Computational algebra is an area of algebra that seeks efficient algorithms to answer fundamental problems concerning basic algebraic objects (groups, rings, fields etc), such as, for example, deciding whether two groups are isomorphic, finding the decomposition of a group element in terms of the group generators, computing the lattice of subgroups of a group, etc. (see, for example, http://www.maths.nuigalway.ie/deBrun6/Brooksbank/Galway-1.pdf).

Thus, computational algebra differs from computer algebra, since the latter deals with questions like carrying out symbolic manipulations with mathematical expressions (through, of course, practical implementations may overlap in some areas).

Please use these notes to distinguish between computer-algebra-systems tag for questions about generic computer algebra systems, and computational-algebra tag for questions about the topics outlined above.

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