Harlan Crowder, Ron S. Dembo, et al.
ACM Transactions on Mathematical Software (TOMS)
The explicitly elementary functions of complex variables z1,…, zn are those functions built up from C(z1,…, zn) by exponentiation, taking logarithms, and algebraic operations. The implicitly elementary functions are obtained by solving, via the implicit function theorem, for some of the variables in terms of the others, in systems of equations formed by setting a set of explicitly elementary functions equal to 0. Here we prove a 1923 conjecture of J. F. Ritt to the effect that if the indefinite integral of an explicitly elementary function is implicitly elementary, then it is explicitly elementary. The method features a geometrization of the concepts involved. © American Mathematical Society 1976.
Harlan Crowder, Ron S. Dembo, et al.
ACM Transactions on Mathematical Software (TOMS)
David A. Harville
Linear Algebra and Its Applications
Hang-Yip Liu, Steffen Schulze, et al.
Proceedings of SPIE - The International Society for Optical Engineering
Frances A. Houle, William D. Hinsberg, et al.
Microlithography 2003