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+%% 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