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