William Hart's Blog

What I am working on in the short term (next three months)

1. Writing paper on new factoring algorithm I discovered - majority done
2. Studying L-series/theta series of number fields - partly done
3. Parallel implementation of polynomial multiplication in FLINT using multimodular method and Montgomery multiplication (with Tornaria, Watkins, Elkies)
4. Class number project with Michael Jacobson (Calgary)
5. Write paper on algorithm for computing Hermite Normal Form over ZZ which I have been working on

Medium term projects (within the next year)

1. Port of GMP/MPIR to Cell processor
2. Linear algebra in FLINT (specifically over Z/pZ and Q)
3. Put FLINT FFT into MPIR
4. Fast point counting code and p-adic Elkies (with Ronald van Luik)
5. Finish paper with Chapman and Toh on theta series
6. Finish paper on computing special values of Weber functions
7. Working with Peter Shrimpton on sieve based primality testing

Long term objectives (next five years)

1. Compute tables of symmetric Hilbert modular forms
2. Compute modular equations for Hilbert modular forms and investigate Shimura reciprocity as it applies to HMF's
3. Develop new algorithms for computing group structure using sieving (e.g. class groups)
4. Test Vandiver conjecture further than Harvey/Buhler
5. Implement number field sieve
6. Organise conference with Samir Siksek on L-series

Things that are done or that I am working on right now

• Attended Kevin Buzzard's TCC lectures on L-functions and Tate's thesis - Oct--Dec-08
• Andy Novocin visit - developing customised LLL for his factoring algorithm - 11--26-Dec-08
• Testing, documenting, build testing and releasing FLINT 1.1.0 - Done 21-Dec-08
• Merge Peter Shrimpton's implementations of the "n-1", Fibonacci and BSPW primality tests - Done 20-Dec-08
• Writing new F_mpz_poly module for fast polynomial arithmetic in FLINT - Done 22-Nov-08
• Develop and implement new F_mpz integer library - Done 15-Nov-08
• Implementing heuristic GCD algorithm in Z[x] - Done 15-Nov-08
• Implementing half GCD algorithm in Z/pZ[x] - Done 30-Oct-08
• Implement fast 2x2 polynomial matrix multiplication (including Strassen) - done 25-Oct-08
• Reimplement fpLLL:fast to use new matrix library - done 23-Oct-08
• Implement basic matrix library over multiprecision integers - done 15-Oct-08
• Implement new algorithm for polynomial composition - done 15-Oct-08
• Sage Days 10 Nancy, France- 10-15-Oct-08
• Write paper with Martin Albrecht and Gregory Bard on fast matrix multiplication over GF2 in M4RI - done 1-Oct-08
• Implement proved 32 bit precomputed inverses in FLINT - done 5-Oct-08
• Write proofs of middle product code in FLINT- done 4-Oct-08
• Implement polynomial evaluation and derivative in FLINT - 24-Sep-08
• Get new QS ready for use in SAGE - done 23-Sep-08
• Bring MPIR to the point required to release version 0.8.0 - done 16-Sep-08
• Implement hash tables in quadratic sieve - done 14-Sep-08
• Fix mpQS and tinyQS so they will factor integers reliably - done 9-Sep-08
• Move house, travel to Australia and apply for visa - Done 3-Sep-08
• Merging Peter Shrimpton's Lucas primality test code into FLINT - Done 23-Aug-08
• Merging Richard Howell-Peak's irreducibility test and polynomial factorisation code into FLINT - Done 22-Aug-08
• Implement odd/even Kronecker Substitution algorithm as described by David Harvey - Done 21-Aug-08
• Work with Daniel Ellam to plan FLINT module for p-adic arithmetic - Done 20-Aug-08
• Attend conference on modular forms at Bristol University - 19-Aug-08
• Implement odd/even Karatsuba algorithm as described by David Harvey - Done 17-Aug-08
• Implementation of basic infrastructure for new F_mpz_poly model in FLINT - Done 10-Aug-08
• Merge Peter Shrimpton's Jacobi symbol code into FLINT - Done 8-Aug-08
• Implementation of Pocklington-Lehmer's primality test with Peter Shrimpton - Done 7-Aug-08
• Implementation of Berlekamp's polynomial factoring algorithm with Richard Howell-Peak - Done 5-Aug-08
• Testing gcc 4.3.1 builds against MPIR (gcc relies on GMP these days) - Done 2-Aug-08
• Implement Gauss-Jordan elimination for matrices over Z/pZ in FLINT with Richard Howell-Peak - Done 2-Aug-08
• Implementation of algorithm of Musser for square-free factoring of polynomials over Z/pZ with Richard Howell-Peak - Done 1-Aug-08
• Implement polynomial mulmod and powmod for polynomials over Z/pZ mod a fixed polynomial - Done 1-Aug-08
• Implement efficient algorithm to compute derivative of polynomials over Z/pZ with Richard Howell-Peak - Done 31-Jul-08
• Reading on L-series (Riemann zeta, Hurwitz, Barnes, Epstein) - Done 25-Jul-08
• Code in FLINT for computing theta series (with Gonzalo Tornaria) - Done 22-Jul-08
• Fast integer square root function in FLINT - Done 15-Jul-08
• Fixed a range of memory leak and corruption bugs in FLINT - Done 13-Jul-08
• Added code to FLINT for partial factoring of integers - Done 7-Jul-08
• Added code for pentium 4, prescott, nocona tuning in MPIR - Done 5-Jul-08
• Converted vanilla GMP AMD 64 code to intel format - Done 4-Jul-08
• Implement multimodular polynomial multiplication over Z (with Gonzalo Tornaria) - Done 2-Jul-08
• Get build system in MPIR working on numerous architectures - Done 30-Jun-08
• Convert Pierrick Gaudry and Brian Gladman's AMD 64 code to Intel format and Linux calling conventions respectively - Done 30-Jun-08
• Obtain EPSRC grant for research for five years - Done 27-Jun-08
• Conference on L-series at UW - 21-27-Jun-08
• SAGE devel days 1 - 13-20-Jun-08
• Work on fast matrix multiplication over GF2 (with Martin Albrecht) - Done 22-May-08