Xy-pic User's Guide

A Answers to all exercises

 

Answer to exercise 1.

Question.

The target [] is the current entry itself.

 

Answer to exercise 2.

Question.

The author did

\xymatrix{
 {\bullet} \ar@{--}[d]\ar@{=}[dr]\ar@{-}[r]
           & {\bullet} \ar@{.}[d] \\
 {\bullet} & {\bullet} \ar[l] }

Notice how has been enclosed in {} since it is an "expandable" entity, i.e., a defined macro.

 

Answer to exercise 3.

Question.

The author used

\xymatrix{
 A \ar[r]^f \ar[dr]_{f;g}
  & B \ar[d]^g \ar[dr]^{g;h} \\
  & C \ar[r]_h & D           }

 

Answer to exercise 4.

Question.

The author entered

\xymatrix{
 A \ar[d]_f \ar[r]^f
            & B \ar[dl]|{i_B} \ar[d]^g \\
 B \ar[r]_g & C }

 

Answer to exercise 5.

Question.

The author did

\xymatrix{
 x \ar@(ul,dl)[]|{id} \ar@/^/[rr]|f
 && f(x) \ar@/^/[ll]|{f^{-1}} }

Note that both arrows are curved "above" relative to their direction.

 

Answer to exercise 6.

Question.

The author used the display

\xymatrix{
 1 \ar[rr] ^-{1000000x}
   \ar[dr] _(.2){2000x} |!{[d];[rr]}\hole
                        && 1000000 \\
 1000 \ar[r] _{2x}
      \ar[urr] _>>>>{x^2}
                        & 2000 }

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 12 last in section 2.7.

 

Answer to exercise 7.

Question.

The author typed

\xymatrix@1{ A \ar[r]^*+[o][F-]{x} & B }

 

Answer to exercise 8.

Question.

The author did

\xymatrix@1{
 A \ar @{/*\composite{{+}*{\times}}/} [rr]
       ^*+\txt{High\\label}
 && B}

 

Answer to exercise 9.

Question.

The author entered

\xymatrix{
 A \ar @/^/ @{^{<}-_{>}} [r]
   \ar @/_/ @{{*}{x}{*}} [r] & B }

 

Answer to exercise 10.

Question.

The author typed

\xymatrix@1{
 A \ar@/^/[r] \ar@/^/@<-1ex>[r] & B }

 

Answer to exercise 11.

Question.

The size: t+0 always has zero size.

 

Answer to exercise 12.

Question.

The author constructed

\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]
}

A special thing is added: @! forces rows and columns to be equally spaced as discussed in section 3.3; @!0 furthermore makes the spacing ignore the entry sizes, giving a completely fixed grid. The gaps could also be made with the !... crossing notation of exercise 6 last in section 2.1 but the above is shorter.

 

Answer to exercise 13.

Question.

The author typed

\xymatrix@1{
 A \ar@<-2pt> `d[r] `[r] [r]
   \ar@<+2pt> `d[r] `[r] [r] & B }

 

Answer to exercise 14.

Question.

The author used

\newdir{ >}{{}*!/-5pt/@{>}}

 

Answer to exercise 15.

Question.

The author typed

\xymatrix@1{
 A \ar[r] |-{\SelectTips{cm}{}\object@{>>}}
          |>{\SelectTips{eu}{}\object@{>}}
 & B }

 

Answer to exercise 16.

Question.

The author typed

\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}
}

 

Answer to exercise 17.

Question.

The author entered the display

\xymatrix@dr@C=1pc{
 a \ar[r]\ar@{->>}[d] & a' \ar@{.>>}[d] \\
 b \ar@{.>>}[r]       & b' }

 

Answer to exercise 18.

Question.

The author typed

\xymatrix{
 A \ar[r] ^a="a" & B \ar[r] ^b="b" & C
  \ar @/^/ "a";"b" }

Notice the use of both explicit base and target in the arrow between the labels.

 

Answer to exercise 19.

Question.

The author added the Xy-code

\save [].[dd].[ddrr].[rr]*[F.]\frm{}="back"
 \restore

in the entry with , and

 \save [].[dd].[ddrr].[rr]*[F.]\frm{}
  \ar@{.} +UL;"back"+UL \ar@{.} +UR;"back"+UR
  \ar@{.} +DL;"back"+DL \ar@{.} +DR;"back"+DR
  \restore

in the entry with to produce

 

Xy-pic User's Guide