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Using computer-aid approach to solve algebraic problems. Questions with this tag should typically include at least one other tag indicating what sort of algebraic problem is involved, such as ac.commutative-algebra or rt.representation-theory or ag.algebraic-geometry.

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Algorithms for Polynomials Over a Real Algebraic Number Field, a reference

The thesis can be found here.
Carl-Fredrik Nyberg Brodda's user avatar
2 votes

Is there a CAS that can solve a given system of equations in a finite group algebra $kG$?

As you say you have a given system of equations, you can do this by brute-force in GAP. The following constructs a group algebra $kG$ in GAP -- this one constructs $kG$ when $k = GF(4)$ and $G = C_2$. …
Carl-Fredrik Nyberg Brodda's user avatar