| EPSRC Reference: |
GR/J85912/01 |
| Title: |
COMPUTATIONAL NUMBER THEORY |
| Principal Investigator: |
Stephens, Professor N |
| Other Investigators: |
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| Department: |
Computer Science |
| Organisation: |
Cardiff University |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
13 June 1994 |
Ends: |
12 June 1995 |
Value (£): |
6,000
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Summary on Grant Application Form |
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The project is to design and implement algorithms to find all rational integer points on any elliptic or hyperelliptic curve. This will be achieved by considering associated Thue equations and using techniques developed by De Weger and modifications due to Smart which improve their efficiency. For hyperelliptic curves, another technique due to Smart is to transform the equation to another defined over the ring of integers of an algebraic number field. The algorithms required are recent and some, due to Smart, unpublished. They are computationally intensive but feasible and they will be used to determine for example all elliptic curves of a given conductor and all hyperelliptic curves with good reduction outside a given set of primes.The algorithms are to be implemented on the department's nCUBE2 hypercube computer to achieve faster results and allow harder problems to be solved with the same software on computers with more processors. The implementation will involve porting some software from packages in number theory (eg KANT and PARI) to the nCUBE2.
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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.cf.ac.uk |