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Gi lnh xypic.sty - lm cc loi biu

Nguyn Hu inKhoa Ton - C - Tin hc

HKHTN H Ni, HQGHN

1 Gii thiu gi lnh

Gi lnh c thit k nh dng cc biu khc nhau. Gi lnh ny c th chy cng vi gi

lnh amstex. Hy a vo phn u lnh \usepackage{xypic}http://tug.ctan.org/tex-archive/macros/generic/diagrams/xypic/xy

Gi lnh ny c trong MiKTeX, nn ci t chng trnh qun l ny v c nhiu phng vtp km theo.

2 S dng

2.1 Gi gi lnh v mi trng

1. Gi gi lnh vi ty chn \usepackage[all]{xy}

2. Mi trng chnh l \xymatrix{ . . . }. Trong du 3 chm l cc hng v ct theo ccphn t cn mi tn theo k hiu:

7 8

\xymatrix{

A &*+[F]{\sum_{i=n}^m {i^2}} \\

& {\bullet} & D \ar[ul] }

: 2

Am

i=n i2

D

2.2 Mi tn

7 8

$$

\xymatrix{

{\bullet } \ar@{--}[d] \ar@{=}[dr] \ar@{-}[r]

& {\bullet } \ar@{.}[d] \\

{\bullet } & {\bullet } \ar[l]

}

$$

: 2

oo

1

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http://nhdien.wordpress.com - Nguyn Hu in 2

7 8

$$

\xymatrix{A \ar[dr] \ar[drr] & & \\

& A + B \ar[r] & X \\B \ar[ur] \ar[urr] & &

}

$$

: 2

A

55 AAA + B GG X

B

YY SS

7 8

$$

\xymatrix{

1\ar@{-}[r]\ar@(r,l)@/_0pt/@{-}[dr]&2\\

3\ar@{-}[r]\ar@(r,l)@/_0pt/@{-}[ur]&4\\}

$$

: 2

1 2

3 4

7 8

$$

\xymatrix{

1\ar@{-}[r]\ar@(r,l)@/_0pt/@{-}[]!R;[dr]!L&2\\

3\ar@{-}[r]\ar@(r,l)@/_0pt/@{-}[]!R;[ur]!L&4\\

}

$$

: 2

1 2

3 4

2.3 Nhn trn mi tn

7 8

$$

\xymatrix{

X \ar@{->}[r]^{f}\ar@{->}[d]_{\pi}

& Z \ar@{->}[dl]^{g}\\

Y & \\

}

$$

: 2

Xf GG

Z

g~~

Y

7 8

$$\xymatrix{

a \ar[dr] \ar[r]^s &B \ar@{=}[d]^{ddd}_{ttt} \\

&c

}

$$

: 2

a

11

s GG B

dddttt

c

7 8

$$

\xymatrix{

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

& C \ar[r]^h & D

}

$$

: 2

Af GG

f;g 11

B

g

g;h

22C

h GG D

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2.4 Ngt mi tn

7 8

$$\xymatrix{

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

B \ar[r]_g & C }

$$

: 2

A

f

f GG B

iB

~~g

B

gGG C

7 8

$$

\xymatrix{

A \ar[dr]^[@]{z} & B \\

C & D

}\qquad

\xymatrix{

A \ar[dr]|*[@]{z} & B \\

C & D

}

$$

: 2

Az

22

B

C D

A

z

22

B

C D

7 8

$$

\xymatrix{

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

& f(x) \ar@/^/[ll]|{f^{-1}} }

$$

: 2

xid WWf DD

f(x)f1

kk

7 8

$$

\xymatrix{

1 \ar[rr] ^-{1000000x}

\ar[dr] _(.2){2000x} |!{[d];[rr]}\hole

&& 1000000 \\

1000 \ar[r] _{2x}\ar[urr] _>>>>{x^2}& 2000 }

$$

: 2

11000000x GG

2000x

55

1000000

10002x

GG

x2

RR

2000

2.5 Cn li

7 8

$$

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

$$

: 2

Ax GGB

7 8

$$

\xymatrix@1{

A \ar @{/*\composite{{+}*{\times}}/} [rr]^*

+\txt{High\\label}&& B}$$

: 2

A

Highlabel

++++++ B

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7 8

$$

\xymatrix{

A \ar @/^/ @{^{}} [r]\ar @/_/ @{{*}{x}{*}} [r] & B }$$

: 2

Av A 0 6?HN B

7 8

$$

\xymatrix@1{A \ar@/^/[r] \ar@/^/@[r] & B }

$$

: 2

A9999B

7 8

$$

\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]

}

$$

: 2

C

2 P2

P

P

7 8

$$

\xymatrix@1{

A \ar@ d[r] [r] [r]\ar@ d[r] [r] [r] & B }

$$

: 2

A xxB

7 8

$$

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

\xymatrix{ A \ar @{>->} @< 2pt> [r]

\ar @{ >->} @ [r] & B }

$$

: 2

A GG GG

GG GGB

7 8

$$

\xymatrix@1{

A \ar[r] |-{\SelectTips{cm}{}\object@{>>}}

|>{\SelectTips{eu}{}\object@{>}}

& B }

$$

: 2

A // // //GGB

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7 8

$$

\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}

}

$$

: 2

1

2

33

3

99

x xx

xxx

7 8

$$

\xymatrix@dr@C=1pc{

a \ar[r]\ar@{->>}[d] & a \ar@{.>>}[d] \\

b \ar@{.>>}[r] & b }

$$

: 2

a11

a

b

11 11b

7 8

$$

\xymatrix{

A \ar[r] ^a="a" & B \ar[r] ^b="b" & C

\ar @/^/ "a";"b" }

$$

: 2

Aa GG B

b GG C@@

7 8

$$

\xymatrix@!0{& \lambda\omega \ar@{-}[rr]\ar@{-}[d][dd]

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

\restore

& & \lambda C \ar@{-}[dd]\\

\lambda2 \ar@{-}[ur]\ar@{-}[rr]\ar@{-}[dd]

\save [].[dd].[ddrr].[rr]*[F.]\frm{}

\ar@{.} +UL;"back"+UL \ar@{.} +UR;"back"+UR

\ar@{.} +DL;"back"+DL \ar@{.} +DR;"back"+DR

\restore& & \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]

}

$$

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: 2

C

2 P2

P

P

2.6 Hnh cy

7 8

$$

\xymatrix{&&& \text{A} \ar@{-}[dll] \ar@{-}[dd] \ar@{-}[drr]&&& \\

&\text{B} \ar@{-}[dl] \ar@{-}[d] \ar@{-}[dr]

&&&& \text{C} \ar@{-}[dl] \ar@{-}[d] \ar@{-}[dr] \\

D&E&F&G&H&I&J}

$$

: 2

A

B C

D E F G H I J

7 8

{\tiny

$$

\xymatrix{

&&& \text{A} \ar@{-}[dll] \ar@{-}[dd] \ar@{-}[drr]&&& \\

&\text{B} \ar@{-}[dl] \ar@{-}[d] \ar@{-}[dr]

&&&& \text{C} \ar@{-}[dl] \ar@{-}[d] \ar@{-}[dr] \\

D&E&F&G&H&I&J}$$

}

: 2

A

B C

D E F G H I J

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{\tiny

$$

\xymatrix{&&&&&&\text{A1} \ar@{-}[dlll] \ar@{-}[dddr] \ar@{-}[ddrr]& \\

&&&\text{A2}\ar@{-}[dll] \ar@{-}[dd] \ar@{-}[drr]&&&&&\\

&\text{A3}\ar@{-}[dl] \ar@{-}[d] \ar@{-}[dr]

&&&&\text{A4}\ar@{-}[dl]\ar@{-}[d]\ar@{-}[dr]

&&&\text{A5} \ar@{-}[d] \ar@{-}[dr]\\

a&b&c&d&e&f&g&h&i&j}

$$

}

: 2

A1

A2

A3 A4 A5

a b c d e f g h i j

7 8

{\tiny$$

\xymatrix{

&&&&&&&\text{A1} \ar@{-}[dllll] \ar@{-}[ddd] \ar@{-}[ddr]& \\

&&&\text{A2}\ar@{-}[dll] \ar@{-}[dd] \ar@{-}[drr]&&&&&\\


&&&&\text{A4}\ar@{-}[dl]\ar@{-}[d]\ar@{-}[dr]

&&&\text{A5} \ar@{-}[d] \ar@{-}[dr]\\


$$

}

: 2

A1

A2

A3 A4 A5

a b c d e f g h i j

7 8

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{\tiny

$$

\xymatrix{

&\text{B1} \ar@{-}[dl] \ar@{-}[d] \ar@{-}[dr]& \\

\text{B2}&h&\text{B5}}

$$

}

: 2

B1

B2 h B5

7 8

{\tiny

$$

\xymatrix{

&&\text{A1} \ar@{-}[dl] \ar@{-}[ddr] \ar@{-}[drr]& \\


&&&\text{A5} \ar@{-}[d] \ar@{-}[dr]\\

\text{A3}&d&\text{A4}&h&i&j

}

$$

}

: 2

A1

A2 A5

A3 d A4 h i j

7 8

{\tiny

$$

\xymatrix{

&&&&&&\text{A1} \ar@{-}[dlll] \ar@{-}[dddr] \ar@{-}[drr]& \\

&&&\text{A2}\ar@{-}[dll] \ar@{-}[dd] \ar@{-}[drr]

&&&&&\text{A5} \ar@{-}[dd] \ar@{-}[ddr]\\


&&&&\text{A4}\ar@{-}[dl]\ar@{-}[d]\ar@{-}[dr]&&&\\


$$

}

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: 2

A1

A2 A5

A3 A4

a b c d e f g h i j

2.7 inh dng khc

7 8

$$

\xymatrix{

& & C \\

& B \ar@{-}[ru] \ar@{-}[rd] & \\

A \ar@{-}[ru] \ar@{-}[rd]& & D \\

& C \ar@{-}[ru] \ar@{-}[rd] & \\

& & E }

$$

: 2

C

B

A D

C

E

7 8

\xymatrix{ 1,1 & 1,2 & 1,3 & 1,4 & 1,5 \\

2,1 & 2,2 & 2,3 & 2,4 & 2,5

\save "1,2"."2,4"*[F.]\frm{}

\ar"1,1" \ar"2,1" \ar"1,5" \ar"2,5"

\restore }

: 2

1, 1 1, 2 1, 3 1, 4 1, 5

2, 1 2, 2 2, 3 2, 4 2, 5

oo

}}

GG

BB

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7 8

$$

\xymatrix{

{\begin{matrix} R \\ \oplus \\ S \end{matrix}

}

\ar[r]

&

H

}

$$

: 2

R

S

GG H

7 8

\xymatrix{

& A \ar@{->}[d] \ar@{->}[r] & B \ar@{=>}[ddl]

& A \ar@{->}[d] \ar@{->}[r] & B \ar@/^/@{=>}[ddl] \\& C \ar@{=>}[d] & & C \ar@{=>}[d] & \\

& D & & D & }

: 2

A

GG B

A

GG B

~

C

C

D D

7 8

\xy

( 0, 0)*[o]=\hbox{(0,0)}="o"*\frm{o},

( 20, 0)*[o]=+\hbox{( 20, 0)}="o1" *\frm{o},

( 20, 20)*[o]=+\hbox{( 20, 20)}="o2" *\frm{o},

( 0, 20)*[o]=+\hbox{( 0, 20)}="o3" *\frm{o},

(-20, 20)*[o]=+\hbox{(-20, 20)}="o4" *\frm{o},

(-20, 0)*[o]=+\hbox{(-20, 0)}="o5" *\frm{o},

(-20,-20)*[o]=+\hbox{(-20,-20)}="o6" *\frm{o},

( 0,-20)*[o]=+\hbox{( 0,-20)}="o7" *\frm{o},

( 20,-20)*[o]=+\hbox{( 20,-20)}="o8" *\frm{o},

"o";"o1" **\dir{-} ?>*\dir{>},"o";"o2" **\dir{-} ?>*\dir{>},

"o";"o3" **\dir{-} ?>*\dir{>},

"o";"o4" **\dir{-} ?>*\dir{>},

"o";"o5" **\dir{-} ?>*\dir{>},

"o";"o6" **\dir{-} ?>*\dir{>},

"o";"o7" **\dir{--} ?>*\dir{>},

"o";"o8" **\dir{--} ?>*\dir{>},

\endxy

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: 2

(0,0) ( 20, 0)

( 20, 20)( 0, 20)(-20, 20)

(-20, 0)

(-20,-20) ( 0,-20) ( 20,-20)

GG

ccyy

oo

11

7 8

$$

\xymatrix{

A

\ar@{=>}[r]|-{}="a"

\ar@{=>}[d]|-{}="b"

\save

\POS"a"*{\diagup}

\POS"b"*{\diagdown}

\restore

& B

\\

C}

$$

: 2

A CQ

B

C

7 8

$$

\xymatrix{A\POS[];[d]**\dir{~},[];[dr]**\dir{-} & B & C\\

D & E\POS[];[l]**\dir{.},[];[r]**\dir{~} & F\POS[];[dl]**\dir{~}\\

G & H & I}

$$

: 2

A B C

D E F

G H I

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