TikZ /PGF and other LATEX Tricks

TikZ /PGF and other L A TEX Tricks
Erica Shannon
Contents
1 Resources 1
2 Polygons 2
3 Subgroup Lattices 3
4 Coxeter graphs and Dynkin diagrams 4
5 Tableau(x) 5
6 Graphs of Functions 6
7 Vector Diagrams / Root Systems 11
8 Adding extra space in tables 14
TikZ stands for TikZ ist kein Zeichenprogramm; PGF stands for Portable Graphics Format.
1 Resources
• Comprehensive TikZ Manual:
http://ftp.math.purdue.edu/mirrors/ctan.org/graphics/pgf/base/doc/generic/pgf/pgfmanual.
pdf
• pgfplots Manual:
http://www.bakoma-tex.com/doc/latex/pgfplots/pgfplots.pdf
• A nice tutorial for basic drawing using TikZ :
http://www.math.uni-leipzig.de/~hellmund/LaTeX/pgf-tut.pdf
• List of colors available from the dvipsnames package:
http://en.wikibooks.org/wiki/LaTeX/Colors
1

2 Polygons
Here are some triangles with labels.
1
2
π/3
1
√
2
2
π/4
1
π/6
π/4
√
3
√
2
2
2
Here are some regular polygons, drawn using the foreach command for loops.
n = 3 n = 4 n = 5
n = 6 n = 7 n = 8
The TikZ manual has examples of how to draw pretty much any type of shape or diagram
you might come up with. In particular, there’s a list of cool available node shapes starting
on p.435. (Forbidden sign, clouds, magnifying glass, starburst, etc.)
2

3 Subgroup Lattices
There is supposed to be a TikZ library (graphs) for typesetting graphs. However, I found it
extremely difficult to get this library to work correctly (or at all!). As a result, the examples
here are made using the standard TikZ nodes and lines.
S 3
〈(123)〉
〈(13)〉
〈(23)〉
〈(13)〉
{e}
Here’s a more complicated one:
D 8 = 〈r, s〉
〈s, r 2 〉 〈r〉
〈sr, r 2 〉
〈sr 2 〉 〈s〉 〈r 2 〉 〈sr 3 〉 〈sr〉
{e}
3

4 Coxeter graphs and Dynkin diagrams
Finite Coxeter groups can be classified by their Coxeter graphs.
A n
E 7
· · ·
B n
4
· · ·
E 6 I 2 (m)
m
C n · · ·
4
E 8
F 4
4
D n
· · ·
H 3
5
H 4
5
If Φ is an irreducible root system of rank l, its Dynkin diagram is one of the following (l
vertices in each case):
A l
E 6
· · ·
D l · · ·
B l · · ·
E 7
C l · · ·
E 8
F 4
G 2
4

5 Tableau(x)
Here’s a standard Young tableau.
1 4 5 10 11
2 6 8
3 9 12
7
Here’s a domino tableau.
1
4
3
6
5
2
Both of these images use macros from Tyson Gern – you’ll need to copy these from the
header section.
5

6 Graphs of Functions
Here’s a simple graph of the function f(x) = x − x2
2 + 1.
3
2
1
−2 −1 1 2
−1
−2
−3
Here’s a graph of a piecewise linear function, with background grid.
2
1
−2 −1 1 2 3
−1
−2
−3
6

Here’s a graph of f(x) = sin(x) − cos(x), with a shaded region.
1
y
f(x) = sin(x) − cos(x)
x
π
4
π
2
3π
4
π
5π
4
3π
2
−1
Here’s another graph, this time with an annoyingly starred region. See p.393 of the TikZ
manual for a list of patterns.
10
y
8
6
f(x) = 6 − 4 sin(x)
4
2
1 2 3 4
x
Here’s a function and its tangent line. This graph has a legend.
1
ln(2)
y
1 2
x
f(x) = ln(x)
y = x − 1
7

Here are some various blank axes for a student to draw a graph on.
4
y
3
2
1
x
−6 −5 −4 −3 −2 −1 1 2 3 4 5 6
−1
−2
−3
−4
y
3
2
1
x
−5 −4 −3 −2 −1 1 2 3 4 5
−1
−2
−3
8

Here are some 3d graphs.
0.5
5
−0.5
2
4
6
8
10
−2
−2
2
2
9

Here is a 3d plot of a parameterized curve:
2
−1
−1
1
1
And a parameterized torus:
10

7 Vector Diagrams / Root Systems
Here are some 2d root systems.
y
α 2 = ε 2 ˜α = ε 1 + ε 2
Type B 2
x
α 1 = ε 1 − ε 2
y
α 2 = 2ε 2
˜α = 2ε 1
Type C 2
x
α 1 = ε 1 − ε 2
y (
α 2 =
0, √ 3
2
)
= ( 0, cos ( ))
π
6
x
Type I 2 (6)
α 1 =
(
1
, − √ )
3
= ( sin ( ) (
π
2 2
6 , − cos π
))
6
11

Here are some root systems in 3d, using tikz-3dplot.
z
Type A 2
α 1 = ε 1 − ε 2
y
α 2 = ε 2 − ε 3
˜α = ε 1 − ε 3
x
s ε1 −ε 2
z
α 3 = ε 2 + ε 3
Type D 3
12
α 1 = ε 1 − ε 2
α 2 = ε 2 − ε 3
˜α = ε 1 + ε 2
y
x

z
α 3 = ε 3
˜α = ε 1 + ε 2
Type B 3
α 1 = ε 1 − ε 2
α 2 = ε 2 − ε 3
y
x
z
α 3 = 2ε 3
α 1 = ε 1 − ε 2
α 2 = ε 2 − ε 3
˜α = 2ε 1
Type C 3
y
x
13

8 Adding extra space in tables
Here’s a table with a little extra height added to the columns and extra padding added in
the cells:
x 0 π/4 π/2 3π/4 π
cos(x) 1
sin(x) 0
√
2/2 0 −
√
2/2 −1
√
2/2 1
√
2/2 0
14