How do I show Sage results computation in my LaTeX file?

Question

I am new to SageMath so I apologize in advance if this question is not exactly appropriate for this site but since I don't really have any other way to know the answers, I 'll ask it anyway. (I am using UBUNTU 14.04 with source code installation of Sage in terminal)

1. How do I show sage computations in my tex file? I am able to have the sage code show up in my tex file but not the results of that computation. How do I do that?

2. I saw someone's thesis here: 1812.10415 (not able to post link but googling this number leads to that pdf), page 68. They have shown the results of two descent like, they computed the bounds on the fans of weak Mordell Weil groups and I couldn't find the relevant codes to do the same in the basic Sage manual available online. How do I do that? Plus they have not only shown what sage codes they typed(which I didn't understand) but have also embedded their results in their latex file. How do I go on about doing the same?

I will appreciate any helpful comments or answers I can get.

Thank you.

Answer 1

With respect to how do you show Sage calculations in LaTeX, it depends on your sage output. You have \sage for typical calculations, \sagestr if calculations result in a string, \sageplot for graphs, and sagecommandline to get the look of running a Sage session. It sounds like you're talking about the look and feel of a Sage session. I would start first by looking at my answer to the question here about including source code in a tex file. The link to a William Stein file still works; this will give you the look and feel of Sage documentation. After that look into the sagecommandline environment. There are examples here, here, and here.

With respect to your second question, calculations like that are done by Sage using the sagesilent environment and the answer can be output to a string, like my answer here. It's also possible they ran the session in Sage and copy/pasted the results into their tex file. I tend to think using the William Stein tex file and copy/pasting the results in would be quickest way. You say, "They have shown the results of two descent like, they computed the bounds on the fans of weak Mordell Weil groups and I couldn't find the relevant codes to do the same in the basic Sage manual available online.". I think that is done in lines 27-32 of example.sage on page 68. Searching: two_descent_by_two_isogeny sagemath gives me this page in the documentation.