I haven’t used CAS for nontrivial algebra and number theory in a while (think half a decade), but IIRC Magma is a fair bit more powerful than Sage on these topi

I haven’t used CAS for nontrivial algebra and number theory in a while (think half a decade), but IIRC Magma is a fair bit more powerful than Sage on these topics and more consistent as well. But alas, it’s not open source and not free. There’s a free calculator though subject to limits. http://magma.maths.usyd.edu.au/calc/ http://magma.maths.usyd.edu.au/calc/