Magma Computational Algebra System

Magma defines algebraic structures before operating on them. Its version 2.29 handbook distinguishes Roots over the polynomial's finite field from RootsInSplittingField, which returns roots with multiplicities and the extension field; the worked example evaluates the polynomial at returned roots to check zero residuals. Keep that base field and returned structure with the answer. The free online calculator currently runs V2.29-10, accepting at most 50,000 input bytes and 60 seconds per calculation. Institutional distribution instead uses a quoted subscription, usually three years, with releases/support during the term and continued use of the last installed version afterward. Student distributions are handled through eligible institutions and capped at 150MB memory. Some US non-profit educational/research institutions have separately funded access; this is not universal free desktop licensing.