Implementation for solid angle measure

[Allison Fitisone]

Hi all,

I am new to sage development and am hoping to contribute by implementing the normalized solid angle measure (also called the volumetric modulus) of polyhedral cones. The normalized solid angle measure of a polyhedral cone is the amount of space the cone takes up in reference to some other set. There is a formula, due to Jason Ribando, for the solid angle measure that takes the form of a multivariate hypergeometric series. This formula works for any polyhedral cone of dimension at least 2. My ultimate goal is to have a function for this built into sage. However, I first want to start with the two-dimensional and three-dimensional cases, which are special because in addition to the power series method, these cases have closed formulas that rely on basic trigonometry.

I am unsure whether this class of functions should be appended to an already existing class (and if so, to which one it would belong) or if it should be on its own. I would appreciate any feedback regarding this.

Best,

Alli

[Matthias Koeppe]

On Friday, April 1, 2022 at 3:39:24 PM UTC-7 allison...@gmail.com wrote:

I am new to sage development and am hoping to contribute by implementing the normalized solid angle measure (also called the volumetric modulus) of polyhedral cones. The normalized solid angle measure of a polyhedral cone is the amount of space the cone takes up in reference to some other set. There is a formula, due to Jason Ribando, for the solid angle measure that takes the form of a multivariate hypergeometric series. This formula works for any polyhedral cone of dimension at least 2. My ultimate goal is to have a function for this built into sage. However, I first want to start with the two-dimensional and three-dimensional cases, which are special because in addition to the power series method, these cases have closed formulas that rely on basic trigonometry.

I am unsure whether this class of functions should be appended to an already existing class (and if so, to which one it would belong) or if it should be on its own. I would appreciate any feedback regarding this.

It sounds like this should become a new module in the package sage.geometry for the main part of your work, perhaps src/sage/geometry/solid_angle.py

In addition, you would add a method solid_angle to the class ConvexRationalPolyhedralCone (defined in src/sage/geometry/cone.py);

and perhaps methods such as tangent_cone_solid_angle and normal_cone_solid_angle to the class PolyhedronFace (defined in src/sage/geometry/polyhedron/face.py).