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<P ALIGN=RIGHT><FONT SIZE=1>Xy-pic User's Guide</FONT> <A HREF="18pt.html"><IMG SRC="./quest.gif" ALIGN=TOP HEIGHT=27 WIDTH=21 BORDER=0 ALT="?"></A><A NAME="tex2html463" HREF="node32.html"><IMG WIDTH=27 HEIGHT=27 BORDER=0 ALIGN=ABSMIDDLE ALT="previous" SRC="./previous.gif"></A><A NAME="tex2html467" HREF="node28.html"><IMG WIDTH=27 HEIGHT=27 BORDER=0 ALIGN=ABSMIDDLE ALT="previous" SRC="./previoussection.gif"></A><A NAME="tex2html469" HREF="xyguide-html.html"><IMG WIDTH=27 HEIGHT=27 BORDER=0 ALIGN=ABSMIDDLE ALT="up" SRC="./up.gif"></A><A NAME="tex2html465" HREF="node34.html"><IMG WIDTH=27 HEIGHT=27 BORDER=0 ALIGN=ABSMIDDLE ALT="next" SRC="./nextsection.gif"></A><A NAME="tex2html471" HREF="node34.html"><IMG WIDTH=27 HEIGHT=27 BORDER=0 ALIGN=ABSMIDDLE ALT="next" SRC="./next.gif"></A></P><H1><A NAME="SECTION00070000000000000000">A Answers to all exercises</A></H1><A NAME="Answer1"> </A><H4><A NAME="SECTION00070010000000000000">Answer to exercise 1.</A></H4>
<P>
<A HREF="node6.html#Exercise1">Question.</A>
<P>
The target <code>[]</code> is the current entry itself.
<P>
<A NAME="Answer2"> </A><H4><A NAME="SECTION00070020000000000000">Answer to exercise 2.</A></H4><A HREF="node6.html#Exercise2">Question.</A>
<P>
The author did
<BLOCKQUOTE><PRE>\xymatrix{
{\bullet} \ar@{--}[d]\ar@{=}[dr]\ar@{-}[r]
& {\bullet} \ar@{.}[d] \\
{\bullet} & {\bullet} \ar[l] }</PRE></BLOCKQUOTE>
Notice how <IMG WIDTH=8 HEIGHT=8 ALIGN=BOTTOM ALT="tex2html_wrap_inline2476" SRC="img5.gif"> has been enclosed in <code>{}</code> since it is an "expandable" entity, <I>i.e.</I>, a defined macro.
<P>
<A NAME="Answer3"> </A><H4><A NAME="SECTION00070030000000000000">Answer to exercise 3.</A></H4><A HREF="node7.html#Exercise3">Question.</A>
<P>
The author used
<BLOCKQUOTE><PRE>\xymatrix{
A \ar[r]^f \ar[dr]_{f;g}
& B \ar[d]^g \ar[dr]^{g;h} \\
& C \ar[r]_h & D }</PRE></BLOCKQUOTE>
<P>
<A NAME="Answer4"> </A><H4><A NAME="SECTION00070040000000000000">Answer to exercise 4.</A></H4><A HREF="node8.html#Exercise4">Question.</A>
<P>
The author entered
<BLOCKQUOTE><PRE>\xymatrix{
A \ar[d]_f \ar[r]^f
& B \ar[dl]|{i_B} \ar[d]^g \\
B \ar[r]_g & C }</PRE></BLOCKQUOTE>
<P>
<A NAME="Answer5"> </A><H4><A NAME="SECTION00070050000000000000">Answer to exercise 5.</A></H4><A HREF="node9.html#Exercise5">Question.</A>
<P>
The author did
<BLOCKQUOTE><PRE>\xymatrix{
x \ar@(ul,dl)[]|{id} \ar@/^/[rr]|f
&& f(x) \ar@/^/[ll]|{f^{-1}} }</PRE></BLOCKQUOTE>
Note that both arrows are curved "above" relative to their direction.
<P>
<A NAME="Answer6"> </A><H4><A NAME="SECTION00070060000000000000">Answer to exercise 6.</A></H4><A HREF="node12.html#Exercise6">Question.</A>
<P>
The author used the display
<BLOCKQUOTE><PRE>\xymatrix{
1 \ar[rr] ^-{1000000x}
\ar[dr] _(.2){2000x} |!{[d];[rr]}\hole
&& 1000000 \\
1000 \ar[r] _{2x}
\ar[urr] _>>>>{x^2}
& 2000 }</PRE></BLOCKQUOTE>
In particular notice how the break was specified to happen exactly where the two arrows cross. For an easier but not so general method see exercise <A HREF="#xcube">12</A> last in section <A HREF="node18.html#arrowspass">2.7</A>.
<P>
<A NAME="Answer7"> </A><H4><A NAME="SECTION00070070000000000000">Answer to exercise 7.</A></H4><A HREF="node13.html#Exercise7">Question.</A>
<P>
The author typed
<BLOCKQUOTE><PRE>\xymatrix@1{ A \ar[r]^*+[o][F-]{x} & B }</PRE></BLOCKQUOTE>
<P>
<A NAME="Answer8"> </A><H4><A NAME="SECTION00070080000000000000">Answer to exercise 8.</A></H4><A HREF="node13.html#Exercise8">Question.</A>
<P>
The author did
<BLOCKQUOTE><PRE>\xymatrix@1{
A \ar @{/*\composite{{+}*{\times}}/} [rr]
^*+\txt{High\\label}
&& B}</PRE></BLOCKQUOTE>
<P>
<A NAME="Answer9"> </A><H4><A NAME="SECTION00070090000000000000">Answer to exercise 9.</A></H4><A HREF="node14.html#Exercise9">Question.</A>
<P>
The author entered
<BLOCKQUOTE><PRE>\xymatrix{
A \ar @/^/ @{^{<}-_{>}} [r]
\ar @/_/ @{{*}{x}{*}} [r] & B }</PRE></BLOCKQUOTE>
<P>
<A NAME="Answer10"> </A><H4><A NAME="SECTION000700100000000000000">Answer to exercise 10.</A></H4><A HREF="node15.html#Exercise10">Question.</A>
<P>
The author typed
<BLOCKQUOTE><PRE>\xymatrix@1{
A \ar@/^/[r] \ar@/^/@<-1ex>[r] & B }</PRE></BLOCKQUOTE>
<P>
<A NAME="Answer11"> </A><H4><A NAME="SECTION000700110000000000000">Answer to exercise 11.</A></H4><A HREF="node17.html#Exercise11">Question.</A>
<P>
The size: <I>t</I><code>+0</code> always has zero size.
<P>
<A NAME="Answer12"> </A><H4><A NAME="SECTION000700120000000000000">Answer to exercise 12.</A></H4><A HREF="node18.html#Exercise12">Question.</A>
<P>
The author constructed
<BLOCKQUOTE><PRE>\xymatrix@!0{
& \lambda\omega \ar@{-}[rr]\ar@{-}'[d][dd]
& & \lambda C \ar@{-}[dd]
\\
\lambda2 \ar@{-}[ur]\ar@{-}[rr]\ar@{-}[dd]
& & \lambda P2 \ar@{-}[ur]\ar@{-}[dd]
\\
& \lambda\underline\omega \ar@{-}'[r][rr]
& & \lambda P\underline\omega
\\
\lambda{\to} \ar@{-}[rr]\ar@{-}[ur]
& & \lambda P \ar@{-}[ur]
}</PRE></BLOCKQUOTE>
A special thing is added: <code>@!</code> forces rows and columns to be equally spaced as discussed in section <A HREF="node24.html#entriesresizing">3.3</A>; <code>@!0</code> furthermore makes the spacing ignore the entry sizes, giving a completely fixed grid. The gaps could also be made with the <code>!</code>... crossing notation of exercise <A HREF="#xintercept">6</A> last in section <A HREF="node12.html#arrowsplaces">2.1</A> but the above is shorter.
<P>
<A NAME="Answer13"> </A><H4><A NAME="SECTION000700130000000000000">Answer to exercise 13.</A></H4><A HREF="node19.html#Exercise13">Question.</A>
<P>
The author typed
<BLOCKQUOTE><PRE>\xymatrix@1{
A \ar@<-2pt> `d[r] `[r] [r]
\ar@<+2pt> `d[r] `[r] [r] & B }</PRE></BLOCKQUOTE>
<P>
<A NAME="Answer14"> </A><H4><A NAME="SECTION000700140000000000000">Answer to exercise 14.</A></H4><A HREF="node20.html#Exercise14">Question.</A>
<P>
The author used
<BLOCKQUOTE><PRE>\newdir{ >}{{}*!/-5pt/@{>}}</PRE></BLOCKQUOTE>
<P>
<A NAME="Answer15"> </A><H4><A NAME="SECTION000700150000000000000">Answer to exercise 15.</A></H4><A HREF="node20.html#Exercise15">Question.</A>
<P>
The author typed
<BLOCKQUOTE><PRE>\xymatrix@1{
A \ar[r] |-{\SelectTips{cm}{}\object@{>>}}
|>{\SelectTips{eu}{}\object@{>}}
& B }</PRE></BLOCKQUOTE>
<P>
<A NAME="Answer16"> </A><H4><A NAME="SECTION000700160000000000000">Answer to exercise 16.</A></H4><A HREF="node22.html#Exercise16">Question.</A>
<P>
The author typed
<BLOCKQUOTE><PRE>\xymatrix{
*=0{\bullet}
\ar@/^/[dr]!U|1
\ar@/^/[drr]!U|2
\ar@/^/[drrr]!U|3
\\
&*+[F]\txt{x}
&*+[F]\txt{x\\x}
&*+[F]\txt{x\\x\\x}
}</PRE></BLOCKQUOTE>
<P>
<A NAME="Answer17"> </A><H4><A NAME="SECTION000700170000000000000">Answer to exercise 17.</A></H4><A HREF="node24.html#Exercise17">Question.</A>
<P>
The author entered the display
<BLOCKQUOTE><PRE>\xymatrix@dr@C=1pc{
a \ar[r]\ar@{->>}[d] & a' \ar@{.>>}[d] \\
b \ar@{.>>}[r] & b' }</PRE></BLOCKQUOTE>
<P>
<A NAME="Answer18"> </A><H4><A NAME="SECTION000700180000000000000">Answer to exercise 18.</A></H4><A HREF="node26.html#Exercise18">Question.</A>
<P>
The author typed
<BLOCKQUOTE><PRE>\xymatrix{
A \ar[r] ^a="a" & B \ar[r] ^b="b" & C
\ar @/^/ "a";"b" }</PRE></BLOCKQUOTE>
Notice the use of both explicit base and target in the arrow between the labels.
<P>
<A NAME="Answer19"> </A><H4><A NAME="SECTION000700190000000000000">Answer to exercise 19.</A></H4><A HREF="node27.html#Exercise19">Question.</A>
<P>
The author added the Xy-code
<BLOCKQUOTE><PRE>\save [].[dd].[ddrr].[rr]*[F.]\frm{}="back"
\restore</PRE></BLOCKQUOTE>
in the entry with <IMG WIDTH=23 HEIGHT=15 ALIGN=BOTTOM ALT="tex2html_wrap_inline2788" SRC="img71.gif">, and
<BLOCKQUOTE><PRE> \save [].[dd].[ddrr].[rr]*[F.]\frm{}
\ar@{.} +UL;"back"+UL \ar@{.} +UR;"back"+UR
\ar@{.} +DL;"back"+DL \ar@{.} +DR;"back"+DR
\restore</PRE></BLOCKQUOTE>
in the entry with <IMG WIDTH=20 HEIGHT=15 ALIGN=BOTTOM ALT="tex2html_wrap_inline2790" SRC="img72.gif"> to produce
<BR><IMG WIDTH=244 HEIGHT=171 ALIGN=BOTTOM ALT="displaymath2792" SRC="img73.gif"><BR>
<P>
<P> <P ALIGN=RIGHT><FONT SIZE=1>Xy-pic User's Guide</FONT> <A HREF="18pt.html"><IMG SRC="./quest.gif" ALIGN=TOP HEIGHT=27 WIDTH=21 BORDER=0 ALT="?"></A><A NAME="tex2html463" HREF="node32.html"><IMG WIDTH=27 HEIGHT=27 BORDER=0 ALIGN=ABSMIDDLE ALT="previous" SRC="./previous.gif"></A><A NAME="tex2html467" HREF="node28.html"><IMG WIDTH=27 HEIGHT=27 BORDER=0 ALIGN=ABSMIDDLE ALT="previous" SRC="./previoussection.gif"></A><A NAME="tex2html469" HREF="xyguide-html.html"><IMG WIDTH=27 HEIGHT=27 BORDER=0 ALIGN=ABSMIDDLE ALT="up" SRC="./up.gif"></A><A NAME="tex2html465" HREF="node34.html"><IMG WIDTH=27 HEIGHT=27 BORDER=0 ALIGN=ABSMIDDLE ALT="next" SRC="./nextsection.gif"></A><A NAME="tex2html471" HREF="node34.html"><IMG WIDTH=27 HEIGHT=27 BORDER=0 ALIGN=ABSMIDDLE ALT="next" SRC="./next.gif"></A><P><ADDRESS>
<BR><HR>
<a href="COPYING/index.html">�/a> <a href="http://www.brics.dk/~krisrose/">Kristoffer H. Rose</a>
<<a href="mailto:krisrose@brics.dk">krisrose@brics.dk</a>>
January 6, 1997
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