Implement dual subdivision and weight vectors for tropical variety #38536
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Documentation preview for this PR (built with commit 99e8af5; changes) is ready! 🎉 |
tscrim
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Oct 10, 2024
tscrim
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tscrim
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tscrim
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| 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 |
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You should have it also display the maximal cell polytopes in this complex (with their explicit data) and also below.
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The html doc builds properly locally, but the pdf does not. I am still figuring out where the error is. |
tscrim
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| @@ -1103,9 +1611,29 @@ def plot(self): | |||
| T = TropicalSemiring(QQ) | |||
| R = PolynomialRing(T, ('x,y')) | |||
| x, y = R.gen(), R.gen(1) | |||
| p2 = x**6 + R(4)*x**4*y**2 + R(2)*x**3*y**3 + R(3)*x**2*y**4 + \ | |||
| x*y**5 + R(7)*x**2 + R(5)*x*y + R(3)*y**2 + R(2)*x + y + R(10) | |||
| p2 = (x**6 + R(4)*x**4*y^2 + R(2)*x**3*y**3 + R(3)*x**2*y**4 | |||
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Suggested change
| p2 = (x**6 + R(4)*x**4*y^2 + R(2)*x**3*y**3 + R(3)*x**2*y**4 | |
| p2 = (x**6 + R(4)*x**4*y**2 + R(2)*x**3*y**3 + R(3)*x**2*y**4 |
Missed ^ to **.
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…ropical variety
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This PR introduces some new methods in `TropicalVariety` related to dual
subdivision and weight vectors.
### Summary of changes:
1. Add `dual_subdivision` in `TropicalVariety`: return the dual
subdivision for any tropical variety as a Graph object
2. Add `_components_of_vertices` in `TropicalCurve`: intermediate method
the help calculate weight vectors
3. Add `weight_vectors` in `TropicalCurve`: return the weight vectors of
each vertex
4. Add `weight_vectors` in `TropicalSurface`: return the weight vectors
of each unique line of intersection
5. Add a few methods related to dual subdivision of tropical curve such
as:
- `is_smooth`
- `is_simple`
- `genus`
- `contribution`
CC: @tscrim
### 📝 Checklist
<!-- Put an `x` in all the boxes that apply. -->
- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
- [x] I have linked a relevant issue or discussion.
- [x] I have created tests covering the changes.
- [x] I have updated the documentation and checked the documentation
preview.
### ⌛ Dependencies
sagemath#37962: issues related to this PR
sagemath#38291: continuation of this PR
URL: sagemath#38536
Reported by: Verrel Rievaldo Wijaya
Reviewer(s): Travis Scrimshaw, Verrel Rievaldo Wijaya
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This PR introduces some new methods in
TropicalVarietyrelated to dual subdivision and weight vectors.Summary of changes:
Add
dual_subdivisioninTropicalVariety: return the dual subdivision for any tropical variety as a Graph objectAdd
_components_of_verticesinTropicalCurve: intermediate method the help calculate weight vectorsAdd
weight_vectorsinTropicalCurve: return the weight vectors of each vertexAdd
weight_vectorsinTropicalSurface: return the weight vectors of each unique line of intersectionAdd a few methods related to dual subdivision of tropical curve such as:
is_smoothis_simplegenuscontributionCC: @tscrim
📝 Checklist
⌛ Dependencies
#37962: issues related to this PR
#38291: continuation of this PR