Zero-equivalence in function fields defined by algebraic differential equations

John Shackell
1993 Transactions of the American Mathematical Society  
We consider function fields obtained as towers over the field of rational functions, each extension being by a solution of an algebraic differential equation. On the assumption that an oracle exists for the constants, we present two algorithms for determining whether a given expression is functionally equivalent to zero in such a field. The first, which uses Gröbner bases, has the advantage of theoretical simplicity, but is liable to involve unnecessary computations. The second method is designed with a view to eliminating these.
doi:10.1090/s0002-9947-1993-1088022-2 fatcat:g2p7ndag3van5i6m4u7nhqb32y