EPSRC Reference: 
GR/J85912/01 
Title: 
COMPUTATIONAL NUMBER THEORY 
Principal Investigator: 
Stephens, Professor N 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Computer Science 
Organisation: 
Cardiff University 
Scheme: 
Standard Research (PreFEC) 
Starts: 
13 June 1994 
Ends: 
12 June 1995 
Value (£): 
6,000

EPSRC Research Topic Classifications: 

EPSRC Industrial Sector Classifications: 

Related Grants: 

Panel History: 

Summary on Grant Application Form 
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 The algorithms required are recent and some, due to Smart, unpublished.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.

Key Findings 
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Potential use in nonacademic contexts 
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Impacts 
Description 
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Summary 

Date Materialised 


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Project URL: 

Further Information: 

Organisation Website: 
http://www.cf.ac.uk 