Symbolic Integration and Summation Using Homotopy Methods
نویسندگان
چکیده
The homotopy algorithm is a powerful method for indefinite integration of total derivatives, and for the indefinite summation of differences. By combining these ideas with straightforward Gaussian elimination, we construct an algorithm for the optimal symbolic integration or summation of expressions that contain terms that are not total derivatives or differences. The optimization consists of minimizing the number of terms that remain unintegrated or are not summed. Further, the algorithm imposes an ordering of terms so that the differential or difference order of these remaining terms is minimal.
منابع مشابه
2 5 O ct 2 00 5 Continuous and Discrete Homotopy Operators : A Theoretical Approach made Concrete ⋆
Using standard calculus, explicit formulas for the one-dimensional continuous and discrete homotopy operators are derived. It is shown that these formulas are equivalent to those in terms of Euler operators obtained from the variational complex. The continuous homotopy operator automates integration by parts on the jet space. Its discrete analogue can be used in applications where summation by ...
متن کامل2 8 Ju n 20 06 Continuous and Discrete Homotopy Operators : A Theoretical Approach made Concrete ⋆
Using standard calculus, explicit formulas for the one-dimensional continuous and discrete homotopy operators are derived. It is shown that these formulas are equivalent to those in terms of Euler operators obtained from the variational complex. The continuous homotopy operator automates integration by parts on the jet space. Its discrete analogue can be used in applications where summation by ...
متن کاملContinuous and discrete homotopy operators: A theoretical approach made concrete
Using standard calculus, explicit formulas for the one-dimensional continuous and discrete homotopy operators are derived. It is shown that these formulas are equivalent to those in terms of Euler operators obtained from the variational complex. The continuous homotopy operator automates integration by parts on the jet space. Its discrete analogue can be used in applications where summation by ...
متن کاملThe homotopy operator method for symbolic integration by parts and inversion of divergences with applications
Using standard calculus, explicit formulas for one-, twoand three-dimensional homotopy operators are presented. A derivation of the one-dimensional homotopy operator is given. A similar methodology can be used to derive the multi-dimensional versions. The calculus-based formulas for the homotopy operators are easy to implement in computer algebra systems such as Mathematica, Maple, and REDUCE. ...
متن کاملModular Algorithms in Symbolic Summation and Symbolic Integration
Where you can find the modular algorithms in symbolic summation and symbolic integration easily? Is it in the book store? On-line book store? are you sure? Keep in mind that you will find the book in this site. This book is very referred for you because it gives not only the experience but also lesson. The lessons are very valuable to serve for you, that's not about who are reading this modular...
متن کامل