Combining maple and form to decide on integrability questions Original Research Article

We consider the existence problem of (infinitely many) symmetries for equations of the form ut = uk + F(u,…,uk−1) when they are λ-homogeneous (with respect to the scaling uk ↦ μλ+kuk. This involves fairly large calculations which are carried out in a mixture of Form and Maple. We give an introduction to this mixed language style of programming, indicating how the choice of language will be determined by bottlenecks in the computation. We give some fairly complete results for the λ = 0 case, which leads to more difficult computer algebra problems involving differential ideals. Finally we show some results extending the methods to cosymmetries.