Symbolic asymptotics has recently undergone considerable theoretical development, especially in areas where power series are no longer an appropriate tool. Implementation is beginning to follow.
The present book, written by one of the leading specialists in the area, is currently the only one to treat this part of symbolic asymptotics. It contains a good deal of interesting material in a new, developing field of mathematics at the intersection of algebra, analysis and computing, presented in a lively and readable way. The associated areas of zero equivalence and Hardy fields are...
Symbolic asymptotics has recently undergone considerable theoretical development, especially in areas where power series are no longer an appropria...
In the years 1994, 1995, two EIDMA mini courses on Computer Algebra were given at the Eindhoven University of Technology by, apart from ourselves, various invited lecturers. (EIDMA is the Research School 'Euler Institute for Discrete Mathematics and its Applications'.) The idea of the courses was to acquaint young mathematicians with algorithms and software for mathemat ical research and to enable them to incorporate algorithms in their research. A collection of lecture notes was used at these courses. When discussing these courses in comparison with other kinds of courses one might give in a...
In the years 1994, 1995, two EIDMA mini courses on Computer Algebra were given at the Eindhoven University of Technology by, apart from ourselves, var...
In recent years, new algorithms for dealing with rings of differential operators have been discovered and implemented. A main tool is the theory of Grobner bases, which is reexamined here from the point of view of geometric deformations. Perturbation techniques have a long tradition in analysis; Grobner deformations of left ideals in the Weyl algebra are the algebraic analogue to classical perturbation techniques. The algorithmic methods introduced here are particularly useful for studying the systems of multidimensional hypergeometric PDEs introduced by Gelfand, Kapranov and Zelevinsky. The...
In recent years, new algorithms for dealing with rings of differential operators have been discovered and implemented. A main tool is the theory of Gr...
One of the most important and successful theories in computational complex ity is that of NP-completeness. This discrete theory is based on the Turing machine model and achieves a classification of discrete computational prob lems according to their algorithmic difficulty. Turing machines formalize al gorithms which operate on finite strings of symbols over a finite alphabet. By contrast, in algebraic models of computation, the basic computational step is an arithmetic operation (or comparison) of elements of a fixed field, for in stance of real numbers. Hereby one assumes exact arithmetic....
One of the most important and successful theories in computational complex ity is that of NP-completeness. This discrete theory is based on the Turing...
