Fwd: [sage-devel] Return "type" of the `logarithmic_embedding` function

[John Cremona]

---------- Forwarded message ---------
From: Jing Guo <dev....@gmail.com>
Date: Wed, 27 Jul 2022, 10:49
Subject: [sage-devel] Return "type" of the `logarithmic_embedding` function
To: sage-devel <sage-...@googlegroups.com>

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.

[0]: https://trac.sagemath.org/ticket/34212

[1]: https://trac.sagemath.org/ticket/32686

[2]: https://git.sagemath.org/sage.git/diff?id=8129e332b20c8cd73b50f2e1d48222e7a706ba21

Jing

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