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meromorphic differentials #267

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videlec opened this issue Oct 31, 2023 · 1 comment
Open

meromorphic differentials #267

videlec opened this issue Oct 31, 2023 · 1 comment
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@videlec
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videlec commented Oct 31, 2023

We introduce the necessary framework to define meromorphic differentials built from finitely many polygons. To do so we need to extend EuclideanPolygon to be infinite. We

  • create new classes EuclideanPoint and EuclideanSegment as in the hyperbolic setting
  • promote vertices and edges of EuclideanPolygon to the newly created classes
  • extend angle computation and strata to handle points "at infinity" (angles become negative and correspond to poles of the underlying differential)

For ease of use and backward compatibility finite EuclideanPoint and EuclideanSegment will behave as 2-dimensional vectors.

@videlec videlec self-assigned this Oct 31, 2023
@saraedum
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In #213 there are some geometric primitives for geometry in the Euclidean plane. They do not support points at infinity at all yet but might be a starting point nevertheless (I added them because using Polyhedron from SageMath is just very slow for 2D geometry.)

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