}} +\xylet@\Xover=\next +{\xyuncatcodes \gdef\next#1#2#3#4#5#6#7#8#9{\xykflexbase{#1}{#2}{#3}{#4}% + "#1",{\ar @{#5}@'{"#1"+(.1875,.0625)@++(.1875,.1875)@+, + "#2"+(-.1875,.0625)@+}"#2" #6}, + "#3",{\ar @{#5}@'{"#3"+(#9,-.125)@+,"#3"+(.25,-.25)@+, + "#4"+(-#9,-.125)@+}"#4" #7}% +\restore \POS#8}} +\xylet@\Xunover=\next +{\xyuncatcodes \gdef\next#1#2#3#4#5#6#7{\xykflexbase{#1}{#2}{#3}{#4}% + "#1",{\ar @{#5}@'{"#1"+(0,.125)@++(.125,.25)@+, + "#4"+(-.125,.375)@++(.125,-.25)@+}"#4" #6}, +\restore \POS#7}} +\xylet@\Xcap=\next +{\xyuncatcodes \catcode`@=11 + \gdef\next#1#2#3#4#5#6#7#8#9{\dimen@=#1\p@ + \ifdim\dimen@=\z@ \DN@{\Xunover{#2}{#3}{#4}{#5}{#8}{#6}{#7}{"#5"}}% + \else\ifdim\dimen@>\z@ + \DNii@{#6}\ifx\nextii@\empty + \DN@{\Xover{#2}{#3}{#4}{#5}{#8}{|(.45)\knothole}{#7}{"#5"}}% + \else \DN@{\Xover{#2}{#3}{#4}{#5}{#8}{#6}{#7}{"#5"}}\fi + \else + \DNii@{#7}\ifx\nextii@\empty + \DN@{\Xover{#2}{#3}{#4}{#5}{#8}{#6}{|(.45)\knothole}{"#5"}}% + \else\DN@{\Xover{#2}{#3}{#4}{#5}{#8}{#6}{#7}{"#5"}}\fi + \fi\fi + \def\tmp@{{#9}}\ifx\tmp@\empty\def\tmp@{{0}}\else\dimen@=#9\p@\fi + \expandafter\next@\tmp@ }} +\xylet@\XXover=\next +{\xyuncatcodes \catcode`@=11 + \gdef\next#1#2#3#4#5#6#7#8{\dimen@=#1\p@ + \ifdim\dimen@=\z@ \DN@{\Xuntwist{#2}{#4}{#3}{#5}{#8}{#6}{#7}{"#5"}}% + \else\ifdim\dimen@>\z@ + \DNii@{#6}\ifx\nextii@\empty + \DN@{\Xtwist{#2}{#4}{#3}{#5}{#8}{|(.45)\knothole}{#7}{"#5"}}% + \else \DN@{\Xtwist{#2}{#4}{#3}{#5}{#8}{#6}{#7}{"#5"}}\fi + \else + \DNii@{#7}\ifx\nextii@\empty + \DN@{\Xtwist{#2}{#4}{#3}{#5}{#8}{#6}{|(.45)\knothole}{"#5"}}% + \else\DN@{\Xtwist{#2}{#4}{#3}{#5}{#8}{#6}{#7}{"#5"}}\fi + \fi\fi \next@ }} +\xylet@\XXtwist=\next +{\xyuncatcodes \catcode`@=11 + \gdef\next#1#2#3#4{\dimen@=#1\p@ + \ifdim\dimen@=\z@ \DN@{\xykuncrossv{#4}{#2}{#3}{+(0,-1)}}% + \else\ifdim\dimen@>\z@ + \DNii@{#2}\ifx\nextii@\empty + \DN@{\xyktwistv{#4}{|\knothole}{#3}{+(1,0)}}% + \else \DN@{\xyktwistv{#4}{#2}{#3}{+(1,0)}}\fi + \else + \DNii@{#3}\ifx\nextii@\empty + \DN@{\xyktwistv{#4}{#2}{|\knothole}{+(0,-1)}}% + \else\DN@{\xyktwistv{#4}{#2}{#3}{+(0,-1)}}\fi + \fi\fi \next@ }} +\xylet@\Vcross=\next +{\xyuncatcodes \catcode`@=11 + \gdef\next#1#2#3#4{\dimen@=#1\p@ + \ifdim\dimen@=\z@ \DN@{\xykuncrossh{#4}{#2}{#3}{+(0,-1)}}% + \else\ifdim\dimen@<\z@ + \DNii@{#2}\ifx\nextii@\empty + \DN@{\xyktwisth{#4}{|\knothole}{#3}{+(1,0)}}% + \else \DN@{\xyktwisth{#4}{#2}{#3}{+(1,0)}}\fi + \else + \DNii@{#3}\ifx\nextii@\empty + \DN@{\xyktwisth{#4}{}{|\knothole}{+(1,0)}}% + \else\DN@{\xyktwisth{#4}{#2}{#3}{+(1,0)}}\fi + \fi\fi \next@ }} +\xylet@\Hcross=\next +{\xyuncatcodes \catcode`@=11 + \gdef\next#1#2#3{\dimen@=#1\p@ \save + \ifdim\dimen@<\z@ + \DN@{\POS="@",p="@@",(0,0);(-1,0):(0,-1)::"@@";"@",}% + \else\DN@{}\fi + \next@ \xykcaph{#3}{#2}\restore }} +\xylet@\Hcap=\next +{\xyuncatcodes \catcode`@=11 + \gdef\next#1#2#3{\dimen@=#1\p@ \save + \ifdim\dimen@<\z@ + \DN@{\POS="@",p="@@",(0,0);(0,-1)::"@@";"@",}% + \else\DN@{}\fi + \next@ \xykcapv{#3}{#2}\restore }} +\xylet@\Vcap=\next +\xyendinput |