\xycompiled{thesis-27}{1999/12/13:887 [thesis:567]}{Xy-pic 3.7}%
{\xymatrixnocompile { & E(K) \\ *++{E(\Q )}\ar @{^(->}[ur]&& *++{E'(\Q )}\ar @{_(->}[ul] }}\relax 
\xy@{\xymatrix }{\enter@ {\def \noexpand \xy@minX@@ {\xy@minX@@ }\def \noexpand \xy@maxX@@ {\xy@maxX@@ }\def \noexpand \xy@minY@@ {\xy@minY@@ }\def \noexpand \xy@maxY@@ {\xy@maxY@@ }\edef \noexpand \xymatrixprefix@@ {\codeof \xymatrixprefix@@ }}}%
\xy@{}{\save@ \edef \matrixorigin@ {\X@c =\the \X@c \Y@c =\the \Y@c }\edef \xy@minX@@ {\the \X@c }\edef \xy@maxX@@ {\the \X@c }\edef \xy@minY@@ {\the \Y@c }\edef \xy@maxY@@ {\the \Y@c }}%
\xy@{""}{\edef \xymatrixprefix@@ {}}%
\xy@{}{\matrixorigin@ }%
\xy@{}{\L@c =3.0pt\R@c =3.0pt\D@c =3.0pt\U@c =3.0pt\Edge@c ={\rectangleEdge }\idfromc@ {1,1}}%
\xy@{}{\dimen@ =\X@c \advance \dimen@ -\L@c \ifdim \dimen@ <\xy@minX@@ \edef \xy@minX@@ {\the \dimen@ }\fi \dimen@ =\X@c \advance \dimen@ +\R@c \ifdim \dimen@ >\xy@maxX@@ \edef \xy@maxX@@ {\the \dimen@ }\fi \dimen@ =\Y@c \advance \dimen@ -\D@c \ifdim \dimen@ <\xy@minY@@ \edef \xy@minY@@ {\the \dimen@ }\fi \dimen@ =\Y@c \advance \dimen@ +\U@c \ifdim \dimen@ >\xy@maxY@@ \edef \xy@maxY@@ {\the \dimen@ }\fi }%
\xy@{}{\dimen@ =11.5778pt\R@ =\xy@cotabs@@ \dimen@ \dimen@ =19.34529pt\relax \ifdim \R@ >\dimen@ \R@ =\dimen@ \fi \dimen@ =11.5778pt\B@ =\xy@cotabs@@ \dimen@ \dimen@ =16.65709pt\relax \ifdim \B@ >\dimen@ \B@ =\dimen@ \fi \advance \R@ \B@ }%
\xy@{}{\dimen@ =\xymatrixcolsep@ \dimen@ =\xy@cosabs@@ \dimen@ \advance \R@ \dimen@ \advance \X@c \xy@cossign@@ \R@ }%
\xy@{}{\dimen@ =19.34529pt\R@ =\xy@tanabs@@ \dimen@ \dimen@ =11.5778pt\relax \ifdim \R@ >\dimen@ \R@ =\dimen@ \fi \dimen@ =16.65709pt\B@ =\xy@tanabs@@ \dimen@ \dimen@ =11.5778pt\relax \ifdim \B@ >\dimen@ \B@ =\dimen@ \fi \advance \R@ \B@ }%
\xy@{}{\dimen@ =\xymatrixcolsep@ \dimen@ =\xy@sinabs@@ \dimen@ \advance \R@ \dimen@ \advance \Y@c \xy@sinsign@@ \R@ }%
\xy@{}{\L@c =16.65709pt\R@c =16.65709pt\D@c =8.47499pt\U@c =8.47499pt\Edge@c ={\rectangleEdge }\idfromc@ {1,2}}%
\xy@{}{\dimen@ =\X@c \advance \dimen@ -\L@c \ifdim \dimen@ <\xy@minX@@ \edef \xy@minX@@ {\the \dimen@ }\fi \dimen@ =\X@c \advance \dimen@ +\R@c \ifdim \dimen@ >\xy@maxX@@ \edef \xy@maxX@@ {\the \dimen@ }\fi \dimen@ =\Y@c \advance \dimen@ -\D@c \ifdim \dimen@ <\xy@minY@@ \edef \xy@minY@@ {\the \dimen@ }\fi \dimen@ =\Y@c \advance \dimen@ +\U@c \ifdim \dimen@ >\xy@maxY@@ \edef \xy@maxY@@ {\the \dimen@ }\fi }%
\xy@{}{\cfromid@ {1,1}}%
\xy@{}{\dimen@ =8.47499pt\R@ =\xy@tanabs@@ \dimen@ \dimen@ =20.74806pt\relax \ifdim \R@ >\dimen@ \R@ =\dimen@ \fi \dimen@ =11.5778pt\B@ =\xy@tanabs@@ \dimen@ \dimen@ =20.74806pt\relax \ifdim \B@ >\dimen@ \B@ =\dimen@ \fi \advance \R@ \B@ }%
\xy@{}{\dimen@ =\xymatrixrowsep@ \dimen@ =\xy@sinabs@@ \dimen@ \advance \R@ \dimen@ \advance \X@c \xy@sinsign@@ \R@ }%
\xy@{}{\dimen@ =20.74806pt\R@ =\xy@cotabs@@ \dimen@ \dimen@ =8.47499pt\relax \ifdim \R@ >\dimen@ \R@ =\dimen@ \fi \dimen@ =20.74806pt\B@ =\xy@cotabs@@ \dimen@ \dimen@ =11.5778pt\relax \ifdim \B@ >\dimen@ \B@ =\dimen@ \fi \advance \R@ \B@ }%
\xy@{}{\dimen@ =\xymatrixrowsep@ \dimen@ =\xy@cosabs@@ \dimen@ \advance \R@ \dimen@ \advance \Y@c -\xy@cossign@@ \R@ }%
\xy@{}{\L@c =19.34529pt\R@c =19.34529pt\D@c =11.47499pt\U@c =11.47499pt\Edge@c ={\rectangleEdge }\idfromc@ {2,1}}%
\xy@{}{\dimen@ =\X@c \advance \dimen@ -\L@c \ifdim \dimen@ <\xy@minX@@ \edef \xy@minX@@ {\the \dimen@ }\fi \dimen@ =\X@c \advance \dimen@ +\R@c \ifdim \dimen@ >\xy@maxX@@ \edef \xy@maxX@@ {\the \dimen@ }\fi \dimen@ =\Y@c \advance \dimen@ -\D@c \ifdim \dimen@ <\xy@minY@@ \edef \xy@minY@@ {\the \dimen@ }\fi \dimen@ =\Y@c \advance \dimen@ +\U@c \ifdim \dimen@ >\xy@maxY@@ \edef \xy@maxY@@ {\the \dimen@ }\fi }%
\xy@{}{\dimen@ =11.5778pt\R@ =\xy@cotabs@@ \dimen@ \dimen@ =19.34529pt\relax \ifdim \R@ >\dimen@ \R@ =\dimen@ \fi \dimen@ =11.5778pt\B@ =\xy@cotabs@@ \dimen@ \dimen@ =16.65709pt\relax \ifdim \B@ >\dimen@ \B@ =\dimen@ \fi \advance \R@ \B@ }%
\xy@{}{\dimen@ =\xymatrixcolsep@ \dimen@ =\xy@cosabs@@ \dimen@ \advance \R@ \dimen@ \advance \X@c \xy@cossign@@ \R@ }%
\xy@{}{\dimen@ =19.34529pt\R@ =\xy@tanabs@@ \dimen@ \dimen@ =11.5778pt\relax \ifdim \R@ >\dimen@ \R@ =\dimen@ \fi \dimen@ =16.65709pt\B@ =\xy@tanabs@@ \dimen@ \dimen@ =11.5778pt\relax \ifdim \B@ >\dimen@ \B@ =\dimen@ \fi \advance \R@ \B@ }%
\xy@{}{\dimen@ =\xymatrixcolsep@ \dimen@ =\xy@sinabs@@ \dimen@ \advance \R@ \dimen@ \advance \Y@c \xy@sinsign@@ \R@ }%
\xy@{}{\L@c =3.0pt\R@c =3.0pt\D@c =3.0pt\U@c =3.0pt\Edge@c ={\rectangleEdge }\idfromc@ {2,2}}%
\xy@{}{\dimen@ =\X@c \advance \dimen@ -\L@c \ifdim \dimen@ <\xy@minX@@ \edef \xy@minX@@ {\the \dimen@ }\fi \dimen@ =\X@c \advance \dimen@ +\R@c \ifdim \dimen@ >\xy@maxX@@ \edef \xy@maxX@@ {\the \dimen@ }\fi \dimen@ =\Y@c \advance \dimen@ -\D@c \ifdim \dimen@ <\xy@minY@@ \edef \xy@minY@@ {\the \dimen@ }\fi \dimen@ =\Y@c \advance \dimen@ +\U@c \ifdim \dimen@ >\xy@maxY@@ \edef \xy@maxY@@ {\the \dimen@ }\fi }%
\xy@{}{\dimen@ =11.5778pt\R@ =\xy@cotabs@@ \dimen@ \dimen@ =16.65709pt\relax \ifdim \R@ >\dimen@ \R@ =\dimen@ \fi \dimen@ =11.5778pt\B@ =\xy@cotabs@@ \dimen@ \dimen@ =20.74806pt\relax \ifdim \B@ >\dimen@ \B@ =\dimen@ \fi \advance \R@ \B@ }%
\xy@{}{\dimen@ =\xymatrixcolsep@ \dimen@ =\xy@cosabs@@ \dimen@ \advance \R@ \dimen@ \advance \X@c \xy@cossign@@ \R@ }%
\xy@{}{\dimen@ =16.65709pt\R@ =\xy@tanabs@@ \dimen@ \dimen@ =11.5778pt\relax \ifdim \R@ >\dimen@ \R@ =\dimen@ \fi \dimen@ =20.74806pt\B@ =\xy@tanabs@@ \dimen@ \dimen@ =11.5778pt\relax \ifdim \B@ >\dimen@ \B@ =\dimen@ \fi \advance \R@ \B@ }%
\xy@{}{\dimen@ =\xymatrixcolsep@ \dimen@ =\xy@sinabs@@ \dimen@ \advance \R@ \dimen@ \advance \Y@c \xy@sinsign@@ \R@ }%
\xy@{}{\L@c =20.74806pt\R@c =20.74808pt\D@c =11.5778pt\U@c =11.5778pt\Edge@c ={\rectangleEdge }\idfromc@ {2,3}}%
\xy@{}{\dimen@ =\X@c \advance \dimen@ -\L@c \ifdim \dimen@ <\xy@minX@@ \edef \xy@minX@@ {\the \dimen@ }\fi \dimen@ =\X@c \advance \dimen@ +\R@c \ifdim \dimen@ >\xy@maxX@@ \edef \xy@maxX@@ {\the \dimen@ }\fi \dimen@ =\Y@c \advance \dimen@ -\D@c \ifdim \dimen@ <\xy@minY@@ \edef \xy@minY@@ {\the \dimen@ }\fi \dimen@ =\Y@c \advance \dimen@ +\U@c \ifdim \dimen@ >\xy@maxY@@ \edef \xy@maxY@@ {\the \dimen@ }\fi }%
\xy@{}{\ifx \xymatrixsavedCOORD@ \relax \enter@ {\noexpand \let \noexpand \COORD@ \noexpand \xymatrixsavedCOORD@ }\let \xymatrixsavedCOORD@ =\COORD@ \let \COORD@ =\xymatrixCOORD@ \else \enter@ {}\fi }%
\xy@{ENTRY "1,1"}{\Row =1 \Col =1\relax \cfromid@ {1,1}\pfromc@ }%
\xy@@ix@{{\entrybox }{}}\relax 
\xy@{}{\expandafter \dropentry@ \the \toks 9}%
\xy@{ENTRY "1,2"}{\Row =1 \Col =2\relax \cfromid@ {1,2}\pfromc@ }%
\xy@@ix@{{\entrybox }{E(K) }}\relax 
\xy@{}{\expandafter \dropentry@ \the \toks 9}%
\xy@{ENTRY "2,1"}{\Row =2 \Col =1\relax \cfromid@ {2,1}\pfromc@ }%
\xy@@ix@{{++}{E(\Q )}}\relax 
\xy@{}{\expandafter \dropentry@ \the \toks 9}%
\xy@{\save }{\save@ }%
\xy@{\afterPATH {\afterar@@ }}{\def \PATHslide@@ {\z@ }}%
\xy@{~={\preconnect \dir {-}}}{}%
\xy@{~/{}}{}%
\xy@{~<{|<*h\dir ^{(}}}{}%
\xy@{~>{|>*h\dir {>}}}{}%
\xy@{~+{}}{}%
\xy@{}{\pfromc@ }%
\xy@{[ur]}{\def \thematrixCOORD@@ {[ur]}}%
\xy@{}{\expandafter \let \expandafter \next@ \csname Q@1,2\endcsname \ifx \next@ \relax \xyerror@RC {1,2}\else \next@ \fi }%
\xy@{}{\setupDirection@ \dimen@ =\PATHslide@@ \dimen@ii =-\sinDirection \dimen@ \ifPATHomitslide@@ \else \advance \X@p \dimen@ii \fi \advance \X@c \dimen@ii \dimen@ii = \cosDirection \dimen@ \ifPATHomitslide@@ \else \advance \Y@p \dimen@ii \fi \advance \Y@c \dimen@ii \PATHomitslide@@false \resetupDirection@ }%
\xy@{PATHaction={\preconnect \dir {-}}}{}%
\xy@@ix@{{\dir }{-}}\relax 
\xy@{\connect \dir {-}}{\expandafter \preconnect@ \the \toks 9 }%
\xy@{|}{}%
\xy@{}{\enter@ {\pfromthep@ }\Creset@@ \def \PLACEf@ {{.5}}\let \PLACEedgep@@ =\PLACEedgep@ \let \PLACEedgec@@ =\PLACEedgec@ }%
\xy@{<}{\def \PLACEf@ {{0}}\PLACEedgep@@ }%
\xy@{}{\expandafter \Calong@@ \PLACEf@ \czeroEdge@ }%
\xy@{}{\leave@ }%
\xy@@ix@{{!Ch\dir ^}{(}}\relax 
\xy@{\drop !Ch\dir ^{(}}{\expandafter \drop@ \the \toks 9 }%
\xy@{}{\Cbreak@@ }%
\xy@{|}{}%
\xy@{}{\enter@ {\pfromthep@ }\Creset@@ \def \PLACEf@ {{.5}}\let \PLACEedgep@@ =\PLACEedgep@ \let \PLACEedgec@@ =\PLACEedgec@ }%
\xy@{>}{\def \PLACEf@ {{1}}\PLACEedgec@@ }%
\xy@{}{\expandafter \Calong@@ \PLACEf@ \czeroEdge@ }%
\xy@{}{\leave@ }%
\xy@@ix@{{!Ch\dir }{>}}\relax 
\xy@{\drop !Ch\dir {>}}{\expandafter \drop@ \the \toks 9 }%
\xy@{}{\Cbreak@@ }%
\xy@{}{\Clast@@ }%
\xy@{}{\setupDirection@ }%
\xy@{PATHaction/{}}{}%
\xy@{\restore }{\leave@ }%
\xy@{ENTRY "2,2"}{\Row =2 \Col =2\relax \cfromid@ {2,2}\pfromc@ }%
\xy@@ix@{{\entrybox }{}}\relax 
\xy@{}{\expandafter \dropentry@ \the \toks 9}%
\xy@{ENTRY "2,3"}{\Row =2 \Col =3\relax \cfromid@ {2,3}\pfromc@ }%
\xy@@ix@{{++}{E'(\Q )}}\relax 
\xy@{}{\expandafter \dropentry@ \the \toks 9}%
\xy@{\save }{\save@ }%
\xy@{\afterPATH {\afterar@@ }}{\def \PATHslide@@ {\z@ }}%
\xy@{~={\preconnect \dir {-}}}{}%
\xy@{~/{}}{}%
\xy@{~<{|<*h\dir _{(}}}{}%
\xy@{~>{|>*h\dir {>}}}{}%
\xy@{~+{}}{}%
\xy@{}{\pfromc@ }%
\xy@{[ul]}{\def \thematrixCOORD@@ {[ul]}}%
\xy@{}{\expandafter \let \expandafter \next@ \csname Q@1,2\endcsname \ifx \next@ \relax \xyerror@RC {1,2}\else \next@ \fi }%
\xy@{}{\setupDirection@ \dimen@ =\PATHslide@@ \dimen@ii =-\sinDirection \dimen@ \ifPATHomitslide@@ \else \advance \X@p \dimen@ii \fi \advance \X@c \dimen@ii \dimen@ii = \cosDirection \dimen@ \ifPATHomitslide@@ \else \advance \Y@p \dimen@ii \fi \advance \Y@c \dimen@ii \PATHomitslide@@false \resetupDirection@ }%
\xy@{PATHaction={\preconnect \dir {-}}}{}%
\xy@@ix@{{\dir }{-}}\relax 
\xy@{\connect \dir {-}}{\expandafter \preconnect@ \the \toks 9 }%
\xy@{|}{}%
\xy@{}{\enter@ {\pfromthep@ }\Creset@@ \def \PLACEf@ {{.5}}\let \PLACEedgep@@ =\PLACEedgep@ \let \PLACEedgec@@ =\PLACEedgec@ }%
\xy@{<}{\def \PLACEf@ {{0}}\PLACEedgep@@ }%
\xy@{}{\expandafter \Calong@@ \PLACEf@ \czeroEdge@ }%
\xy@{}{\leave@ }%
\xy@@ix@{{!Ch\dir _}{(}}\relax 
\xy@{\drop !Ch\dir _{(}}{\expandafter \drop@ \the \toks 9 }%
\xy@{}{\Cbreak@@ }%
\xy@{|}{}%
\xy@{}{\enter@ {\pfromthep@ }\Creset@@ \def \PLACEf@ {{.5}}\let \PLACEedgep@@ =\PLACEedgep@ \let \PLACEedgec@@ =\PLACEedgec@ }%
\xy@{>}{\def \PLACEf@ {{1}}\PLACEedgec@@ }%
\xy@{}{\expandafter \Calong@@ \PLACEf@ \czeroEdge@ }%
\xy@{}{\leave@ }%
\xy@@ix@{{!Ch\dir }{>}}\relax 
\xy@{\drop !Ch\dir {>}}{\expandafter \drop@ \the \toks 9 }%
\xy@{}{\Cbreak@@ }%
\xy@{}{\Clast@@ }%
\xy@{}{\setupDirection@ }%
\xy@{PATHaction/{}}{}%
\xy@{\restore }{\leave@ }%
\xy@{}{\leave@ }%
\xy@{}{}%
\xy@{\restore }{\leave@ }%
\xy@{}{\edef \nextii@ {{\xy@minX@@ }{\xy@maxX@@ }{\xy@minY@@ }{\xy@maxY@@ }}\expandafter \xymatrix@insert@ \nextii@ }%
\xy@{}{\leave@ }%
\xyendcompiled
