aboutsummaryrefslogtreecommitdiffstats
path: root/vorlesungen/punktgruppen
diff options
context:
space:
mode:
Diffstat (limited to 'vorlesungen/punktgruppen')
-rw-r--r--vorlesungen/punktgruppen/crystals.py269
-rw-r--r--vorlesungen/punktgruppen/poetry.lock591
-rw-r--r--vorlesungen/punktgruppen/pyproject.toml15
3 files changed, 875 insertions, 0 deletions
diff --git a/vorlesungen/punktgruppen/crystals.py b/vorlesungen/punktgruppen/crystals.py
new file mode 100644
index 0000000..0f97a0f
--- /dev/null
+++ b/vorlesungen/punktgruppen/crystals.py
@@ -0,0 +1,269 @@
+from manim import *
+
+import math as m
+import numpy as np
+
+# configure style
+config.background_color = '#202020'
+config.tex_template.add_to_preamble(
+ r"\usepackage[p,osf]{scholax}"
+ r"\usepackage{amsmath}"
+ r"\usepackage[scaled=1.075,ncf,vvarbb]{newtxmath}"
+)
+
+# scenes
+class Geometric2DSymmetries(Scene):
+ def construct(self):
+ # title
+ title = Tex(r"Geometrische \\ Symmetrien")
+ title.scale(1.5)
+ self.play(Write(title))
+ self.wait()
+ self.play(FadeOut(title))
+ self.wait()
+
+ self.intro()
+ self.cyclic()
+ self.dihedral()
+
+ def intro(self):
+ # create square
+ square = Square()
+ square.set_fill(PINK, opacity=.5)
+ self.play(SpinInFromNothing(square))
+ self.wait()
+
+ # the action of doing nothing
+ action = MathTex(r"1")
+ self.play(Write(action))
+ self.play(ApplyMethod(square.scale, 1.2))
+ self.play(ApplyMethod(square.scale, 1/1.2))
+ self.play(FadeOut(action))
+
+ # show some reflections
+ axis = DashedLine(2 * LEFT, 2 * RIGHT)
+ sigma = MathTex(r"\sigma")
+ sigma.next_to(axis, RIGHT)
+
+ self.play(Create(axis))
+ self.play(Write(sigma))
+
+ self.play(ApplyMethod(square.flip, RIGHT))
+ self.wait()
+
+ for d in [UP + RIGHT, UP]:
+ self.play(
+ Rotate(axis, PI/4),
+ Rotate(sigma, PI/4, about_point=ORIGIN))
+
+ self.play(Rotate(sigma, -PI/4), run_time=.5)
+ self.play(ApplyMethod(square.flip, d))
+
+ self.play(
+ FadeOutAndShift(sigma),
+ Uncreate(axis))
+
+ # show some rotations
+ dot = Dot(UP + RIGHT)
+ figure = VGroup()
+ figure.add(square)
+ figure.add(dot)
+
+ rot = MathTex(r"r")
+ self.play(Write(rot), Create(dot))
+
+ last = rot
+ for newrot in map(MathTex, [r"r", r"r^2", r"r^3"]):
+ self.play(
+ ReplacementTransform(last, newrot),
+ Rotate(figure, PI/2, about_point=ORIGIN))
+ self.wait()
+ last = newrot
+
+ self.play(Uncreate(dot), FadeOut(square), FadeOut(last))
+
+
+ def cyclic(self):
+ # create symmetric figure
+ figure = VGroup()
+ prev = [1.5, 0, 0]
+ for i in range(1,6):
+ pos = [
+ 1.5*m.cos(2 * PI/5 * i),
+ 1.5*m.sin(2 * PI/5 * i),
+ 0
+ ]
+
+ if prev:
+ line = Line(prev, pos)
+ figure.add(line)
+
+ dot = Dot(pos, radius=.1)
+ if i == 5:
+ dot.set_fill(RED)
+
+ prev = pos
+ figure.add(dot)
+
+ group = MathTex(r"G = \langle r \rangle")
+ self.play(Write(group), run_time = 2)
+ self.wait()
+ self.play(ApplyMethod(group.to_corner, UP))
+
+ actions = map(MathTex, [r"1", r"r", r"r^2", r"r^3", r"r^4", r"1"])
+ action = next(actions, MathTex(r"r"))
+
+ self.play(Create(figure))
+ self.play(Write(action))
+ self.wait()
+
+ for i in range(5):
+ newaction = next(actions, MathTex(r"r"))
+ self.play(
+ ReplacementTransform(action, newaction),
+ Rotate(figure, 2*PI/5, about_point=ORIGIN))
+ action = newaction
+
+ self.play(Uncreate(figure), FadeOut(action))
+
+ whole_group = MathTex(
+ r"G = \langle r \rangle"
+ r"= \left\{1, r, r^2, r^3, r^4 \right\}")
+
+ self.play(ApplyMethod(group.move_to, ORIGIN))
+ self.play(ReplacementTransform(group, whole_group))
+ self.wait()
+
+ cyclic = MathTex(
+ r"C_n = \langle r \rangle"
+ r"= \left\{1, r, r^2, \dots, r^n \right\}")
+
+ cyclic_title = Tex(r"Zyklische Gruppe")
+ cyclic_title.next_to(cyclic, UP * 2)
+
+ cyclic.scale(1.2)
+ cyclic_title.scale(1.2)
+
+ self.play(ReplacementTransform(whole_group, cyclic))
+ self.play(FadeInFrom(cyclic_title, UP))
+
+ self.wait(5)
+ self.play(FadeOut(cyclic), FadeOut(cyclic_title))
+
+ def dihedral(self):
+ # create square
+ square = Square()
+ square.set_fill(PINK, opacity=.5)
+
+ # generator equation
+ group = MathTex(
+ r"G = \langle \sigma, r \,|\,",
+ r"\sigma^2 = 1,",
+ r"r^4 = 1,",
+ r"(\sigma r)^2 = 1 \rangle")
+
+ self.play(Write(group), run_time = 2)
+ self.wait()
+ self.play(ApplyMethod(group.to_corner, UP))
+ self.play(FadeIn(square))
+
+ axis = DashedLine(2 * LEFT, 2 * RIGHT)
+ sigma = MathTex(r"\sigma^2 = 1")
+ sigma.next_to(axis, RIGHT)
+ self.play(Create(axis), Write(sigma))
+ self.play(ApplyMethod(square.flip, RIGHT))
+ self.play(ApplyMethod(square.flip, RIGHT))
+ self.play(Uncreate(axis), FadeOut(sigma))
+
+ # rotations
+ dot = Dot(UP + RIGHT)
+ rot = MathTex(r"r^4 = 1")
+ rot.next_to(square, DOWN * 3)
+
+ figure = VGroup()
+ figure.add(dot)
+ figure.add(square)
+
+ self.play(Write(rot), Create(dot))
+ for i in range(4):
+ self.play(Rotate(figure, PI/2))
+ self.play(FadeOut(rot), Uncreate(dot))
+
+ # rotation and flip
+ action = MathTex(r"(\sigma r)^2 = 1")
+ action.next_to(square, DOWN * 5)
+
+ dot = Dot(UP + RIGHT)
+ axis = DashedLine(2 * LEFT, 2 * RIGHT)
+ self.play(Create(dot), Create(axis), Write(action))
+
+ figure = VGroup()
+ figure.add(dot)
+ figure.add(square)
+
+ for i in range(2):
+ self.play(Rotate(figure, PI/2))
+ self.play(ApplyMethod(figure.flip, RIGHT))
+ self.wait()
+
+ self.play(Uncreate(dot), Uncreate(axis), FadeOut(action))
+ self.play(FadeOut(square))
+
+ # equation for the whole
+ whole_group = MathTex(
+ r"G &= \langle \sigma, r \,|\,"
+ r"\sigma^2 = r^4 = (\sigma r)^2 = 1 \rangle \\"
+ r"&= \left\{"
+ r"1, r, r^2, r^3, \sigma, \sigma r, \sigma r^2, \sigma r^3"
+ r"\right\}")
+
+ self.play(ApplyMethod(group.move_to, ORIGIN))
+ self.play(ReplacementTransform(group, whole_group))
+ self.wait(2)
+
+ dihedral = MathTex(
+ r"D_n &= \langle \sigma, r \,|\,"
+ r"\sigma^2 = r^n = (\sigma r)^2 = 1 \rangle \\"
+ r"&= \left\{"
+ r"1, r, r^2, \dots, \sigma, \sigma r, \sigma r^2, \dots"
+ r"\right\}")
+
+ dihedral_title = Tex(r"Diedergruppe: Symmetrien eines \(n\)-gons")
+ dihedral_title.next_to(dihedral, UP * 2)
+
+ dihedral.scale(1.2)
+ dihedral_title.scale(1.2)
+
+ self.play(ReplacementTransform(whole_group, dihedral))
+ self.play(FadeInFrom(dihedral_title, UP))
+
+ self.wait(5)
+ self.play(FadeOut(dihedral), FadeOut(dihedral_title))
+
+
+class Geometric3DSymmetries(ThreeDScene):
+ def construct(self):
+ self.symmetric()
+
+ def symmetric(self):
+ self.renderer.camera.light_source.move_to(3*IN) # changes the source of the light
+ self.set_camera_orientation(phi=60 * DEGREES, theta=-20 * DEGREES)
+
+ cube = Cube()
+ axes = ThreeDAxes()
+
+ axis = np.array([2,2,2])
+ line = DashedLine(-axis, axis)
+
+ self.play(Create(axes), Create(cube))
+ self.play(Create(line))
+
+ self.play(ApplyMethod(cube.rotate, PI, axis / abs(axis)))
+
+ self.begin_ambient_camera_rotation(rate=0.1)
+ self.wait(7)
+
+
+class AlgebraicSymmetries(Scene):
+ def construct(self):
+ pass
diff --git a/vorlesungen/punktgruppen/poetry.lock b/vorlesungen/punktgruppen/poetry.lock
new file mode 100644
index 0000000..13c5100
--- /dev/null
+++ b/vorlesungen/punktgruppen/poetry.lock
@@ -0,0 +1,591 @@
+[[package]]
+name = "colorama"
+version = "0.4.4"
+description = "Cross-platform colored terminal text."
+category = "main"
+optional = false
+python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*, !=3.4.*"
+
+[[package]]
+name = "colour"
+version = "0.1.5"
+description = "converts and manipulates various color representation (HSL, RVB, web, X11, ...)"
+category = "main"
+optional = false
+python-versions = "*"
+
+[package.extras]
+test = ["nose"]
+
+[[package]]
+name = "commonmark"
+version = "0.9.1"
+description = "Python parser for the CommonMark Markdown spec"
+category = "main"
+optional = false
+python-versions = "*"
+
+[package.extras]
+test = ["flake8 (==3.7.8)", "hypothesis (==3.55.3)"]
+
+[[package]]
+name = "decorator"
+version = "4.4.2"
+description = "Decorators for Humans"
+category = "main"
+optional = false
+python-versions = ">=2.6, !=3.0.*, !=3.1.*"
+
+[[package]]
+name = "glcontext"
+version = "2.3.3"
+description = "Portable OpenGL Context"
+category = "main"
+optional = false
+python-versions = "*"
+
+[[package]]
+name = "importlib-metadata"
+version = "3.10.0"
+description = "Read metadata from Python packages"
+category = "main"
+optional = false
+python-versions = ">=3.6"
+
+[package.dependencies]
+typing-extensions = {version = ">=3.6.4", markers = "python_version < \"3.8\""}
+zipp = ">=0.5"
+
+[package.extras]
+docs = ["sphinx", "jaraco.packaging (>=8.2)", "rst.linker (>=1.9)"]
+testing = ["pytest (>=4.6)", "pytest-checkdocs (>=2.4)", "pytest-flake8", "pytest-cov", "pytest-enabler (>=1.0.1)", "packaging", "pep517", "pyfakefs", "flufl.flake8", "pytest-black (>=0.3.7)", "pytest-mypy", "importlib-resources (>=1.3)"]
+
+[[package]]
+name = "manim"
+version = "0.5.0"
+description = "Animation engine for explanatory math videos."
+category = "main"
+optional = false
+python-versions = ">=3.6.2,<4.0.0"
+
+[package.dependencies]
+colour = "*"
+importlib-metadata = {version = "*", markers = "python_version < \"3.8\""}
+manimpango = ">=0.2.4,<0.3.0"
+mapbox-earcut = ">=0.12.10,<0.13.0"
+moderngl = ">=5.6.3,<6.0.0"
+moderngl-window = ">=2.3.0,<3.0.0"
+networkx = ">=2.5,<3.0"
+numpy = ">=1.9,<2.0"
+Pillow = "*"
+pycairo = ">=1.19,<2.0"
+pydub = "*"
+pygments = "*"
+rich = ">=6.0,<7.0"
+scipy = "*"
+tqdm = "*"
+
+[package.extras]
+webgl_renderer = ["grpcio (>=1.33.0,<1.34.0)", "grpcio-tools (>=1.33.0,<1.34.0)", "watchdog"]
+jupyterlab = ["jupyterlab (>=3.0,<4.0)"]
+
+[[package]]
+name = "manimpango"
+version = "0.2.5.post0"
+description = "Bindings for Pango for using with Manim."
+category = "main"
+optional = false
+python-versions = ">=3.6"
+
+[[package]]
+name = "mapbox-earcut"
+version = "0.12.10"
+description = "Python bindings for the mapbox earcut C++ polygon triangulation library."
+category = "main"
+optional = false
+python-versions = "*"
+
+[package.dependencies]
+numpy = "*"
+
+[[package]]
+name = "moderngl"
+version = "5.6.4"
+description = "ModernGL: High performance rendering for Python 3"
+category = "main"
+optional = false
+python-versions = "*"
+
+[package.dependencies]
+glcontext = ">=2,<3"
+
+[[package]]
+name = "moderngl-window"
+version = "2.3.0"
+description = "A cross platform helper library for ModernGL making window creation and resource loading simple"
+category = "main"
+optional = false
+python-versions = ">=3.5"
+
+[package.dependencies]
+moderngl = "<6"
+numpy = ">=1.16,<2"
+Pillow = ">=5"
+pyglet = ">=1.5.8,<2"
+pyrr = ">=0.10.3,<1"
+
+[package.extras]
+pysdl2 = ["pysdl2"]
+pyside2 = ["PySide2 (<6)"]
+glfw = ["glfw"]
+pygame = ["pygame (==2.0.0.dev10)"]
+pyqt5 = ["pyqt5"]
+pywavefront = ["pywavefront (>=1.2.0,<2)"]
+tk = ["pyopengltk (>=0.0.3)"]
+trimesh = ["trimesh (>=3.2.6,<4)", "scipy (>=1.3.2)"]
+
+[[package]]
+name = "multipledispatch"
+version = "0.6.0"
+description = "Multiple dispatch"
+category = "main"
+optional = false
+python-versions = "*"
+
+[package.dependencies]
+six = "*"
+
+[[package]]
+name = "networkx"
+version = "2.5.1"
+description = "Python package for creating and manipulating graphs and networks"
+category = "main"
+optional = false
+python-versions = ">=3.6"
+
+[package.dependencies]
+decorator = ">=4.3,<5"
+
+[package.extras]
+all = ["numpy", "scipy", "pandas", "matplotlib", "pygraphviz", "pydot", "pyyaml", "lxml", "pytest"]
+gdal = ["gdal"]
+lxml = ["lxml"]
+matplotlib = ["matplotlib"]
+numpy = ["numpy"]
+pandas = ["pandas"]
+pydot = ["pydot"]
+pygraphviz = ["pygraphviz"]
+pytest = ["pytest"]
+pyyaml = ["pyyaml"]
+scipy = ["scipy"]
+
+[[package]]
+name = "numpy"
+version = "1.20.2"
+description = "NumPy is the fundamental package for array computing with Python."
+category = "main"
+optional = false
+python-versions = ">=3.7"
+
+[[package]]
+name = "pillow"
+version = "8.2.0"
+description = "Python Imaging Library (Fork)"
+category = "main"
+optional = false
+python-versions = ">=3.6"
+
+[[package]]
+name = "pycairo"
+version = "1.20.0"
+description = "Python interface for cairo"
+category = "main"
+optional = false
+python-versions = ">=3.6, <4"
+
+[[package]]
+name = "pydub"
+version = "0.25.1"
+description = "Manipulate audio with an simple and easy high level interface"
+category = "main"
+optional = false
+python-versions = "*"
+
+[[package]]
+name = "pyglet"
+version = "1.5.15"
+description = "Cross-platform windowing and multimedia library"
+category = "main"
+optional = false
+python-versions = "*"
+
+[[package]]
+name = "pygments"
+version = "2.8.1"
+description = "Pygments is a syntax highlighting package written in Python."
+category = "main"
+optional = false
+python-versions = ">=3.5"
+
+[[package]]
+name = "pyrr"
+version = "0.10.3"
+description = "3D mathematical functions using NumPy"
+category = "main"
+optional = false
+python-versions = "*"
+
+[package.dependencies]
+multipledispatch = "*"
+numpy = "*"
+
+[[package]]
+name = "rich"
+version = "6.2.0"
+description = "Render rich text, tables, progress bars, syntax highlighting, markdown and more to the terminal"
+category = "main"
+optional = false
+python-versions = ">=3.6,<4.0"
+
+[package.dependencies]
+colorama = ">=0.4.0,<0.5.0"
+commonmark = ">=0.9.0,<0.10.0"
+pygments = ">=2.6.0,<3.0.0"
+typing-extensions = ">=3.7.4,<4.0.0"
+
+[package.extras]
+jupyter = ["ipywidgets (>=7.5.1,<8.0.0)"]
+
+[[package]]
+name = "scipy"
+version = "1.6.1"
+description = "SciPy: Scientific Library for Python"
+category = "main"
+optional = false
+python-versions = ">=3.7"
+
+[package.dependencies]
+numpy = ">=1.16.5"
+
+[[package]]
+name = "six"
+version = "1.15.0"
+description = "Python 2 and 3 compatibility utilities"
+category = "main"
+optional = false
+python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*"
+
+[[package]]
+name = "tqdm"
+version = "4.60.0"
+description = "Fast, Extensible Progress Meter"
+category = "main"
+optional = false
+python-versions = "!=3.0.*,!=3.1.*,!=3.2.*,!=3.3.*,>=2.7"
+
+[package.extras]
+dev = ["py-make (>=0.1.0)", "twine", "wheel"]
+notebook = ["ipywidgets (>=6)"]
+telegram = ["requests"]
+
+[[package]]
+name = "typing-extensions"
+version = "3.7.4.3"
+description = "Backported and Experimental Type Hints for Python 3.5+"
+category = "main"
+optional = false
+python-versions = "*"
+
+[[package]]
+name = "zipp"
+version = "3.4.1"
+description = "Backport of pathlib-compatible object wrapper for zip files"
+category = "main"
+optional = false
+python-versions = ">=3.6"
+
+[package.extras]
+docs = ["sphinx", "jaraco.packaging (>=8.2)", "rst.linker (>=1.9)"]
+testing = ["pytest (>=4.6)", "pytest-checkdocs (>=1.2.3)", "pytest-flake8", "pytest-cov", "pytest-enabler", "jaraco.itertools", "func-timeout", "pytest-black (>=0.3.7)", "pytest-mypy"]
+
+[metadata]
+lock-version = "1.1"
+python-versions = "^3.7"
+content-hash = "f990b445406f5bbce3e53cd28ef3362be09615b40062f11233a62f99bcd59a79"
+
+[metadata.files]
+colorama = [
+ {file = "colorama-0.4.4-py2.py3-none-any.whl", hash = "sha256:9f47eda37229f68eee03b24b9748937c7dc3868f906e8ba69fbcbdd3bc5dc3e2"},
+ {file = "colorama-0.4.4.tar.gz", hash = "sha256:5941b2b48a20143d2267e95b1c2a7603ce057ee39fd88e7329b0c292aa16869b"},
+]
+colour = [
+ {file = "colour-0.1.5-py2.py3-none-any.whl", hash = "sha256:33f6db9d564fadc16e59921a56999b79571160ce09916303d35346dddc17978c"},
+ {file = "colour-0.1.5.tar.gz", hash = "sha256:af20120fefd2afede8b001fbef2ea9da70ad7d49fafdb6489025dae8745c3aee"},
+]
+commonmark = [
+ {file = "commonmark-0.9.1-py2.py3-none-any.whl", hash = "sha256:da2f38c92590f83de410ba1a3cbceafbc74fee9def35f9251ba9a971d6d66fd9"},
+ {file = "commonmark-0.9.1.tar.gz", hash = "sha256:452f9dc859be7f06631ddcb328b6919c67984aca654e5fefb3914d54691aed60"},
+]
+decorator = [
+ {file = "decorator-4.4.2-py2.py3-none-any.whl", hash = "sha256:41fa54c2a0cc4ba648be4fd43cff00aedf5b9465c9bf18d64325bc225f08f760"},
+ {file = "decorator-4.4.2.tar.gz", hash = "sha256:e3a62f0520172440ca0dcc823749319382e377f37f140a0b99ef45fecb84bfe7"},
+]
+glcontext = [
+ {file = "glcontext-2.3.3-cp35-cp35m-macosx_10_9_x86_64.whl", hash = "sha256:f518379551a2b60d45c1eec23759cb1ee85517d4b943fc31530b6ab13e304fe4"},
+ {file = "glcontext-2.3.3-cp35-cp35m-manylinux1_i686.whl", hash = "sha256:d3a8fbc27f43766d168bae02474790459f4050adeb25832ff0a227cc5006c933"},
+ {file = "glcontext-2.3.3-cp35-cp35m-manylinux1_x86_64.whl", hash = "sha256:aa1d9e4f9bd6eda3d195f39c47c849b3721caf65813a4ad1e006a20fa02d33e4"},
+ {file = "glcontext-2.3.3-cp35-cp35m-win32.whl", hash = "sha256:8b4ee9cb5573e2ae313e1681fdfe2c5ac5b8780b20e857daf8f95e318c36aa2f"},
+ {file = "glcontext-2.3.3-cp35-cp35m-win_amd64.whl", hash = "sha256:b92ca447a04c3a05afb3974a6e94f584e60f55444c3e55ecd31fbfacad6ee07a"},
+ {file = "glcontext-2.3.3-cp36-cp36m-macosx_10_9_x86_64.whl", hash = "sha256:b102a00e7bbce03a5e8bb02692197f96fcb77c51dbe133859b70afa361eef5b7"},
+ {file = "glcontext-2.3.3-cp36-cp36m-manylinux1_i686.whl", hash = "sha256:ea3975a9d86a97b49f9524713c8e3f0df92044715cfbe5a24102e10762673b23"},
+ {file = "glcontext-2.3.3-cp36-cp36m-manylinux1_x86_64.whl", hash = "sha256:5f2e7fb61ea1f69c44db0799f8929ea66ad207619c18063ae60cfb26ad0f447f"},
+ {file = "glcontext-2.3.3-cp36-cp36m-win32.whl", hash = "sha256:bf8c3fa5f3a8962c9bcc03a869a0bb178bd1681619225b9f0a070a65ff3f766d"},
+ {file = "glcontext-2.3.3-cp36-cp36m-win_amd64.whl", hash = "sha256:e0b637f2ac1c2dd1e0dbfcbad6d7be2dae75290f9af8f82aa67aa55b977766e1"},
+ {file = "glcontext-2.3.3-cp37-cp37m-macosx_10_9_x86_64.whl", hash = "sha256:2002d29dee90e9ba800c8699e13e1ff8b0fa1292a7c5bb0a98ef50b5f6cd3f14"},
+ {file = "glcontext-2.3.3-cp37-cp37m-manylinux1_i686.whl", hash = "sha256:941be8972ad64e70080ad4702c037c64c09d1378ddd9b1b4576b957bc2d7f1c2"},
+ {file = "glcontext-2.3.3-cp37-cp37m-manylinux1_x86_64.whl", hash = "sha256:0eb69c4add7f724017169bcefc2a8ef8ce053183e9384cc4770162e934090592"},
+ {file = "glcontext-2.3.3-cp37-cp37m-win32.whl", hash = "sha256:f63aed2116907225f7392921df790a391fd1a843cd1af0756dcd533e9d3ecf2b"},
+ {file = "glcontext-2.3.3-cp37-cp37m-win_amd64.whl", hash = "sha256:2fa9b939c15f5f7e63110a1021e8d20341c03921b8d3aebbb4bb191f11414d86"},
+ {file = "glcontext-2.3.3-cp38-cp38-macosx_10_9_x86_64.whl", hash = "sha256:44f95953bbd6a26caa9489b4f838b106470ede432c5ef837cd3e0d3657ca2a06"},
+ {file = "glcontext-2.3.3-cp38-cp38-manylinux1_i686.whl", hash = "sha256:843d3361bf46aec487f268bb7f680700166640995a82424fa86e53f428dc43ae"},
+ {file = "glcontext-2.3.3-cp38-cp38-manylinux1_x86_64.whl", hash = "sha256:be3e25a8595976699b6d30a2619ca4faf7bd5e60ff38dcd4445fa38a8f3b2cf9"},
+ {file = "glcontext-2.3.3-cp38-cp38-win32.whl", hash = "sha256:7abbd227bf9e4e62ec196360fa0f440143a66b7aae3d3deb7960b87aac654043"},
+ {file = "glcontext-2.3.3-cp38-cp38-win_amd64.whl", hash = "sha256:b91010d033789d1f876789e4aa4e6498e87cd284b4d0cb7a4aa1b7e620caaf57"},
+ {file = "glcontext-2.3.3-cp39-cp39-macosx_10_9_x86_64.whl", hash = "sha256:0a851f569f165a13f8fedf60dd4f2831f7c2ffbb9bc9f867d6e0e3fdd1846c8d"},
+ {file = "glcontext-2.3.3-cp39-cp39-win32.whl", hash = "sha256:f36935ba84e8c52ed22bb9f683875bdf1690abd318ae704f40511f1afca5f71a"},
+ {file = "glcontext-2.3.3-cp39-cp39-win_amd64.whl", hash = "sha256:69e3a04c677e4925c0b6daf5efc5469a86d0982b05bb1d0ca29bce57f4aaf7d1"},
+ {file = "glcontext-2.3.3.tar.gz", hash = "sha256:f86a6c4ad99f941623911f964da74c443dc3f833fac7eb03cd485fae82acb80c"},
+]
+importlib-metadata = [
+ {file = "importlib_metadata-3.10.0-py3-none-any.whl", hash = "sha256:d2d46ef77ffc85cbf7dac7e81dd663fde71c45326131bea8033b9bad42268ebe"},
+ {file = "importlib_metadata-3.10.0.tar.gz", hash = "sha256:c9db46394197244adf2f0b08ec5bc3cf16757e9590b02af1fca085c16c0d600a"},
+]
+manim = [
+ {file = "manim-0.5.0-py3-none-any.whl", hash = "sha256:1a164c8caa6058f67c6fcd7cf1e6f5dbb9833b292117885dc470dabad1cc00c7"},
+ {file = "manim-0.5.0.tar.gz", hash = "sha256:e4284648cbb5d463c6dbced1d4e60fa9b68c14f4bb3b10c8eab0f8f49ca5da88"},
+]
+manimpango = [
+ {file = "ManimPango-0.2.5.post0-cp36-cp36m-macosx_10_9_x86_64.whl", hash = "sha256:53f754594ccedeaf464028777d4502fb31f2251b9dca7e99b40786b3e4ff394d"},
+ {file = "ManimPango-0.2.5.post0-cp36-cp36m-win32.whl", hash = "sha256:ac33cc00a89aabe7459043b7aab8851e4ec4c7fa78cea2b3dacb618b2b03c98b"},
+ {file = "ManimPango-0.2.5.post0-cp36-cp36m-win_amd64.whl", hash = "sha256:87e205f5a35ff5504104cd30b8d086e9f97c17f95cf490de7cc1d4aa8c2a8425"},
+ {file = "ManimPango-0.2.5.post0-cp37-cp37m-macosx_10_9_x86_64.whl", hash = "sha256:70e59f888ca5ad0be37777f761cee8fb3d6e28c5d949e5da13f727326b46da60"},
+ {file = "ManimPango-0.2.5.post0-cp37-cp37m-win32.whl", hash = "sha256:d9cc5ac80dd363fd4f3fa233f7fad74e9749965b6e4af10a2174f946fe1d9813"},
+ {file = "ManimPango-0.2.5.post0-cp37-cp37m-win_amd64.whl", hash = "sha256:3bef549783fc5e3f39598880e7cc41bb44dc2e37ceb8c7e20f0381fd8d67b3e8"},
+ {file = "ManimPango-0.2.5.post0-cp38-cp38-macosx_10_9_x86_64.whl", hash = "sha256:978bcf4c6cf145f723ec551ed18a1959f6952f100d61c7b4431939ee850f9308"},
+ {file = "ManimPango-0.2.5.post0-cp38-cp38-win32.whl", hash = "sha256:db877a3a037739ce2f647f747bc750c7e9a881ce5175a4ad764170f24fb2d68a"},
+ {file = "ManimPango-0.2.5.post0-cp38-cp38-win_amd64.whl", hash = "sha256:2876c64724a73893ba22c250ddf603724865c650a925ddca76102eea0e489373"},
+ {file = "ManimPango-0.2.5.post0-cp39-cp39-macosx_10_9_x86_64.whl", hash = "sha256:e3694ae99ef758a8eaf847f77b0fa2bf7318ed2ee55a32b3a3bb155dd2d6ec9b"},
+ {file = "ManimPango-0.2.5.post0-cp39-cp39-win32.whl", hash = "sha256:139469a6130270e3cf94c4b01fa9b17dc516170a11b901ff0ce0f6cdff6752e9"},
+ {file = "ManimPango-0.2.5.post0-cp39-cp39-win_amd64.whl", hash = "sha256:aad57df6ec62585f52c662b84f2d5ff2c686daa8ca753326b6cde8b798c4da96"},
+ {file = "ManimPango-0.2.5.post0.tar.gz", hash = "sha256:c33d073d4389ad93bbac13029b8a0da5d8ee0b8fe7f282379ff95012e34d324e"},
+]
+mapbox-earcut = [
+ {file = "mapbox_earcut-0.12.10-cp27-cp27m-macosx_10_9_x86_64.whl", hash = "sha256:2aaf7bdb002d36d38d1412088329a9176de3fcadc24a53951b76e49a27e34d78"},
+ {file = "mapbox_earcut-0.12.10-cp27-cp27m-manylinux2010_i686.whl", hash = "sha256:ddda755c63cf5f9bff338cd375e4e937035898827fef960102e2f4c8984cb068"},
+ {file = "mapbox_earcut-0.12.10-cp27-cp27m-manylinux2010_x86_64.whl", hash = "sha256:3475382dd573986d0dfe3f6b6fd3b1f576e74af7fd7d95066d2506ce8f4b38e5"},
+ {file = "mapbox_earcut-0.12.10-cp27-cp27mu-manylinux2010_i686.whl", hash = "sha256:f2b9079df53258766c3108a1c46a7942963c26f216f9bc2d216f93eeed1da76c"},
+ {file = "mapbox_earcut-0.12.10-cp27-cp27mu-manylinux2010_x86_64.whl", hash = "sha256:124cc27486d0e9c9b185a6d80e551e736e2bc81d28e077e297ac39980c14e588"},
+ {file = "mapbox_earcut-0.12.10-cp35-cp35m-macosx_10_9_x86_64.whl", hash = "sha256:04228ff704d5edc49d71ba3fd07c4a8621a4f416d2ad5c2504a80d0cabd51c18"},
+ {file = "mapbox_earcut-0.12.10-cp35-cp35m-manylinux2010_i686.whl", hash = "sha256:9a15cb52f3f6d5980e41b6ca31976cc2048acf290f2e5159d7527e16e5c5d748"},
+ {file = "mapbox_earcut-0.12.10-cp35-cp35m-manylinux2010_x86_64.whl", hash = "sha256:6b083a065afd40961cc311b425c54275f531d91a27bdd34a2049993a68d8a651"},
+ {file = "mapbox_earcut-0.12.10-cp35-cp35m-win32.whl", hash = "sha256:fa3355248d3beaab67438373315e55a37ecc2694a4a4b1965e9d8f582a210479"},
+ {file = "mapbox_earcut-0.12.10-cp35-cp35m-win_amd64.whl", hash = "sha256:90b2977a9eda2a1873e44d7821ecf3b18062aa0878e957cb306e6018aba105c9"},
+ {file = "mapbox_earcut-0.12.10-cp36-cp36m-macosx_10_9_x86_64.whl", hash = "sha256:553688de45e73fa7d192fd6c29b87a4c5ea60a728b3c7b4c5f1715a89e6a8e54"},
+ {file = "mapbox_earcut-0.12.10-cp36-cp36m-manylinux2010_i686.whl", hash = "sha256:498b7f35c6a7c5c25829bcf1a79015ae64e94e8e36b84bd06e93131352b409f0"},
+ {file = "mapbox_earcut-0.12.10-cp36-cp36m-manylinux2010_x86_64.whl", hash = "sha256:8b9c6147249edf5049ccf7a7bca5bb29c9d512b3a5b62510659cfc51f1b8f806"},
+ {file = "mapbox_earcut-0.12.10-cp36-cp36m-win32.whl", hash = "sha256:4eaf2a9e86bbf808bf045eb587ec93a393e9d75ab87e7c1c9c8a5d9e122e30ac"},
+ {file = "mapbox_earcut-0.12.10-cp36-cp36m-win_amd64.whl", hash = "sha256:cb82e4ea9a67a9cdd46c9fc39bcb24e11f49569010368f9c5d376489bb2d0317"},
+ {file = "mapbox_earcut-0.12.10-cp37-cp37m-macosx_10_9_x86_64.whl", hash = "sha256:619a31a4d9748a30fbea82fd45beec6ab9e7f8a7ae7818be46f09d03ea0d9185"},
+ {file = "mapbox_earcut-0.12.10-cp37-cp37m-manylinux2010_i686.whl", hash = "sha256:054cd56cf8adf179d0aa0e8a061774e5afa767aaf6507851f4d2731b58f03d43"},
+ {file = "mapbox_earcut-0.12.10-cp37-cp37m-manylinux2010_x86_64.whl", hash = "sha256:ebeef32d504bf7e1ba986f86d87a8d3c96a54b6e03b0535ccdf0ce8f2f56e563"},
+ {file = "mapbox_earcut-0.12.10-cp37-cp37m-win32.whl", hash = "sha256:62a8787e30f7bbc6e1ebe8b11591119ed85aa5044b2cf3f6afb058e6fffeb8a3"},
+ {file = "mapbox_earcut-0.12.10-cp37-cp37m-win_amd64.whl", hash = "sha256:5f854a887f854bdea62c4b58785b82cf70056d53dc3bf23146ce68c125ceed96"},
+ {file = "mapbox_earcut-0.12.10-cp38-cp38-macosx_10_9_x86_64.whl", hash = "sha256:19f16be13a40d20419362f8ce27cf2dca8f0b8f4c7caa24caaff8351bcdf853e"},
+ {file = "mapbox_earcut-0.12.10-cp38-cp38-manylinux2010_i686.whl", hash = "sha256:cac7c8c332d1e802f478b5b79166ab38005b6d1bd908fb96857a8941e702f70d"},
+ {file = "mapbox_earcut-0.12.10-cp38-cp38-manylinux2010_x86_64.whl", hash = "sha256:24cc595987932b5d47b93ddb733c6bd084d91ff0af66ff2205aa717f0a5a13b8"},
+ {file = "mapbox_earcut-0.12.10-cp38-cp38-win32.whl", hash = "sha256:fe4b4e1c53fe0fde8e5fee86d868344f47d4d9fd89d9599548ea4b98349f10d6"},
+ {file = "mapbox_earcut-0.12.10-cp38-cp38-win_amd64.whl", hash = "sha256:6f4601b949ab43cf21dca86ffb6b4e2b30974ab3112f089d16b5f365e8b446f4"},
+ {file = "mapbox_earcut-0.12.10-cp39-cp39-macosx_10_9_x86_64.whl", hash = "sha256:ca00bdcb162b6a543f3061f49e2dcde42d6b780a545b5054da437e4ff5e33905"},
+ {file = "mapbox_earcut-0.12.10-cp39-cp39-manylinux2010_i686.whl", hash = "sha256:031132cdfa4d20e640f24d6817b65a91e3292c34ed527b4309617c9992284133"},
+ {file = "mapbox_earcut-0.12.10-cp39-cp39-manylinux2010_x86_64.whl", hash = "sha256:f284c0fc7f3c84664e9dddabae4eae729e6458e96ec5f30c9d7000c9b0dadca7"},
+ {file = "mapbox_earcut-0.12.10-cp39-cp39-win32.whl", hash = "sha256:c94a263767a841a5f7e8f03c725bdf41c87b8936c1a5fe18a5a77f3b9344d68f"},
+ {file = "mapbox_earcut-0.12.10-cp39-cp39-win_amd64.whl", hash = "sha256:742bd1f94113f44f1adcb5f3e2dca6e288695645b7eeab5d94f589dacda092af"},
+ {file = "mapbox_earcut-0.12.10-pp27-pypy_73-macosx_10_9_x86_64.whl", hash = "sha256:ad76defd6188e71023e43e5aed32ab5d540c0452a74918fc5de9bcccdee6c053"},
+ {file = "mapbox_earcut-0.12.10-pp27-pypy_73-manylinux2010_x86_64.whl", hash = "sha256:a3a9a81f696627f3c331f16c8d628b494949fa68067a42d2f1a6a56ee115eb0d"},
+ {file = "mapbox_earcut-0.12.10-pp27-pypy_73-win32.whl", hash = "sha256:044f70ed230bdb94f08356ec84f4bd30e4ea493d63700c3cc6fa86c5cf57623e"},
+ {file = "mapbox_earcut-0.12.10-pp36-pypy36_pp73-macosx_10_9_x86_64.whl", hash = "sha256:e352482e6022cc113dd008886012f0966bd2511933f888805fa87f070423d5b1"},
+ {file = "mapbox_earcut-0.12.10-pp36-pypy36_pp73-manylinux2010_x86_64.whl", hash = "sha256:41a282c485e96135ff15c01e0e1eb334cf1a05235edde8154b7b6e30187e54f4"},
+ {file = "mapbox_earcut-0.12.10-pp36-pypy36_pp73-win32.whl", hash = "sha256:5e1e3cf5a881eafeba7a7e5c4b1b9e7376710c48513513894e2a082ebf870326"},
+ {file = "mapbox_earcut-0.12.10-pp37-pypy37_pp73-macosx_10_9_x86_64.whl", hash = "sha256:7b6c2bfc28dc82a27071079885ffbe0836c0ad5dbd4ab47a5edaa24a86218daf"},
+ {file = "mapbox_earcut-0.12.10-pp37-pypy37_pp73-manylinux2010_x86_64.whl", hash = "sha256:6e6614f7b437b4b0a69ab642cf35569079408ac25c193013d5ad26e82c71fc01"},
+ {file = "mapbox_earcut-0.12.10-pp37-pypy37_pp73-win32.whl", hash = "sha256:d016823e863309b9cc542bb1d3bcdc274ec65fb23f2566de298188dcd4a75c0e"},
+ {file = "mapbox_earcut-0.12.10.tar.gz", hash = "sha256:50d995673ac9ce8cb9abb7ab64b709d611c1d27557907e00b631b5272345c453"},
+]
+moderngl = [
+ {file = "moderngl-5.6.4-cp35-cp35m-macosx_10_9_x86_64.whl", hash = "sha256:bc3764d67f037b67051871345a1d0b7a3d2c19cb5c0c0af0a84c532e802d6642"},
+ {file = "moderngl-5.6.4-cp35-cp35m-manylinux1_i686.whl", hash = "sha256:90006d9dfd5333da604a7d26b2a5e70e1a570f291cd745b8bf80e4833d8821b6"},
+ {file = "moderngl-5.6.4-cp35-cp35m-manylinux1_x86_64.whl", hash = "sha256:af44437545380a840dafd09658eb56592831dbd4fb481d320249d0d42c591bae"},
+ {file = "moderngl-5.6.4-cp35-cp35m-win32.whl", hash = "sha256:b5023633bcbfbab90be6a6f4edcde75f9c1e244d9acbda94678f3e3fb238b363"},
+ {file = "moderngl-5.6.4-cp35-cp35m-win_amd64.whl", hash = "sha256:ffc48fc4deeb525ed33a828d13ca4c12c5af8e5cb0449011f1802e18b5fc3c25"},
+ {file = "moderngl-5.6.4-cp36-cp36m-macosx_10_9_x86_64.whl", hash = "sha256:331fd4bce60b10a08eed81a3ed4c70b7c297c38f981fdf3968d03a1c892af247"},
+ {file = "moderngl-5.6.4-cp36-cp36m-manylinux1_i686.whl", hash = "sha256:1bd864b5cc2fc1255785e33575cec98fa5ded698503c4f8f3fa9230abeaa3a04"},
+ {file = "moderngl-5.6.4-cp36-cp36m-manylinux1_x86_64.whl", hash = "sha256:b22534529f5bc52c1fe43336787c06d51123ae978fb56e74e47cabd85056c934"},
+ {file = "moderngl-5.6.4-cp36-cp36m-win32.whl", hash = "sha256:ee5b1eced39d7f6dc68782c2abf01c1130a40b6d83d333d175ee71adbea7c721"},
+ {file = "moderngl-5.6.4-cp36-cp36m-win_amd64.whl", hash = "sha256:52ee915a559762f0e992344961b35e0d241be32f8aa7464494e958f777e0534c"},
+ {file = "moderngl-5.6.4-cp37-cp37m-macosx_10_9_x86_64.whl", hash = "sha256:f83f6ab1fafdba2d9c06a7a1c8a4e460689ea1d514146606acc74f14e0831d93"},
+ {file = "moderngl-5.6.4-cp37-cp37m-manylinux1_i686.whl", hash = "sha256:c350e06affea9fabc636b2350cf6e58d83ee2e7264527eee0f5d142c167f5463"},
+ {file = "moderngl-5.6.4-cp37-cp37m-manylinux1_x86_64.whl", hash = "sha256:3eb65afc8ec4a1d4a4c48696fb0f4f6cf7a7ada6bef97818d717dbca73c57b11"},
+ {file = "moderngl-5.6.4-cp37-cp37m-win32.whl", hash = "sha256:4fd721eb83e73d34c3f7b5a11aec656fef461b51bbe7503b07ea27370c593cbd"},
+ {file = "moderngl-5.6.4-cp37-cp37m-win_amd64.whl", hash = "sha256:01c71d94dbd59b5d37ead463991e2998c0924426cffa393b9da2b8334551c998"},
+ {file = "moderngl-5.6.4-cp38-cp38-macosx_10_9_x86_64.whl", hash = "sha256:d2ec6ecd845f21ba44a08c11521cb71f2a9c2ea2ec189b7ed30d17837d392d70"},
+ {file = "moderngl-5.6.4-cp38-cp38-manylinux1_i686.whl", hash = "sha256:40f74a2246e5302f93f2d46f76c0d2a26cbed1eb29731674c4052476f1e9c9ea"},
+ {file = "moderngl-5.6.4-cp38-cp38-manylinux1_x86_64.whl", hash = "sha256:5e158e6881034c7e1d0c583d7c82ff608439606f2359dc6098e4be4fd93cef9d"},
+ {file = "moderngl-5.6.4-cp38-cp38-win32.whl", hash = "sha256:a28dc741469eeb69549ee85b4ddbf8e9cfca6a2b19ce0406df9fde20f78082c8"},
+ {file = "moderngl-5.6.4-cp38-cp38-win_amd64.whl", hash = "sha256:ce87962b91635d857cac4a753c5d5f647d94dc66dcb0f090bb8d758fd226c3e8"},
+ {file = "moderngl-5.6.4-cp39-cp39-macosx_10_9_x86_64.whl", hash = "sha256:3fb139bcdd25eae2c546e5788e9d8719f6c4b18a2ba68a9df31699b4ac57d62d"},
+ {file = "moderngl-5.6.4-cp39-cp39-win32.whl", hash = "sha256:fc5cc1601a3df8f45f1901c6b9960731e0619d1781b0d036e12341fbf2ef55d3"},
+ {file = "moderngl-5.6.4-cp39-cp39-win_amd64.whl", hash = "sha256:1c74b71c9acee9f0e69807a086d76e92f37c1960c3bb1d6a6e2472fd03f7be5b"},
+ {file = "moderngl-5.6.4.tar.gz", hash = "sha256:8c6d04559f5e3bf75a18525cd46d213c0f3a8409363718978e6de691bdb551fb"},
+]
+moderngl-window = [
+ {file = "moderngl_window-2.3.0-py3-none-any.whl", hash = "sha256:79056e6b6a1e8c540031166d2ec308a40806baf461e5d492730966c3cf372a31"},
+]
+multipledispatch = [
+ {file = "multipledispatch-0.6.0-py2-none-any.whl", hash = "sha256:407e6d8c5fa27075968ba07c4db3ef5f02bea4e871e959570eeb69ee39a6565b"},
+ {file = "multipledispatch-0.6.0-py3-none-any.whl", hash = "sha256:a55c512128fb3f7c2efd2533f2550accb93c35f1045242ef74645fc92a2c3cba"},
+ {file = "multipledispatch-0.6.0.tar.gz", hash = "sha256:a7ab1451fd0bf9b92cab3edbd7b205622fb767aeefb4fb536c2e3de9e0a38bea"},
+]
+networkx = [
+ {file = "networkx-2.5.1-py3-none-any.whl", hash = "sha256:0635858ed7e989f4c574c2328380b452df892ae85084144c73d8cd819f0c4e06"},
+ {file = "networkx-2.5.1.tar.gz", hash = "sha256:109cd585cac41297f71103c3c42ac6ef7379f29788eb54cb751be5a663bb235a"},
+]
+numpy = [
+ {file = "numpy-1.20.2-cp37-cp37m-macosx_10_9_x86_64.whl", hash = "sha256:e9459f40244bb02b2f14f6af0cd0732791d72232bbb0dc4bab57ef88e75f6935"},
+ {file = "numpy-1.20.2-cp37-cp37m-manylinux1_i686.whl", hash = "sha256:a8e6859913ec8eeef3dbe9aed3bf475347642d1cdd6217c30f28dee8903528e6"},
+ {file = "numpy-1.20.2-cp37-cp37m-manylinux1_x86_64.whl", hash = "sha256:9cab23439eb1ebfed1aaec9cd42b7dc50fc96d5cd3147da348d9161f0501ada5"},
+ {file = "numpy-1.20.2-cp37-cp37m-manylinux2010_i686.whl", hash = "sha256:9c0fab855ae790ca74b27e55240fe4f2a36a364a3f1ebcfd1fb5ac4088f1cec3"},
+ {file = "numpy-1.20.2-cp37-cp37m-manylinux2010_x86_64.whl", hash = "sha256:61d5b4cf73622e4d0c6b83408a16631b670fc045afd6540679aa35591a17fe6d"},
+ {file = "numpy-1.20.2-cp37-cp37m-manylinux2014_aarch64.whl", hash = "sha256:d15007f857d6995db15195217afdbddfcd203dfaa0ba6878a2f580eaf810ecd6"},
+ {file = "numpy-1.20.2-cp37-cp37m-win32.whl", hash = "sha256:d76061ae5cab49b83a8cf3feacefc2053fac672728802ac137dd8c4123397677"},
+ {file = "numpy-1.20.2-cp37-cp37m-win_amd64.whl", hash = "sha256:bad70051de2c50b1a6259a6df1daaafe8c480ca98132da98976d8591c412e737"},
+ {file = "numpy-1.20.2-cp38-cp38-macosx_10_9_x86_64.whl", hash = "sha256:719656636c48be22c23641859ff2419b27b6bdf844b36a2447cb39caceb00935"},
+ {file = "numpy-1.20.2-cp38-cp38-manylinux1_i686.whl", hash = "sha256:aa046527c04688af680217fffac61eec2350ef3f3d7320c07fd33f5c6e7b4d5f"},
+ {file = "numpy-1.20.2-cp38-cp38-manylinux1_x86_64.whl", hash = "sha256:2428b109306075d89d21135bdd6b785f132a1f5a3260c371cee1fae427e12727"},
+ {file = "numpy-1.20.2-cp38-cp38-manylinux2010_i686.whl", hash = "sha256:e8e4fbbb7e7634f263c5b0150a629342cc19b47c5eba8d1cd4363ab3455ab576"},
+ {file = "numpy-1.20.2-cp38-cp38-manylinux2010_x86_64.whl", hash = "sha256:edb1f041a9146dcf02cd7df7187db46ab524b9af2515f392f337c7cbbf5b52cd"},
+ {file = "numpy-1.20.2-cp38-cp38-manylinux2014_aarch64.whl", hash = "sha256:c73a7975d77f15f7f68dacfb2bca3d3f479f158313642e8ea9058eea06637931"},
+ {file = "numpy-1.20.2-cp38-cp38-win32.whl", hash = "sha256:6c915ee7dba1071554e70a3664a839fbc033e1d6528199d4621eeaaa5487ccd2"},
+ {file = "numpy-1.20.2-cp38-cp38-win_amd64.whl", hash = "sha256:471c0571d0895c68da309dacee4e95a0811d0a9f9f532a48dc1bea5f3b7ad2b7"},
+ {file = "numpy-1.20.2-cp39-cp39-macosx_10_9_x86_64.whl", hash = "sha256:4703b9e937df83f5b6b7447ca5912b5f5f297aba45f91dbbbc63ff9278c7aa98"},
+ {file = "numpy-1.20.2-cp39-cp39-manylinux2010_i686.whl", hash = "sha256:abc81829c4039e7e4c30f7897938fa5d4916a09c2c7eb9b244b7a35ddc9656f4"},
+ {file = "numpy-1.20.2-cp39-cp39-manylinux2010_x86_64.whl", hash = "sha256:377751954da04d4a6950191b20539066b4e19e3b559d4695399c5e8e3e683bf6"},
+ {file = "numpy-1.20.2-cp39-cp39-manylinux2014_aarch64.whl", hash = "sha256:6e51e417d9ae2e7848314994e6fc3832c9d426abce9328cf7571eefceb43e6c9"},
+ {file = "numpy-1.20.2-cp39-cp39-win32.whl", hash = "sha256:780ae5284cb770ade51d4b4a7dce4faa554eb1d88a56d0e8b9f35fca9b0270ff"},
+ {file = "numpy-1.20.2-cp39-cp39-win_amd64.whl", hash = "sha256:924dc3f83de20437de95a73516f36e09918e9c9c18d5eac520062c49191025fb"},
+ {file = "numpy-1.20.2-pp37-pypy37_pp73-manylinux2010_x86_64.whl", hash = "sha256:97ce8b8ace7d3b9288d88177e66ee75480fb79b9cf745e91ecfe65d91a856042"},
+ {file = "numpy-1.20.2.zip", hash = "sha256:878922bf5ad7550aa044aa9301d417e2d3ae50f0f577de92051d739ac6096cee"},
+]
+pillow = [
+ {file = "Pillow-8.2.0-cp36-cp36m-macosx_10_10_x86_64.whl", hash = "sha256:dc38f57d8f20f06dd7c3161c59ca2c86893632623f33a42d592f097b00f720a9"},
+ {file = "Pillow-8.2.0-cp36-cp36m-manylinux1_i686.whl", hash = "sha256:a013cbe25d20c2e0c4e85a9daf438f85121a4d0344ddc76e33fd7e3965d9af4b"},
+ {file = "Pillow-8.2.0-cp36-cp36m-manylinux1_x86_64.whl", hash = "sha256:8bb1e155a74e1bfbacd84555ea62fa21c58e0b4e7e6b20e4447b8d07990ac78b"},
+ {file = "Pillow-8.2.0-cp36-cp36m-manylinux2014_aarch64.whl", hash = "sha256:c5236606e8570542ed424849f7852a0ff0bce2c4c8d0ba05cc202a5a9c97dee9"},
+ {file = "Pillow-8.2.0-cp36-cp36m-win32.whl", hash = "sha256:12e5e7471f9b637762453da74e390e56cc43e486a88289995c1f4c1dc0bfe727"},
+ {file = "Pillow-8.2.0-cp36-cp36m-win_amd64.whl", hash = "sha256:5afe6b237a0b81bd54b53f835a153770802f164c5570bab5e005aad693dab87f"},
+ {file = "Pillow-8.2.0-cp37-cp37m-macosx_10_10_x86_64.whl", hash = "sha256:cb7a09e173903541fa888ba010c345893cd9fc1b5891aaf060f6ca77b6a3722d"},
+ {file = "Pillow-8.2.0-cp37-cp37m-manylinux1_i686.whl", hash = "sha256:0d19d70ee7c2ba97631bae1e7d4725cdb2ecf238178096e8c82ee481e189168a"},
+ {file = "Pillow-8.2.0-cp37-cp37m-manylinux1_x86_64.whl", hash = "sha256:083781abd261bdabf090ad07bb69f8f5599943ddb539d64497ed021b2a67e5a9"},
+ {file = "Pillow-8.2.0-cp37-cp37m-manylinux2014_aarch64.whl", hash = "sha256:c6b39294464b03457f9064e98c124e09008b35a62e3189d3513e5148611c9388"},
+ {file = "Pillow-8.2.0-cp37-cp37m-win32.whl", hash = "sha256:01425106e4e8cee195a411f729cff2a7d61813b0b11737c12bd5991f5f14bcd5"},
+ {file = "Pillow-8.2.0-cp37-cp37m-win_amd64.whl", hash = "sha256:3b570f84a6161cf8865c4e08adf629441f56e32f180f7aa4ccbd2e0a5a02cba2"},
+ {file = "Pillow-8.2.0-cp38-cp38-macosx_10_10_x86_64.whl", hash = "sha256:031a6c88c77d08aab84fecc05c3cde8414cd6f8406f4d2b16fed1e97634cc8a4"},
+ {file = "Pillow-8.2.0-cp38-cp38-manylinux1_i686.whl", hash = "sha256:66cc56579fd91f517290ab02c51e3a80f581aba45fd924fcdee01fa06e635812"},
+ {file = "Pillow-8.2.0-cp38-cp38-manylinux1_x86_64.whl", hash = "sha256:6c32cc3145928c4305d142ebec682419a6c0a8ce9e33db900027ddca1ec39178"},
+ {file = "Pillow-8.2.0-cp38-cp38-manylinux2014_aarch64.whl", hash = "sha256:624b977355cde8b065f6d51b98497d6cd5fbdd4f36405f7a8790e3376125e2bb"},
+ {file = "Pillow-8.2.0-cp38-cp38-win32.whl", hash = "sha256:5cbf3e3b1014dddc45496e8cf38b9f099c95a326275885199f427825c6522232"},
+ {file = "Pillow-8.2.0-cp38-cp38-win_amd64.whl", hash = "sha256:463822e2f0d81459e113372a168f2ff59723e78528f91f0bd25680ac185cf797"},
+ {file = "Pillow-8.2.0-cp39-cp39-macosx_10_10_x86_64.whl", hash = "sha256:95d5ef984eff897850f3a83883363da64aae1000e79cb3c321915468e8c6add5"},
+ {file = "Pillow-8.2.0-cp39-cp39-macosx_11_0_arm64.whl", hash = "sha256:b91c36492a4bbb1ee855b7d16fe51379e5f96b85692dc8210831fbb24c43e484"},
+ {file = "Pillow-8.2.0-cp39-cp39-manylinux1_i686.whl", hash = "sha256:d68cb92c408261f806b15923834203f024110a2e2872ecb0bd2a110f89d3c602"},
+ {file = "Pillow-8.2.0-cp39-cp39-manylinux1_x86_64.whl", hash = "sha256:f217c3954ce5fd88303fc0c317af55d5e0204106d86dea17eb8205700d47dec2"},
+ {file = "Pillow-8.2.0-cp39-cp39-manylinux2014_aarch64.whl", hash = "sha256:5b70110acb39f3aff6b74cf09bb4169b167e2660dabc304c1e25b6555fa781ef"},
+ {file = "Pillow-8.2.0-cp39-cp39-win32.whl", hash = "sha256:a7d5e9fad90eff8f6f6106d3b98b553a88b6f976e51fce287192a5d2d5363713"},
+ {file = "Pillow-8.2.0-cp39-cp39-win_amd64.whl", hash = "sha256:238c197fc275b475e87c1453b05b467d2d02c2915fdfdd4af126145ff2e4610c"},
+ {file = "Pillow-8.2.0-pp36-pypy36_pp73-macosx_10_10_x86_64.whl", hash = "sha256:0e04d61f0064b545b989126197930807c86bcbd4534d39168f4aa5fda39bb8f9"},
+ {file = "Pillow-8.2.0-pp36-pypy36_pp73-manylinux2010_i686.whl", hash = "sha256:63728564c1410d99e6d1ae8e3b810fe012bc440952168af0a2877e8ff5ab96b9"},
+ {file = "Pillow-8.2.0-pp36-pypy36_pp73-manylinux2010_x86_64.whl", hash = "sha256:c03c07ed32c5324939b19e36ae5f75c660c81461e312a41aea30acdd46f93a7c"},
+ {file = "Pillow-8.2.0-pp37-pypy37_pp73-macosx_10_10_x86_64.whl", hash = "sha256:4d98abdd6b1e3bf1a1cbb14c3895226816e666749ac040c4e2554231068c639b"},
+ {file = "Pillow-8.2.0-pp37-pypy37_pp73-manylinux2010_i686.whl", hash = "sha256:aac00e4bc94d1b7813fe882c28990c1bc2f9d0e1aa765a5f2b516e8a6a16a9e4"},
+ {file = "Pillow-8.2.0-pp37-pypy37_pp73-manylinux2010_x86_64.whl", hash = "sha256:22fd0f42ad15dfdde6c581347eaa4adb9a6fc4b865f90b23378aa7914895e120"},
+ {file = "Pillow-8.2.0-pp37-pypy37_pp73-win32.whl", hash = "sha256:e98eca29a05913e82177b3ba3d198b1728e164869c613d76d0de4bde6768a50e"},
+ {file = "Pillow-8.2.0.tar.gz", hash = "sha256:a787ab10d7bb5494e5f76536ac460741788f1fbce851068d73a87ca7c35fc3e1"},
+]
+pycairo = [
+ {file = "pycairo-1.20.0-cp36-cp36m-win32.whl", hash = "sha256:e5a3433690c473e073a9917dc8f1fc7dc8b9af7b201bf372894b8ad70d960c6d"},
+ {file = "pycairo-1.20.0-cp36-cp36m-win_amd64.whl", hash = "sha256:a942614923b88ae75c794506d5c426fba9c46a055d3fdd3b8db7046b75c079cc"},
+ {file = "pycairo-1.20.0-cp37-cp37m-win32.whl", hash = "sha256:8cfa9578b745fb9cf2915ec580c2c50ebc2da00eac2cf4c4b54b63aa19da4b77"},
+ {file = "pycairo-1.20.0-cp37-cp37m-win_amd64.whl", hash = "sha256:273a33c56aba724ec42fe1d8f94c86c2e2660c1277470be9b04e5113d7c5b72d"},
+ {file = "pycairo-1.20.0-cp38-cp38-win32.whl", hash = "sha256:2088100a099c09c5e90bf247409ce6c98f51766b53bd13f96d6aac7addaa3e66"},
+ {file = "pycairo-1.20.0-cp38-cp38-win_amd64.whl", hash = "sha256:ceb1edcbeb48dabd5fbbdff2e4b429aa88ddc493d6ebafe78d94b050ac0749e2"},
+ {file = "pycairo-1.20.0-cp39-cp39-win32.whl", hash = "sha256:57a768f4edc8a9890d98070dd473a812ac3d046cef4bc1c817d68024dab9a9b4"},
+ {file = "pycairo-1.20.0-cp39-cp39-win_amd64.whl", hash = "sha256:57166119e424d71eccdba6b318bd731bdabd17188e2ba10d4f315f7bf16ace3f"},
+ {file = "pycairo-1.20.0.tar.gz", hash = "sha256:5695a10cb7f9ae0d01f665b56602a845b0a8cb17e2123bfece10c2e58552468c"},
+]
+pydub = [
+ {file = "pydub-0.25.1-py2.py3-none-any.whl", hash = "sha256:65617e33033874b59d87db603aa1ed450633288aefead953b30bded59cb599a6"},
+ {file = "pydub-0.25.1.tar.gz", hash = "sha256:980a33ce9949cab2a569606b65674d748ecbca4f0796887fd6f46173a7b0d30f"},
+]
+pyglet = [
+ {file = "pyglet-1.5.15-py3-none-any.whl", hash = "sha256:4401cc176580e4e17e2df8bbf7536f27e691327dc3f38f209a12f1859c70aed2"},
+ {file = "pyglet-1.5.15.zip", hash = "sha256:da9d8337388cedabf1f1c5dc21a45bb2b0e5327fba47f996c8573818c3dfa478"},
+]
+pygments = [
+ {file = "Pygments-2.8.1-py3-none-any.whl", hash = "sha256:534ef71d539ae97d4c3a4cf7d6f110f214b0e687e92f9cb9d2a3b0d3101289c8"},
+ {file = "Pygments-2.8.1.tar.gz", hash = "sha256:2656e1a6edcdabf4275f9a3640db59fd5de107d88e8663c5d4e9a0fa62f77f94"},
+]
+pyrr = [
+ {file = "pyrr-0.10.3-py3-none-any.whl", hash = "sha256:d8af23fb9bb29262405845e1c98f7339fbba5e49323b98528bd01160a75c65ac"},
+ {file = "pyrr-0.10.3.tar.gz", hash = "sha256:3c0f7b20326e71f706a610d58f2190fff73af01eef60c19cb188b186f0ec7e1d"},
+]
+rich = [
+ {file = "rich-6.2.0-py3-none-any.whl", hash = "sha256:fa55d5d6ba9a0df1f1c95518891b57b13f1d45548a9a198a87b093fceee513ec"},
+ {file = "rich-6.2.0.tar.gz", hash = "sha256:f99c877277906e1ff83b135c564920590ba31188f424dcdb5d1cae652a519b4b"},
+]
+scipy = [
+ {file = "scipy-1.6.1-cp37-cp37m-macosx_10_9_x86_64.whl", hash = "sha256:a15a1f3fc0abff33e792d6049161b7795909b40b97c6cc2934ed54384017ab76"},
+ {file = "scipy-1.6.1-cp37-cp37m-manylinux1_i686.whl", hash = "sha256:e79570979ccdc3d165456dd62041d9556fb9733b86b4b6d818af7a0afc15f092"},
+ {file = "scipy-1.6.1-cp37-cp37m-manylinux1_x86_64.whl", hash = "sha256:a423533c55fec61456dedee7b6ee7dce0bb6bfa395424ea374d25afa262be261"},
+ {file = "scipy-1.6.1-cp37-cp37m-manylinux2014_aarch64.whl", hash = "sha256:33d6b7df40d197bdd3049d64e8e680227151673465e5d85723b3b8f6b15a6ced"},
+ {file = "scipy-1.6.1-cp37-cp37m-win32.whl", hash = "sha256:6725e3fbb47da428794f243864f2297462e9ee448297c93ed1dcbc44335feb78"},
+ {file = "scipy-1.6.1-cp37-cp37m-win_amd64.whl", hash = "sha256:5fa9c6530b1661f1370bcd332a1e62ca7881785cc0f80c0d559b636567fab63c"},
+ {file = "scipy-1.6.1-cp38-cp38-macosx_10_9_x86_64.whl", hash = "sha256:bd50daf727f7c195e26f27467c85ce653d41df4358a25b32434a50d8870fc519"},
+ {file = "scipy-1.6.1-cp38-cp38-manylinux1_i686.whl", hash = "sha256:f46dd15335e8a320b0fb4685f58b7471702234cba8bb3442b69a3e1dc329c345"},
+ {file = "scipy-1.6.1-cp38-cp38-manylinux1_x86_64.whl", hash = "sha256:0e5b0ccf63155d90da576edd2768b66fb276446c371b73841e3503be1d63fb5d"},
+ {file = "scipy-1.6.1-cp38-cp38-manylinux2014_aarch64.whl", hash = "sha256:2481efbb3740977e3c831edfd0bd9867be26387cacf24eb5e366a6a374d3d00d"},
+ {file = "scipy-1.6.1-cp38-cp38-win32.whl", hash = "sha256:68cb4c424112cd4be886b4d979c5497fba190714085f46b8ae67a5e4416c32b4"},
+ {file = "scipy-1.6.1-cp38-cp38-win_amd64.whl", hash = "sha256:5f331eeed0297232d2e6eea51b54e8278ed8bb10b099f69c44e2558c090d06bf"},
+ {file = "scipy-1.6.1-cp39-cp39-macosx_10_9_x86_64.whl", hash = "sha256:0c8a51d33556bf70367452d4d601d1742c0e806cd0194785914daf19775f0e67"},
+ {file = "scipy-1.6.1-cp39-cp39-manylinux1_i686.whl", hash = "sha256:83bf7c16245c15bc58ee76c5418e46ea1811edcc2e2b03041b804e46084ab627"},
+ {file = "scipy-1.6.1-cp39-cp39-manylinux1_x86_64.whl", hash = "sha256:794e768cc5f779736593046c9714e0f3a5940bc6dcc1dba885ad64cbfb28e9f0"},
+ {file = "scipy-1.6.1-cp39-cp39-manylinux2014_aarch64.whl", hash = "sha256:5da5471aed911fe7e52b86bf9ea32fb55ae93e2f0fac66c32e58897cfb02fa07"},
+ {file = "scipy-1.6.1-cp39-cp39-win32.whl", hash = "sha256:8e403a337749ed40af60e537cc4d4c03febddcc56cd26e774c9b1b600a70d3e4"},
+ {file = "scipy-1.6.1-cp39-cp39-win_amd64.whl", hash = "sha256:a5193a098ae9f29af283dcf0041f762601faf2e595c0db1da929875b7570353f"},
+ {file = "scipy-1.6.1.tar.gz", hash = "sha256:c4fceb864890b6168e79b0e714c585dbe2fd4222768ee90bc1aa0f8218691b11"},
+]
+six = [
+ {file = "six-1.15.0-py2.py3-none-any.whl", hash = "sha256:8b74bedcbbbaca38ff6d7491d76f2b06b3592611af620f8426e82dddb04a5ced"},
+ {file = "six-1.15.0.tar.gz", hash = "sha256:30639c035cdb23534cd4aa2dd52c3bf48f06e5f4a941509c8bafd8ce11080259"},
+]
+tqdm = [
+ {file = "tqdm-4.60.0-py2.py3-none-any.whl", hash = "sha256:daec693491c52e9498632dfbe9ccfc4882a557f5fa08982db1b4d3adbe0887c3"},
+ {file = "tqdm-4.60.0.tar.gz", hash = "sha256:ebdebdb95e3477ceea267decfc0784859aa3df3e27e22d23b83e9b272bf157ae"},
+]
+typing-extensions = [
+ {file = "typing_extensions-3.7.4.3-py2-none-any.whl", hash = "sha256:dafc7639cde7f1b6e1acc0f457842a83e722ccca8eef5270af2d74792619a89f"},
+ {file = "typing_extensions-3.7.4.3-py3-none-any.whl", hash = "sha256:7cb407020f00f7bfc3cb3e7881628838e69d8f3fcab2f64742a5e76b2f841918"},
+ {file = "typing_extensions-3.7.4.3.tar.gz", hash = "sha256:99d4073b617d30288f569d3f13d2bd7548c3a7e4c8de87db09a9d29bb3a4a60c"},
+]
+zipp = [
+ {file = "zipp-3.4.1-py3-none-any.whl", hash = "sha256:51cb66cc54621609dd593d1787f286ee42a5c0adbb4b29abea5a63edc3e03098"},
+ {file = "zipp-3.4.1.tar.gz", hash = "sha256:3607921face881ba3e026887d8150cca609d517579abe052ac81fc5aeffdbd76"},
+]
diff --git a/vorlesungen/punktgruppen/pyproject.toml b/vorlesungen/punktgruppen/pyproject.toml
new file mode 100644
index 0000000..92c06e2
--- /dev/null
+++ b/vorlesungen/punktgruppen/pyproject.toml
@@ -0,0 +1,15 @@
+[tool.poetry]
+name = "presentation"
+version = "0.1.0"
+description = ""
+authors = ["Nao Pross <np@0hm.ch>"]
+
+[tool.poetry.dependencies]
+python = "^3.7"
+manim = "^0.5.0"
+
+[tool.poetry.dev-dependencies]
+
+[build-system]
+requires = ["poetry-core>=1.0.0"]
+build-backend = "poetry.core.masonry.api"