| EPSRC Reference: |
GR/L77928/01 |
| Title: |
COMPLEXITY OF ALGORITHMIC PROBLEMS IN REAL ALGEBRAIC GEOMETRY |
| Principal Investigator: |
Vorobjov, Professor N |
| Other Investigators: |
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| Department: |
Computer Science |
| Organisation: |
University of Bath |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 October 1998 |
Ends: |
30 September 2001 |
Value (£): |
49,477
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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The main aim of the proposed program is to design effective algorithms for deciding geometric and topological properties of semialgebraic sets. In particular we are interested in computing the dimension of a set, its complexification and homology groups, in estimating the degree of a set and parameters of its smooth strata. We intend to use computationally effective decompositions of semialgebraic sets into irreducible components as well as triangulations and stratifications. The resulting algorithms will be far-reaching generalisations of the procedures used in commercial computer algebra software like Maple and Mathematics, or more advanced systems (Axiom, Macauley). Ideally, further refinements of our algorithms should become essential parts of such systems. We shall implement lighter versions of the algorithms in an appropriate computer algebra system and explore the possibilities of implementing full versions.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.bath.ac.uk |