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-rw-r--r--vorlesungen/punktgruppen/crystals.py22
-rw-r--r--vorlesungen/punktgruppen/script.pdfbin25412 -> 25619 bytes
-rw-r--r--vorlesungen/punktgruppen/script.tex6
3 files changed, 21 insertions, 7 deletions
diff --git a/vorlesungen/punktgruppen/crystals.py b/vorlesungen/punktgruppen/crystals.py
index 76dee1f..136481b 100644
--- a/vorlesungen/punktgruppen/crystals.py
+++ b/vorlesungen/punktgruppen/crystals.py
@@ -377,14 +377,14 @@ class AlgebraicSymmetries(Scene):
hom_brace = Brace(hom_bracegrp, direction=RIGHT)
hom_text = Tex("Homomorphismus").next_to(hom_brace.get_tip(), RIGHT)
- hom_text_short = MathTex(r"G \simeq Z_4").next_to(hom_brace.get_tip(), RIGHT)
+ hom_text_short = MathTex(r"\mathrm{Hom}(G, Z_4)").next_to(hom_brace.get_tip(), RIGHT)
self.play(Create(hom_brace))
self.play(Write(hom_text))
self.play(ReplacementTransform(hom_text, hom_text_short))
self.wait()
- self.play(FadeOut(hom_brace), FadeOut(hom_text_short))
+ # self.play(FadeOut(hom_brace), FadeOut(hom_text_short))
# add the isomorphism part
isomorphism = Tex(r"\(\phi\) ist bijektiv")
@@ -397,8 +397,9 @@ class AlgebraicSymmetries(Scene):
iso_text = Tex("Isomorphismus").next_to(iso_brace.get_tip(), RIGHT)
iso_text_short = MathTex("Z_4 \cong G").next_to(iso_brace.get_tip(), RIGHT)
- self.play(Create(iso_brace))
- self.play(Write(iso_text))
+ self.play(
+ ReplacementTransform(hom_brace, iso_brace),
+ ReplacementTransform(hom_text_short, iso_text))
self.wait()
self.play(ReplacementTransform(iso_text, iso_text_short))
@@ -464,9 +465,18 @@ class AlgebraicSymmetries(Scene):
self.wait(3)
def matrices(self):
- question = MathTex(r"D_n \cong \,? \\ S_n \cong \,? \\ A_n \cong \,?")
- question.scale(1.5)
+ question = MathTex(
+ r"D_n &\cong \,? \\"
+ r"S_n &\cong \,? \\"
+ r"A_n &\cong \,?").scale(1.5)
+
+ answer = MathTex(
+ r"D_n &\cong \,?\\"
+ r"S_4 &\cong \mathrm{Aut}(Q_8) \\"
+ r"A_5 &\cong \mathrm{PSL}_2 (5)").scale(1.5)
self.play(Write(question))
+ self.wait()
+ self.play(ReplacementTransform(question, answer))
self.wait(3)
diff --git a/vorlesungen/punktgruppen/script.pdf b/vorlesungen/punktgruppen/script.pdf
index 293b248..a701d6a 100644
--- a/vorlesungen/punktgruppen/script.pdf
+++ b/vorlesungen/punktgruppen/script.pdf
Binary files differ
diff --git a/vorlesungen/punktgruppen/script.tex b/vorlesungen/punktgruppen/script.tex
index 2a6d95c..fe095fb 100644
--- a/vorlesungen/punktgruppen/script.tex
+++ b/vorlesungen/punktgruppen/script.tex
@@ -3,7 +3,7 @@
\usepackage[cm]{manuscript}
\usepackage{xcolor}
-\newcommand{\scene}[1]{\noindent[ #1 ]\par}
+\newcommand{\scene}[1]{\par\noindent[ #1 ]\par}
\newenvironment{totranslate}{\color{blue!70!black}}{}
\begin{document}
@@ -56,6 +56,10 @@ We'll start with geometric symmetries as they are the simplest to grasp.
\scene{Alternierende Gruppe}
\section{Algebra}
+\begin{totranslate}
+Let's now move into something seemingly unrelated: \emph{algebra}.
+\scene{Complex numbers and cyclic groups}
+\end{totranslate}
\section{Krystalle}