Multiscale compactification of veering triangulations

.github/workflows/doc.yml

@@ -11,19 +11,20 @@ jobs:
   build-manual:
     runs-on: ubuntu-22.04
     steps:
-      - uses: actions/checkout@v2
+      - uses: actions/checkout@v4
         with: { submodules: recursive }
-      - uses: conda-incubator/setup-miniconda@v2
-        with: { miniforge-variant: "Mambaforge", miniforge-version: "latest" }
+      - uses: conda-incubator/setup-miniconda@v3
+        with:
+          channels: conda-forge
       - name: install dependencies
         shell: bash -l {0}
         run: |
-          mamba env update --quiet -n test -f environment.yml
+          conda env update --quiet -n test -f environment.yml
           conda list
       - name: install veerer
         shell: bash -l {0}
         run: |
-          pip install --no-index .
+          pip install --no-index --no-build-isolation .
       - name: fix permissions
         shell: bash -l {0}
         run: |

.github/workflows/lint.yml

@@ -11,14 +11,14 @@ jobs:
   codespell:
     runs-on: ubuntu-22.04
     steps:
-      - uses: actions/checkout@v2
+      - uses: actions/checkout@v4
         with: { submodules: recursive }
-      - uses: conda-incubator/setup-miniconda@v2
-        with: { miniforge-variant: "Mambaforge", miniforge-version: "latest" }
+      - uses: conda-incubator/setup-miniconda@v3
+        with: { miniforge-version: "latest" }
       - name: install codespell
         shell: bash -l {0}
         run: |
-          mamba install -y codespell
+          conda install -y codespell
       - name: run codespell
         shell: bash -l {0}
         run: |

.github/workflows/test.yml

@@ -16,42 +16,62 @@ jobs:
           - optionals: "sage"
             sagelib: "10.0"
             python: "3.10"
+            pip: "24.3.1"
+            setuptools: "70.3.0"
           - optionals: "sage,sage_flatsurf,pyeantic,pyintervalxt,pyflatsurf,pynormaliz,surface_dynamics"
             sagelib: "10.3"
             python: "3.10"
+            pip: "24.3.1"
+            setuptools: "70.3.0"
           # Test optional dependencies in isolation
           - optionals: "sage"
             sagelib: "10.3"
             python: "3.10"
+            pip: "24.3.1"
+            setuptools: "70.3.0"
           # Recent sage-flatsurf depends on surface-dynamics
           - optionals: "sage,surface_dynamics,sage_flatsurf"
             sagelib: "10.3"
             python: "3.10"
+            pip: "24.3.1"
+            setuptools: "70.3.0"
           - optionals: "sage,pyeantic"
             sagelib: "10.3"
             python: "3.10"
+            pip: "24.3.1"
+            setuptools: "70.3.0"
           - optionals: "sage,pyintervalxt"
             sagelib: "10.3"
             python: "3.10"
+            pip: "24.3.1"
+            setuptools: "70.3.0"
           - optionals: "sage,pynormaliz"
             sagelib: "10.3"
             python: "3.10"
+            pip: "24.3.1"
+            setuptools: "70.3.0"
           - optionals: "sage,surface_dynamics"
             sagelib: "10.3"
             python: "3.10"
+            pip: "24.3.1"
+            setuptools: "70.3.0"
           - optionals: "sage,pyflatsurf"
             sagelib: "10.3"
             python: "3.10"
+            pip: "24.3.1"
+            setuptools: "70.3.0"
     steps:
-      - uses: actions/checkout@v2
+      - uses: actions/checkout@v4
         with: { submodules: recursive }
-      - uses: conda-incubator/setup-miniconda@v2
-        with: { miniforge-variant: "Mambaforge", miniforge-version: "latest", python-version: "${{ matrix.python }}" }
+      - uses: conda-incubator/setup-miniconda@v3
+        with:
+          channels: conda-forge
+          python-version: ${{ matrix.python }}
       - name: Install dependencies
         shell: bash -l {0}
         run: |
           if (echo "${{ matrix.optionals }}" | grep sage); then
-            mamba install -n test sagelib=${{ matrix.sagelib }}
+            conda install -n test sagelib=${{ matrix.sagelib }}
             echo "sagelib ==${{ matrix.sagelib }}" >> $CONDA_PREFIX/conda-meta/pinned
           fi
 
@@ -60,25 +80,25 @@ jobs:
             (test "$optional" == '' || (echo "${{ matrix.optionals }}" | grep -E '\b'"$optional"'\b') > /dev/null) && echo "$REPLY" || true
           done < environment.yml > environment.test.yml
 
-          mamba env update --quiet -n test -f environment.test.yml
+          conda env update --quiet -n test -f environment.test.yml
 
           conda list
       - name: Install veerer
         shell: bash -l {0}
         run: |
-          pip install --verbose --no-index .
+          pip install --verbose --no-index --no-build-isolation .
           # Show message about cppyy regenerating pre-compiled headers so it does not show during the tests
           python -c 'import cppyy' || true
       - name: Run SageMath doctests
         shell: bash -l {0}
         run: |
-          mamba remove -y pytest  # sage -t breaks in some old versions of SageMath if pytest is installed
+          conda remove -y pytest  # sage -t breaks in some old versions of SageMath if pytest is installed
           sage -tp --force-lib --long --optional=${{ matrix.optionals }} veerer doc
       - name: Run pytest
         shell: bash -l {0}
         working-directory: tests
         run: |
-          mamba install -y pytest pytest-xdist
+          conda install -y pytest pytest-xdist
           pytest -n auto
       - uses: flatsurf/actions/show-logs@main
         if: ${{ always() }}

README.rst

@@ -89,4 +89,5 @@ Authors
 
 - Mark Bell
 - Vincent Delecroix
+- Kai Fu
 - Saul Schleimer

doc/source/background.rst

@@ -4,10 +4,18 @@
 Veering triangulations
 ======================
 
+Geometry
+--------
+
 Veering triangulations were originally defined as 3-dimensional
 triangulation of mapping tori in [Ag11]_, see also [Gu09]_, [Gu16]_. It
 turns out that they also encode nicely train-tracks splitting sequences of
-pseudo-Anosov.
+pseudo-Anosov mapping classes.
 
 The veerer library implements most of the tools from [BeDeGaGuSc]_ which
 shares a lot of ideas with [Ha09]_.
+
+- Embedded graphs
+- Veering triangulation, Strebel graph and parametrization of Abelian and quadratic differentials
+- Linear subvarieties and Veering-Strebel flip graph
+- Degenerations and multiscale compactification

doc/source/ferenczi_zamboni.rst

@@ -17,15 +17,15 @@ There are only two possible moves::
 
     sage: from veerer import VeeringTriangulation, VeeringFlipSequence # random output due to deprecation warnings from realalg
     sage: V = VeeringTriangulation("(0,1,2)", "PBR")
-    sage: R = VeeringFlipSequence(V, "0R", [2,1,0])
-    sage: L = VeeringFlipSequence(V, "0B", [1,0,2])
+    sage: R = VeeringFlipSequence(V, "0R", "(0,2)")
+    sage: L = VeeringFlipSequence(V, "0B", "(0,1)")
 
 The smallest dilatation is the golden rotation::
 
     sage: assert R.is_closed() and L.is_closed()
     sage: fp = R * L
     sage: fp
-    VeeringFlipSequence(VeeringTriangulation("(0,1,2)", "PBR"), "0R 2B", "(0,2,1)")
+    VeeringFlipSequence(VeeringTriangulation("(0,1,2)", "PBR"), "0R 2B", "(0,2,1)(~0,~2,~1)")
     sage: a, S = fp.self_similar_surface()
     sage: SS = S.copy(mutable=True)
     sage: SS.flip(0)
@@ -140,22 +140,22 @@ Some pseudo-Anosov with small dilatation in H(2)
     sage: assert f.is_pseudo_anosov()
     sage: f.self_similar_surface()
     (a,
-     FlatVeeringTriangulation(Triangulation("(0,6,5)(1,2,~6)(3,4,~5)"), [(1, -1), (a, a^3 - a^2 - a - 1), (a^3 - 2*a - 2, a^2), (-a^3 + a^2 + a + 1, -a), (2*a^3 - a^2 - 2*a - 2, a^3 - 2), (-a^3 + a + 1, -a^3 + a + 2), (a^3 - a - 2, a^3 - a - 1), (-a^3 + a + 2, -a^3 + a + 1), (-a^3 + a + 1, -a^3 + a + 2)]))
+     FlatVeeringTriangulation("(0,6,5)(1,2,~6)(3,4,~5)", "BBBBRRR", (1, a, -a^3 + 2*a + 2, -a^3 + a^2 + a + 1, 2*a^3 - a^2 - 2*a - 2, a^3 - a - 1, a^3 - a - 2), (1, -a^3 + a^2 + a + 1, a^2, a, a^3 - 2, a^3 - a - 2, a^3 - a - 1)))
 
     sage: f = R1 * R1 * R5
     sage: assert f.is_pseudo_anosov()
     sage: f.self_similar_surface()
     (a,
-     FlatVeeringTriangulation(Triangulation("(0,6,5)(1,2,~6)(3,4,~5)"), [(1, -1), (a^2, 2*a^3 - 3*a^2 - 2*a - 4), (a^3 - 2*a^2 - 2, a), (a, a^3 - 2*a^2 - 2), (a^3 - a^2 - a - 1, a^3 - a^2 - a - 3), (-a^3 + a^2 + 1, -2*a^3 + 3*a^2 + a + 5), (a^3 - a^2 - 2, 2*a^3 - 3*a^2 - a - 4), (-a^3 + a^2 + 2, -2*a^3 + 3*a^2 + a + 4), (-a^3 + a^2 + 1, -2*a^3 + 3*a^2 + a + 5)]))
+     FlatVeeringTriangulation("(0,6,5)(1,2,~6)(3,4,~5)", "BBBBRRR", (1, a^2, -a^3 + 2*a^2 + 2, a, a^3 - a^2 - a - 1, a^3 - a^2 - 1, a^3 - a^2 - 2), (1, -2*a^3 + 3*a^2 + 2*a + 4, a, -a^3 + 2*a^2 + 2, a^3 - a^2 - a - 3, 2*a^3 - 3*a^2 - a - 5, 2*a^3 - 3*a^2 - a - 4)))
 
     sage: f = R3 * R1 * R2 * CL5
     sage: assert f.is_pseudo_anosov()
     sage: f.self_similar_surface()
     (a,
-     FlatVeeringTriangulation(Triangulation("(0,~5,4)(1,2,~6)(3,5,6)"), [(1, 1), (1, 1), (-1/2*a + 3/2, 1/2*a - 1/2), (1/2*a - 1/2, -1/2*a + 3/2), (a - 4, -a), (-a + 3, a - 1), (1/2*a - 5/2, -1/2*a - 1/2), (1/2*a - 5/2, -1/2*a - 1/2), (-a + 3, a - 1)]))
+     FlatVeeringTriangulation("(0,~5,4)(1,2,~6)(3,5,6)", "RRBBRBR", (1, 1, 1/2*a - 3/2, 1/2*a - 1/2, -a + 4, a - 3, -1/2*a + 5/2), (1, 1, 1/2*a - 1/2, 1/2*a - 3/2, a, a - 1, 1/2*a + 1/2)))
 
     sage: f = R3 * R1 * R2 * CL5 * CR5
     sage: assert f.is_pseudo_anosov()
     sage: f.self_similar_surface()
     (a,
-     FlatVeeringTriangulation(Triangulation("(0,~5,4)(1,2,~6)(3,5,6)"), [(1, 1), (7/33*a^3 - 23/33*a^2 - 19/33*a - 25/33, -10/33*a^3 + 32/33*a^2 + 37/33*a + 16/33), (-20/33*a^3 + 61/33*a^2 + 92/33*a + 62/33, 5/33*a^3 - 16/33*a^2 - 2/33*a - 8/33), (-1/33*a^3 + 8/33*a^2 - 2/33*a - 20/33, -8/33*a^3 + 19/33*a^2 + 56/33*a + 26/33), (4/11*a^3 - 10/11*a^2 - 25/11*a - 30/11, -1/11*a^3 + 1/11*a^2 + 7/11*a - 5/11), (-4/11*a^3 + 10/11*a^2 + 25/11*a + 19/11, 1/11*a^3 - 1/11*a^2 - 7/11*a - 6/11), (13/33*a^3 - 38/33*a^2 - 73/33*a - 37/33, 5/33*a^3 - 16/33*a^2 - 35/33*a - 8/33), (13/33*a^3 - 38/33*a^2 - 73/33*a - 37/33, 5/33*a^3 - 16/33*a^2 - 35/33*a - 8/33), (-4/11*a^3 + 10/11*a^2 + 25/11*a + 19/11, 1/11*a^3 - 1/11*a^2 - 7/11*a - 6/11)]))
+     FlatVeeringTriangulation("(0,~5,4)(1,2,~6)(3,5,6)", "RBBBRBR", (1, 7/33*a^3 - 23/33*a^2 - 19/33*a - 25/33, 20/33*a^3 - 61/33*a^2 - 92/33*a - 62/33, -1/33*a^3 + 8/33*a^2 - 2/33*a - 20/33, -4/11*a^3 + 10/11*a^2 + 25/11*a + 30/11, 4/11*a^3 - 10/11*a^2 - 25/11*a - 19/11, -13/33*a^3 + 38/33*a^2 + 73/33*a + 37/33), (1, 10/33*a^3 - 32/33*a^2 - 37/33*a - 16/33, 5/33*a^3 - 16/33*a^2 - 2/33*a - 8/33, 8/33*a^3 - 19/33*a^2 - 56/33*a - 26/33, 1/11*a^3 - 1/11*a^2 - 7/11*a + 5/11, 1/11*a^3 - 1/11*a^2 - 7/11*a - 6/11, -5/33*a^3 + 16/33*a^2 + 35/33*a + 8/33)))

doc/source/veerer_demo.rst

@@ -31,11 +31,12 @@ part of a project that also involve
   with SageMath (see below).
 - The Python library `PyNormaliz <https://pypi.org/project/PyNormaliz/>`_
   (polytope, in particular over number fields).
-- The software `SageMath <https://www.sagemath.org/>`_ (plotting, linear algebra
-  and many other things)
-- The SageMath library `surface_dynamics
+- The Sagemath libraries `sage-flatsruf
+  <https://flatsurf.github.io/sage-flatsurf/>`_ (plotting and construction of
+  surfaces) and `surface_dynamics
   <https://pypi.org/project/surface-dynamics/>`_ (for analyzing stratum
   components)
+- The software `SageMath <https://www.sagemath.org/>`_ (many things)
 
 To import all features from veerer one usually starts with the following
 lines::
@@ -76,12 +77,12 @@ colors.
 ::
 
     sage: FS0 = T0.flat_structure_min()
-    sage: FS0.plot().show(figsize=5)
+    sage: FS0.plot().show(figsize=5)  # optional - sage_flatsurf
 
 ::
 
     sage: FFS0 = T0.flat_structure_geometric_middle()
-    sage: FFS0.plot().show(figsize=5)
+    sage: FFS0.plot().show(figsize=5) # optional - sage_flatsurf
 
 ::
 
@@ -100,12 +101,12 @@ colors.
 ::
 
     sage: FS1 = T1.flat_structure_min()
-    sage: FS1.plot().show(figsize=5)
+    sage: FS1.plot().show(figsize=5) # optional - sage_flatsurf
 
 ::
 
     sage: FFS1 = T1.flat_structure_geometric_middle()
-    sage: FFS1.plot().show(figsize=5)
+    sage: FFS1.plot().show(figsize=5) # optional - sage_flatsurf
 
 ::
 
@@ -124,20 +125,11 @@ colors.
 ::
 
     sage: FS2 = T2.flat_structure_min()
-    sage: FS2.plot().show(figsize=5)  # not tested (warning from matplotlib)
+    sage: FS2.plot().show(figsize=5)  # optional - sage_flatsurf # not tested
 
 
-Viewing train-tracks!
----------------------
-
-Recall that a veering triangulation is just a pair of transversal
-train-tracks.
-
-::
-
-    sage: TT_horiz = FS1.plot(horizontal_train_track=True, edge_labels=False)
-    sage: TT_vert = FS1.plot(vertical_train_track=True, edge_labels=False)
-    sage: graphics_array([TT_horiz, TT_vert], 1, 2).show(figsize=6)
+More examples
+-------------
 
 ::
 
@@ -211,7 +203,7 @@ Core vs not core
 ::
 
     sage: FS = S.flat_structure_min()
-    sage: FS.plot()
+    sage: FS.plot()  # optional - sage_flatsurf
     Graphics object consisting of ... graphics primitives
 
 ::
@@ -258,15 +250,19 @@ of the product of the two train-track polytopes.
     sage: print(T1.is_delaunay())
     True
     sage: print(T1.delaunay_cone())
-    Cone of dimension 8 in ambient dimension 18 made of 13 facets (backend=ppl)
+    8-dimensional Delaunay cone of VeeringTriangulation("(0,~3,4)(~0,7,~6)(1,2,~7)(~1,~2,3)(~4,5,~8)(~5,8,6)", "RBRRBRBRB") made of
+     2 forward-flip facets
+     2 backward-flip facets
+     5 x-degeneration facets
+     4 y-degeneration facets
 
 Core automaton
 --------------
 
-The core automaton of a given triangulations `T_0` is the directed graph whose
-vertices are core veering triangulations that can be reached from `T_0` by a
-sequence of flips and there is a directed edge `T_i \to T_j` if `T_j` is obtained
-from `T_i` by a flip.
+The core automaton of a given triangulations `T_0` is the automaton (or
+directed graph) whose states (or vertices) are core veering triangulations that
+can be reached from `T_0` by a sequence of flips and there is a transition (or
+directed edge) `T_i \to T_j` if `T_j` is obtained from `T_i` by a flip.
 
 ::
 
@@ -278,7 +274,7 @@ from `T_i` by a flip.
     sage: A0.run()
     0
     sage: A0
-    Core veering automaton with 2 vertices
+    Core veering automaton with 2 states
 
 ::
 
@@ -348,8 +344,8 @@ Some data (orientable case)
 To give an idea about the complexity and timings when generating the
 above data, here are the steps involved. The timings are for the stratum
 component H(4)^hyp that is the fourth row in the above array: -
-generating the core graph ~20 secs for H(4)^hyp (the graph has 9116
-vertices and 44664 edges) - filtering the geometric triangulations
+generating the core graph ~20 secs for H(4)^hyp (the automaton has 9116
+states and 44664 transitions) - filtering the geometric triangulations
 (single test involves a polytope computation) ~20 secs for H(4)^hyp -
 filtering cylindrical (single test is cheap) ~2 sec for H(4)^hyp
 

tests/test_flip.py

@@ -101,7 +101,7 @@ def test_flip_reduced(fp, cols, repeat):
         # actually do the flip
         V.flip(e, col, reduced=True)
         assert V.edge_has_curve(e)
-        assert V.forward_flippable_edges() == [e[0] for e in V.edges() if V.edge_colour(e[0]) == PURPLE], (V0, e, col)
+        assert V.forward_flippable_edges() == V.purple_edges(), (V0, e, col)
 
 if __name__ == '__main__':
     import sys

tests/test_triangulation_relabel.py

@@ -24,10 +24,9 @@
 
 def test_relabel():
     T = Triangulation([(0,1,2), (-1,-2,-3)], mutable=True)
-    p = perm_init([1,5,0,2,4,3])
+    p = perm_init([3,2,0,1,4,5])
     T.relabel(p)
-    assert T.faces() == [[0, 1, 5], [2, 3, 4]]
-    assert T.edges() == [[0, 2], [1, 3], [4, 5]]
+    assert T.faces() == [[0, 4, 3], [1, 5, 2]]
     T._check()
 
 if __name__ == '__main__':

veerer/__init__.py

@@ -26,12 +26,9 @@
 
 from .constants import RED, BLUE, PURPLE, GREEN, HORIZONTAL, VERTICAL, RIGHT, LEFT, UP, DOWN
 from .triangulation import Triangulation
-from .cover import TriangulationCover
 from .veering_triangulation import VeeringTriangulation, VeeringTriangulations
-from .linear_family import VeeringTriangulationLinearFamily, StrebelGraphLinearFamily
+from .linear_family import VeeringTriangulationLinearFamily, StrebelGraphLinearFamily, VeeringTriangulationLinearFamilies
 from .strebel_graph import StrebelGraph
 from .automaton import FlipGraph, CoreAutomaton, ReducedCoreAutomaton, DelaunayAutomaton, DelaunayStrebelAutomaton
 from .flip_sequence import VeeringFlipSequence
 from .flat_structure import FlatVeeringTriangulation
-from .layout import FlatVeeringTriangulationLayout
-from .measured_train_track import MeasuredTrainTrack