Hi,
I am implementing the `logarithmic_embedding` function [0] (based on Krumm's code) for my GSoC project, which is used for implementing `points_of_bounded_height` function [1].
However, we encounter the following problem:
By definition (Def. 4.9.6, on page 208 of "A course in computational algebraic number theory"), the logarithmic embedding is a map from number field K to R^n. We are not sure how this function should return, and we consider two options:
1. The function returns a function closure, see examples in [2]
2. It returns a morphism, which is more mathematically correct:
V = VectorSpace(RR, 1)
K = CyclotomicField(3)
B = Hom(K, V, category=Sets())
phi = B(log_map)
phi
Which one do you think is better from math and software engineering perspectives? Are there any other approaches that would be better for this case?
Thank you.
Jing