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
requested changes
Oct 10, 2024
tscrim
requested changes
Oct 25, 2024
tscrim
requested changes
Oct 28, 2024
tscrim
requested changes
Nov 6, 2024
| 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
requested changes
Nov 7, 2024
tscrim
reviewed
Nov 11, 2024
| @@ -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 **.
tscrim
approved these changes
Nov 12, 2024
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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