2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/153783Classical and nonclassical symmetries of the nonlinear heat equation $$u_t=u_{xx}+f(u),\eqno(1)$$ are considered. The method of differential Gröbner bases is used both to find the conditions on $f(u)$ under which symmetries other than the trivial spatial and temporal translational symmetries exist, and to solve the determining equations for the infinitesimals. A catalogue of symmetry reductions is given including some new reductions for the linear heat equation and a catalogue of exact solutions of (1) for cubic $f(u)$ in terms of the roots of $f(u)=0$.Latex file 32 pages, 13 figures available from authorExactly Solvable and Integrable Systemstext