Symbolic integration using homotopy methods
The homotopy algorithm is a powerful method for indefinite integration of total derivatives. fly combining these ideas with straight forward Gaussian elimination, we construed an algorithm for the optimal symbolic integration that contain terms that are not total derivatives. The optimization consists of minimizing the number of terms that remain unintegrated. Further, the algorithm imposes an ordering of terms so that the differential order of these remaining terms is minimal. A different method for the Summation of difference expressions is presented in Appendix B. (C) 2009 IMACS. Published by Elsevier B.V. All rights reserved.
symbolic integration homotopy methods optimization variational calculus