The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Formal solutions of differential equations
Journal of Symbolic Computation
Symbolic integration: the stormy decade
Communications of the ACM
Landen transformations and the integration of rational functions
Mathematics of Computation
Algorithms for rational function arithmetic operations
STOC '72 Proceedings of the fourth annual ACM symposium on Theory of computing
Symbolic mathematical computation in a Ph.D. computer science program
SIGCSE '72 Proceedings of the second SIGCSE technical symposium on Education in computer science
Symbolic mathematical computation—introduction and overview
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
Modular arithmetic and finite field theory: A tutorial
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
Symbolic integration the stormy decade
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
On square-free decomposition algorithms
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
Algebraic algorithms using p-adic constructions
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
Symbolic mathematical computation in a Ph. D. computer science program
ACM SIGCSE Bulletin
Complexity of creative telescoping for bivariate rational functions
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Appointment Scheduling Under Patient No-Shows and Service Interruptions
Manufacturing & Service Operations Management
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Algorithms for symbolic partial fraction decomposition and indefinite integration of rational functions are described. Two types of partial fraction decomposition are investigated, square-free and complete square-free. A method is derived, based on the solution of a linear system, which produces the square-free decomposition of any rational function, say A/B. The computing time is shown to be O(n4(1n nf)2) where deg(A) 4(1n nf)2). A thorough analysis is then made of the classical method for rational function integration, due to Hermite. It is shown that the most efficient implementation of this method has a computing time of O(k3n5(1n nc) 2), where c is a number closely related to f and k is the number of square-free factors of B. A new method is then presented which avoids entirely the use of partial fraction decomposition and instead relies on the solution of an easily obtainable linear system. Theoretical analysis shows that the computing time for this method is O(n5 (in nf) 2) and extensive testing substantiates its superiority over Hermite's method.