I'm wondering if anyone can let me know advantages to installing/setting up Sage on my computer for doing computational math (work in groups, finite fields, and combinatorics, along with some search algorithms).
Currently, I do a lot of my work with Magma; this is great and fast for implementing permutation groups and doing linear algebra over finite fields. I have also been doing some searching for combinatorial objects by setting up my matrices in Magma (geometric constructs), saving them to a file, then using Gurobi to search by setting up an integer programming problem. Gurobi uses a Python interface, so I have a Python script modify my Magma output and feed it into Gurobi and then initialize my problem.
As I understand Sage, it is based on Python, and can interface with a bunch of other things, including Magma and Gurobi. But the syntax seems really weird for calling Magma through the Sage interface. Is there some advantage to be gained? Mostly in terms of using Sage to interface between the two other programs? Am I better off just using Python?
Update, since this question was closed at some point: To make this less opinion based, I am (was) really interested in knowing if it is possible to attain the functionality of Sage in normal Python by loading packages, or if not, what does Sage provide that can not be easily reproduced in Python?