Computational Algebraic Geometry
{'Code': '05010200', 'Directorate': {'Abbreviation': 'CSE', 'LongName': 'Direct For Computer & Info Scie & Enginr'}, 'Division': {'Abbreviation': 'CCF', 'LongName': 'Division of Computing and Communication Foundations'}}
{'SignBlockName': 'S. Kamal Abdali', 'PO_EMAI': None, 'PO_PHON': None}
An emerging subarea of symbolic manipulation of interest in theoretical         computer science is computational algebraic geometry.  The investigators        have begun to use the techniques of algorithmic design and complexity           theory to study a variety of problems in this area.  The project will           perform complexity analysis of known algorithms, try to design more             efficient algorithms and also investigate lower bounds.  Since many of          the problems in this area have inherently high complexity, the use of           parallelism and randomization becomes important.  Specific problems to          be investigated include the theory of Grobner bases, Wu's algorithm and         cell-decomposition algorithms (such as Collins') for real algebraic             varieties.  In addition, applications to robotics and omputational              geometry will be explored.                                                                                                                                      The project, if successful, will assist in finding faster algorithms for        much more complex computational tasks in geometry than are currently            possible.  Applications include robotics, computer graphics, computer-          aided design.
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{'Code': '286500', 'Text': 'NUMERIC, SYMBOLIC & GEO COMPUT'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8703458.xml'}