I practice theoretical mathematics and I know (almost) nothing about SAGE, MAGMA. I would like to know (in general) what type of questions can I ask SAGE to do? For example, I know that given an explicit number field, softwares like SAGE, MAGMA can compute its Galois group, discriminant and MANY other things. But is the converse possible? That is, if I give a finite (solvable) group $H$ (of course for which Galois inverse problem has been proved), is SAGE able to give me an explicit field $K$ over $\mathbb{Q}$ with $H$ as its Galois group over $\mathbb{Q}$?
2025-01-13 05:54:00.1736747640
Questions that SAGE, MAGMA can answer?
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Of course you can get e.g. sage to run through all polynomials of a given degree and ask it to compute their Galois groups until you get a hit, but this has been done before. In such a case it is a much better idea to look into one of the many existing data bases, e.g. http://galoisdb.math.upb.de/ or http://www.mathematik.uni-kl.de/~numberfieldtables/ .