Implement dual subdivision and weight vectors for tropical variety #38536

verreld7 · 2024-08-20T13:56:28Z

This PR introduces some new methods in TropicalVariety related to dual subdivision and weight vectors.

Summary of changes:

Add dual_subdivision in TropicalVariety: return the dual subdivision for any tropical variety as a Graph object
Add _components_of_vertices in TropicalCurve: intermediate method the help calculate weight vectors
Add weight_vectors in TropicalCurve: return the weight vectors of each vertex
Add weight_vectors in TropicalSurface: return the weight vectors of each unique line of intersection
Add a few methods related to dual subdivision of tropical curve such as:
- is_smooth
- is_simple
- genus
- contribution

CC: @tscrim

📝 Checklist

The title is concise and informative.
The description explains in detail what this PR is about.
I have linked a relevant issue or discussion.
I have created tests covering the changes.
I have updated the documentation and checked the documentation preview.

⌛ Dependencies

#37962: issues related to this PR
#38291: continuation of this PR

github-actions · 2024-08-22T06:42:35Z

Documentation preview for this PR (built with commit 60aa804; changes) is ready! 🎉
This preview will update shortly after each push to this PR.

tscrim

Sorry for taking so long to get to this. Here are my comments.

src/sage/rings/semirings/tropical_mpolynomial.py

src/sage/rings/semirings/tropical_polynomial.py

src/sage/rings/semirings/tropical_mpolynomial.py

src/sage/rings/semirings/tropical_variety.py

tscrim

I think this is all of them that you did not change the case. Please be sure to run the doctests before pushing it.

src/sage/rings/semirings/tropical_mpolynomial.py

tscrim

Thank you. A few other little changes. This should be the last round.

tscrim · 2024-10-28T01:25:21Z

src/sage/rings/semirings/tropical_polynomial.py

-    sage: (x + R(3)*x) * (x^2 + x)
-    3*x^3 + 3*x^2
-    sage: (x^2 + R(1)*x + R(-1))^2
-    0*x^4 + 1*x^3 + 2*x^2 + 0*x + (-2)
+    sage: (R(3)*x + R(1)) * (x^2 + x)
+    3*x^3 + 3*x^2 + 1*x
+    sage: (x^2 + x + R(0))^2
+    0*x^4 + 0*x^3 + 0*x^2 + 0*x + 0


Again, why are you changing these tests? If you want to have different tests, just add them instead.

You haven't answered why these tests are changed instead of adding additional ones.

The test was changed to make it clearer while testing the same functionality.

I would just have both. More examples/tests is not a bad thing. :)

src/sage/rings/semirings/tropical_variety.py

tscrim

Also, the bot is reporting that the doc is not building. Have you checked locally?

src/sage/rings/semirings/tropical_variety.py

src/sage/rings/semirings/tropical_mpolynomial.py

tscrim · 2024-11-06T05:19:33Z

src/sage/rings/semirings/tropical_mpolynomial.py

+            sage: R.<x,y> = PolynomialRing(T)
+            sage: p1 = R(3) + R(2)*x + R(2)*y + R(3)*x*y + x^2 + y^2
+            sage: p1.dual_subdivision()
+            Polyhedral complex with 4 maximal cells


You should have it also display the maximal cell polytopes in this complex (with their explicit data) and also below.

tscrim · 2024-11-06T05:20:05Z

src/sage/rings/semirings/tropical_polynomial.py

-    sage: (x + R(3)*x) * (x^2 + x)
-    3*x^3 + 3*x^2
-    sage: (x^2 + R(1)*x + R(-1))^2
-    0*x^4 + 1*x^3 + 2*x^2 + 0*x + (-2)
+    sage: (R(3)*x + R(1)) * (x^2 + x)
+    3*x^3 + 3*x^2 + 1*x
+    sage: (x^2 + x + R(0))^2
+    0*x^4 + 0*x^3 + 0*x^2 + 0*x + 0


You haven't answered why these tests are changed instead of adding additional ones.

verreld7 · 2024-11-06T16:45:41Z

The html doc builds properly locally, but the pdf does not. I am still figuring out where the error is.

tscrim

This might fix the pdf docbuild issue; that can be more strict with the type of object linked. Other than that, I don't see any latex or formatting issues.

tscrim · 2024-11-07T02:11:27Z

src/sage/rings/semirings/tropical_mpolynomial.py

+        corresponding to the exponents of the monomials of tropical
+        polynomial.
+
+        OUTPUT: :class:`~sage.geometry.polyhedron.constructor.Polyhedron`


Suggested change

OUTPUT: :class:`~sage.geometry.polyhedron.constructor.Polyhedron`

OUTPUT: :func:`~sage.geometry.polyhedron.constructor.Polyhedron`

tscrim · 2024-11-07T02:12:43Z

src/sage/rings/semirings/tropical_polynomial.py

-    sage: (x + R(3)*x) * (x^2 + x)
-    3*x^3 + 3*x^2
-    sage: (x^2 + R(1)*x + R(-1))^2
-    0*x^4 + 1*x^3 + 2*x^2 + 0*x + (-2)
+    sage: (R(3)*x + R(1)) * (x^2 + x)
+    3*x^3 + 3*x^2 + 1*x
+    sage: (x^2 + x + R(0))^2
+    0*x^4 + 0*x^3 + 0*x^2 + 0*x + 0


I would just have both. More examples/tests is not a bad thing. :)

verreld7 added 4 commits August 20, 2024 20:42

Add dual_subdivision

06841b5

Add _components_of_vertices and weight_vectors

6734319

Add is_smooth, is_simple, genus, contribution

8b8c5cc

Add weight_vectors in tropical surface

5c9e8d1

verreld7 added 8 commits August 22, 2024 22:43

Add PLOT section in dual subdvision and add one reference

010149c

Add TESTS to genus and contribution

3f1641a

Small fix on style and white spaces

4795639

Refactor vertices in tropical curve

a601cbd

Move weight_vectors from TropicalSurface to TropicalVariety

2e8592c

Small fix on example

96a0f4c

Another fix

ec4307d

Fix docstring in weight_vectors

401ad51

tscrim self-requested a review August 27, 2024 05:41

verreld7 added 10 commits August 30, 2024 17:08

Change output of dual subdivision from Graph to PolyhedralComplex

792b829

Refine docstring

dd2d14d

Small fix on example

f20838a

Refine the docstring more

f425552

Add more examples to TropicalCurve

4306750

Move dual subdivision to TropicalMPolynomial

3d05257

Add polytope to TropicalMPolynomial

d2d211b

Fix PLOT section in dual subdivision

53f495e

Fix dual subdivision

9f66327

Modify dual subdivisio to utilize weight vectors

2fe9f38

tscrim added c: algebraic geometry c: commutative algebra t: enhancement labels Sep 10, 2024

verreld7 added 3 commits September 15, 2024 15:58

Merge branch 'sagemath:develop' into dualsubdivision

b07189d

Add more examples for dual subdivision

87cd7bc

Merge branch 'develop' into dualsubdivision

d4c1251

Fix lint error

204a525

verreld7 marked this pull request as ready for review September 25, 2024 12:34

github-actions bot added the s: needs review label Sep 25, 2024

tscrim requested changes Oct 10, 2024

View reviewed changes

Fix docstring based on review

03fd6f4

tscrim requested changes Oct 25, 2024

View reviewed changes

verreld7 added 3 commits October 25, 2024 15:13

Fix docstring and weight_vectors

a05ec06

Add test to weight_vectors

1adcd0e

Fix lint error

60aa804

tscrim requested changes Oct 28, 2024

View reviewed changes

verreld7 added 2 commits October 29, 2024 10:36

Refactor code based on review

f135107

Merge branch 'sagemath:develop' into dualsubdivision

c0aa966

verreld7 requested a review from tscrim November 5, 2024 07:39

verreld7 added 2 commits November 5, 2024 21:25

Merge branch 'sagemath:develop' into dualsubdivision

c3011eb

Add mark to long doctest

3cfedc8

tscrim requested changes Nov 6, 2024

View reviewed changes

Add the data for newton polytope and dual subdivision

5cf46b1

tscrim requested changes Nov 7, 2024

View reviewed changes

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Implement dual subdivision and weight vectors for tropical variety #38536

Implement dual subdivision and weight vectors for tropical variety #38536

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	OUTPUT: :class:`~sage.geometry.polyhedron.constructor.Polyhedron`
	OUTPUT: :func:`~sage.geometry.polyhedron.constructor.Polyhedron`

Implement dual subdivision and weight vectors for tropical variety #38536

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Implement dual subdivision and weight vectors for tropical variety #38536

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verreld7 commented Aug 20, 2024 • edited Loading

Summary of changes:

📝 Checklist

⌛ Dependencies

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