Fermat, Computer Algebra System (original) (raw)

M. Fael, F. Lange, K. Schonwald, M. Steinhauser. Massive vector form factors to three loops. arXiv:2202.05276v1 [hep-ph] (2022)

V. Shtabovenko. Towards two- and three-loop QCD corrections to the width difference in Bs − Bs mixing. SciPost Phys. Proc. 7, 025 (2022)

M. Gerlach, U. Nierste, V. Shtabovenko, M. Steinhauser. The width difference in B--B mixing at order alpha_s and beyond. Journal of High Energy Physics V. 2022, article number 6, (2022).

V. Shtabovenko. NNLO QCD corrections to B-meson mixing. arXiv:2110.12044v1 [hep-ph] (2021)

F. Lange, P. Maierhofer, J. Usovitsch. Developments since Kira 2.0. arXiv:2111.01045 [hep-ph] (2021)

B. Agarwal, S. P. Jones, and A. von Manteuffel. Two-loop helicity amplitudes for gg -> ZZ with full top-quark mass effects. J. High Energ. Phys. 2021, 256 (2021)

H. Chawdhry, M. Lim, A. Mitov. Two-loop five-point massless QCD amplitudes within the integration-by-parts approach. PHYSICAL REVIEW D99,076011 (2019)

A. Neumann, Z. Sullivan. Off-shell single-top-quark production in the Standard Model Effective Field Theory. Journal of High Energy Physics volume 2019, Article number: 22 (2019)

J. Bohm, A. Georgoudis, K. J. Larsen, H. Schonemann, and Y. Zhang. Complete integration-by-parts reductions of the non-planar hexagon-box via module intersections. Journal of High Energy Physics 2018. ArXiv ePrint: 1805.01873

Samuel Abreu, Ben Page and Mao Zeng. Differential equations from unitarity cuts: nonplanar hexa-box integrals. Journal of High Energy Physics 2019. DOI: 10.1007/JHEP01(2019)006.

Jonas Klappert and Fabian Lange. Reconstructing Rational Functions with FireFly. arXiv:1904.00009v2 [cs.SC] Oct. 2019.

A. Behring, J. Blumlein, A. De Freitas, A. Goedicke, S. Klein, A. von Manteuffel, C. Schneider, K. Schonwald. The Polarized Three-Loop Anomalous Dimensions from On-Shell Massive Operator Matrix Elements. arXiv:1908.03779 [hep-ph] Aug. 2019.

V. Hirschi, S. Lionetti, and A. Schweitzer. One-loop weak corrections to Higgs production. arXiv:1902.10167 [hep-ph] Feb. 2019.

Patrick Dukes and Joe Rusinko. Commutation Classes of Double Wiring Diagrams. arXiv:1006.1076v1.pdf. June 2010. Also see: Involve: A Journal of Mathematics, V. 5, 2 (2012), 207 - 218.

R. Angeles-Mart́inez, M. Czakon and S. Sapeta. NNLO soft function for top quark pair production at small transverse momentum. arxiv.org/pdf/1809.01459.pdf. Nov. 2018.

L. Almeida, C. Sturm. Two-loop matching factors for light quark masses and three-loop mass anomalous dimensions in the RI/SMOM schemes. arXiv:1004.4613v2 [hep-ph] 2011.

L. Almeida, C. Sturm. Two-loop matching factors for light quark masses and three-loop mass anomalous dimensions in the regularization invariant symmetric momentum-subtraction schemes. PHYSICAL REVIEW D 82, 054017 (2010)

K. Kudashkina, K. Melnikova, C. Wever. Two-loop amplitudes for processes gg → Hg, qg → Hq and qq → Hg at large Higgs transverse momentum. arXiv:1712.06549 [hep-ph]. Dec. 2017.

J. Ablinger, A. Behring, J. Bluemlein, et al. Heavy Flavor Wilson Coefficients in Deep-Inelastic Scattering: Recent Results. arXiv:1711.07957. Nov. 2017.

T. Luthe, A. Maier, P. Marquard, Y. Schreoder. Complete renormalization of QCD at five loops. Journal of high energy physics. 2017 (3). 020

Philipp Maierhoefer, Johann Usovitsch, Peter Uwer. Kira - A Feynman Integral Reduction Program. arXiv:1705.05610 [hep-ph]. May 2017.

J. Ablinger, A. Behring, J. Blumlein, A. De Freitas, A. von Manteuffel, C. Schneider. The Three-Loop Splitting Functions P(2)qg and P(2,NF)gg. arXiv:1705.01508 [hep-ph]. May 2017.

Andreas von Manteuffel, Lorenzo Tancredi. A non-planar two-loop three-point function beyond multiple polylogarithms. arXiv:1701.05905v1. Jan. 2017.

Kirill Melnikov, Lorenzo Tancredi, Christopher Wever. Two-loop amplitudes for qg → Hq and qq¯→ Hg mediated by a nearly massless quark. arXiv:1702.00426 [hep-ph]. Feb 2017.

J. Ablinger, A. Behring, J. Blumlein, G. Falcioni, A. De Freitas, A. Hasselhuhn, et al. New Results on Massive 3-Loop Wilson Coefficients in Deep-Inelastic scattering. arXiv:1609.03397v2 [hep-ph] 2016.

T. Luthe, Y. Schroder. Five-loop massive tadpoles. arXiv:1609.06786v1 [hep-ph] 2016.

T. Luthe and Y. Schröder. Fun with higher-loop Feynman diagrams. 2016 J. Phys.: Conf. Ser. 762 012066.

T. Luthe, A. Maier, P. Marquard and Y. Schroder. Towards the five-loop Beta function for a general gauge group. JHEP 07 (2016) 127.

Sebastiano Vigna. An Experimental Exploration of Marsaglia's xorshift Generators, Scrambled. ACM Transactions on Mathematical Software, June 2016 Article No. 30.

A. Behring, J. Blumlein, A. De Freitas, A. von Manteuffel, and C. Schneider. The 3-Loop Non-Singlet Heavy Flavor Contributions to the Structure Function g_1(x,Q^2) at Large Momentum Transfer. ArXiv ID: 1504.08217, DOI: 10.1016/j.nuclphysb.2015.06.007. June 2015.

A. Behring, J. Blumlein, A. De Freitas, A. Hasselhuhn, A. von Manteuffel, and C. Schneider. "The O(alpha^3) Heavy Flavor Contributions to the Charged Current Structure Function xF3(x,Q^2) at Large Momentum Transfer." Physical Review D 92(114005). November 2015.

A. von Manteuffel, E. Panzer, and R. Schabinger. "On the Computation of Form Factors in Massless QCD with Finite Master Integrals," http://arxiv.org/abs/1510.06758, October 2015.

T. Gehrmann. A. von Manteuffel, L. Tancredi. "The two-loop helicity amplitudes for qq → V1V2 →four leptons," arxiv:1503.04812v2, September 2015.

L. Tancredi, T. Gehrmann. A. von Manteuffel. "Two-loop QCD corrections to vector boson pair production at the LHC," 12th International Symposium on Radiative Corrections (Radcor 2015) and LoopFest XIV (Radiative Corrections for the LHC and Future Colliders), 15-19 June 2015. UCLA Department of Physics & Astronomy Los Angeles, CA, USA.

J. Ablinger, A. Behring, J. Blumlein, A. De Freitas, A. von Manteuffel, C. Schneider. "Calculating Three Loop Ladder and V-Topologies for Massive Operator Matrix Elements by Computer Algebra," arXiv:1509.08324, September 2015.

Li, von Manteuffel, Schabinger, Zhu, "Soft-virtual corrections to Higgs production at N^3LO". arXiv:1412.2771, December 2014.

A. De Freitas, J. Ablinger, A. Behring, J. Bluemlein, A. Hasselhuhn, A. von Manteuffel, C.G. Raab, M. Round, C. Schneider, F. Wissbrock. Recent progress on the calculation of three-loop heavy flavor Wilson coefficients in Deep-Inelastic Scattering. Proceedings of Science. DOI: https://doi.org/10.22323/1.211.0041\. August 2014.

J. Ablinger, A. Behring, J. Blumlein, A. De Freitas, A. Hasselhuhn, A. von Manteuffel, et al. The 3-Loop Non-Singlet Heavy Flavor Contributions and Anomalous Dimensions for the Structure Function F2(x,Q2) and Transversity. arXiv:1406.4654v1 [hep-ph] June 2014.

J. Ablinger, J. Blümlein, A. De Freitas, A. Hasselhuhn, A. von Manteuffel, M. Round, C. Schneider. The O(α_s^3 T_F^2) Contributions to the Gluonic Operator Matrix Element. arXiv:1405.4259v1 [hep-ph] May 2014.

C. Sturm. Higher order QCD results for the fermionic contributions of the Higgs-boson decay into two photons and the decoupling function for the MS renormalized fine-structure constant. The European Physical Journal C volume 74, Article number: 2978 (2014)

J. Ablinger, J. Blumlein, A. De Freitas, A. Hasselhuhn, A. von Manteuffel, M. Round, C. Schneider, F. Wissbrock. 3-Loop Heavy Flavor Corrections in Deep-Inelastic Scattering with Two Heavy Quark Lines. arXiv:1407.2821 [hep-ph] 2014.

Ablinger, Blumlein, DeFreitas, Hasselhuhn, von Manteuffel, Round, Schneider, Wissbrock, "The transition matrix element Agq(N) of the variable flavor number scheme at O(alpha s^3)". Nuclear Physics B, February 2014.

Sebastiano Vigna, "An experimental exploration of Marsaglia's xorshift generators, scrambled". Universita degli Studi di Milano, Italy. http://vigna.di.unimi.it/ftp/papers/xorshift.pdf. May 2014.

Maierhofer, P., Marquard, P., Complete three-loop QCD corrections to the decay H+gamma. Zbl 1307.81067. Phys. Lett., B 721, No. 1-3, 131-135 (2013).

Sturm, Christian. Leptonic contributions to the effective electromagnetic coupling at four-loop order in QED. Zbl 1282.81201. Nucl. Phys., B 874, No. 3, 698-719 (2013).

Schneider, Carsten (ed.) et al., Computer algebra in quantum field theory. Integration, summation and special functions. Wien: Springer (ISBN 978-3-7091-1615-9/hbk; 978-1-4614-8523-0/ebook). Texts and Monographs in Symbolic Computation, 361-379 (2013).

P.A. Baikov, K.G. Chetyrkin, J.H. Kuhn, C. Sturm. The relation between the QED charge renormalized in MSbar and on-shell schemes at four loops, the QED on-shell beta-function at five loops and asymptotic contributions to the muon anomaly at five and six loops. Nucl.Phys.B 867 (2013) 182-202.

Lloyd, Noel G.; Pearson, Jane Margaret. A cubic differential system with nine limit cycles. Zbl 1304.34062. J. Appl. Anal. Comput. 2, No. 3, 293-304 (2012).

David Yuen, "The Utility of Computations" and "The Satake Compactification of the Paramodular Group". First EU-US Conference on Automorphic Forms and Related Topics, Aachen University, August 2012.

William B. Kilgore and Christian Sturm. Two-loop virtual corrections to Drell-Yan production at order alpha_s alpha^3. Phys. Rev. D 85, 033005, Feb 2012.

Czakon, M. Double-real radiation in hadronic top quark pair production as a proof of a certain concept. Zbl 1215.81117. Nucl. Phys., B 849, No. 2, 250-295 (2011).

Shaun Ault. Symmetric Homology of Algebras. arXiv:0902.1274v3 [math.AT] 2011.

Grozin, A. G. Integration by parts: An introduction. International Journal of Modern Physics A 26(17) (2011).

J. M. Pearson and N. G. Lloyd, "Kukles revisited: Advances in computing techniques." Computers and Mathematics with Applications, v. 60, issue 10, 2010, pp. 2797 - 2805.

B. Palancz, J. Awange, P. Zaletnyik, "Computational Mathematics: Theory, Methods and Applications." Peter G. Chareton, ed. Nova Science Publishers, New York, January 2010.

Bekavac, S.; Grozin, A.G.; Seidel, D.; Smirnov, V.A. Three-loop on-shell Feynman integrals with two masses. Zbl 1194.81252. Nucl. Phys., B 819, No. 1-2, 183-200 (2009).

Zhao, ShiZhong; Fu, HongGuang. Three kinds of extraneous factors in Dixon resultants. Zbl 1179.13024. Sci. China, Ser. A 52, No. 1, 160-172 (2009).

A. V. Smirnov, "Algorithm FIRE: Feynman Integral Reduction." July 2008. http://arxiv.org/pdf/0807.3243v3
See also Smirnov's software that links to Fermat, FIRE

M. Oura, C. Poor, and D. S. Yuen, "Towards the Siegel Ring in Genus Four." International Journal of Number Theory, August 2008.

P. A. Baikov, K.G.Chetyrkin, and C. Sturm. New Results in Four and Five Loop QED calculations. Nuclear Physics B - Proceedings Supplements Volume 183, October 2008, Pages 8-13.

J. H. Kuhn, M. Steinhauser and M. Tentyukov, "Massless Four-Loop Integrals and the Total Cross Section in e+ e- Annihilation." High Performance Computing in Science and Engineering '07; Transactions of the High Performance Computing Center, Stuttgart (HLRS) 2008.

Bela Palancz, Robert H. Lewis, Piroska Zaletnyik, and Joseph Awange, "Computational Study of the 3D Affine Transformation Part I. 3-point Problem."
First version online at the Mathematica website, revised versionavailable here. March 2008.

A. Maier, P. Maierhofer and P. Marquard. Higher Moments of Heavy Quark Correlators in the Low Energy Limit at O(alpha^2_s). Nucl. Phys.B Proc.Suppl. 183 (2008) 209-214.

P. Marquard, L. Mihaila, J.H. Piclum and M. Steinhauser, Relation between the pole and the minimally subtracted mass in dimensional regularization and dimensional reduction to three-loop order. Nuclear Physics B Volume 773, Issues 1–2, 25 June 2007, Pages 1-18.

A.G. Grozin, P. Marquard, J.H. Piclum, and M. Steinhauser. Three-Loop Chromomagnetic Interaction in HQET. arXiv:0707.1388v1 [hep-ph] 2007.

S. Bekavac, D. Seidel, "On-shell renormalisation constants including two different nonzero masses." October 2007. http://aps.arxiv.org/list/hep-ph/0710\.

S. Bekavac, D. Seidel1, M. Steinhauser and A. Grozin, Light quark mass effects in the on-shell renormalization constants. Journal of High Energy Physics, Volume 2007, JHEP10(2007)

Nazar Khan, "Silhouette-Based 2D-3D Pose Estimation Using Implicit Algebraic Surfaces", Master Thesis, Saarland University, Germany, 2007. advisor: Bodo Rosenhahn.download pdf version.

K. G. Chetyrkin, M. Faisst, J. H. Kuhn, P. Maierhofer, and C. Sturm. Four-Loop QCD Corrections to the Electroweak rho Parameter. Phys. Rev. Lett. 97, 102003 (2006).

Fiala, Nick C.; Agre, Keith M. Searching for shortest single axioms for groups of exponent 6. Zbl 1107.68097 J. Autom. Reasoning 36, No. 3, 241-257 (2006).

K. Chetyrkin, J. Kuhn, and C. Sturm. Four-loop moments of the heavy quark vacuum polarization function in perturbative QCD. Eur. Phys. J. C 48, 107–110 (2006). https://doi.org/10.1140/epjc/s2006-02610-y

Fotiou, I.A.; Rostalski, P.; Parrilo, P.A.; Morari, M. Parametric optimization and optimal control using algebraic geometry methods. Zbl 1133.93337 Int. J. Control 79, No. 11, 1340-1358 (2006).

Lewis, Robert H. and E. A. Coutsias, "Algorithmic Search for Flexibility using Resultants of Polynomial Systems." Proceedings of the ADG 2006 Conference (Automatic Deduction in Geometry), Pontevedra Spain, August 31 - September 2, 2006.download pdf version.

P. Marquard, J.H. Piclum, Dirk Seidel, M. Steinhauser. Fermionic corrections to the three-loop matching coefficient of the non-relativistic vector current. Nuclear Physics B 758(1): 144 - 160. August 2006.

K.G. Chetyrkin, J.H. Kuhn, C. Sturm. QCD decoupling at four loops. Nuclear Physics B 744 (2006) 121–135.

K. G. Chetyrkina, C. Sturm. Recent Results on Four-loop Tadpoles. NUCL PHYS B-PROC SUPPL, vol. 160, pp. 230-234, 2006.

Bozoki, Sandor and Robert H. Lewis, "Solving the Least Squares Method Problem in the AHP for 3 x 3 and 4 x 4 Matrices," Central European Journal for Operations Research, September 2005.download pdf version.

K.G. Chetyrkin, M. Faisst, C. Sturm, and M. Tentyukov. e-Finite Basis of Master Integrals for the Integration-By-Parts Method. January 2006. 28pp. http://arxiv.org/pdf/hep-ph/0601165\.

Zhao, Shizhong; Fu, Hongguang. An extended fast algorithm for constructing the Dixon resultant matrix. Zbl 1122.14302 Sci. China, Ser. A 48, No. 1, 131-143 (2005).

M. Czakon. "The Four-loop QCD Beta-Function and Anomalous Dimensions." DESY-04-223, SFB-CPP-04-62, Nov 2004. 14pp. Published in Nucl.Phys.B710:485-498, 2005. http://arxiv.org/pdf/hep-ph/0411261.

K. G. Chetyrkin, J. H. Kuhn, P. Mastrolia, C. Sturm. Heavy-quark vacuum polarization: first two moments of the O(alphas^3 nf^2) contribution. http://arxiv.org/abs/hep-ph/0412055

M. Czakon, J. Gluza, T. Riemann. "Master Integrals for Massive Two-Loop BHABHA Scattering in QED." DESY-04-222, SFB-CPP-04-61, Dec 2004. 21pp. Published in Phys.Rev.D71: 073009, 2005. http://arxiv.org/pdf/hep-ph/0412164

M. Awramik, M. Czakon, A. Freitas, and G. Weiglein. Complete Two-Loop Electroweak Fermionic Corrections to the Effective Leptonic Weak Mixing Angle and Indirect Determination of the Higgs Boson Mass. Phys. Rev. Lett. 93, 201805 (2004)

Little, John. "Solving the Selesnick-Burrus Filter Design Equations Using Computational Algebra and Algebraic Geometry", Advances in Applied Mathematics, 31 (2003), p. 463-500.

Brumer, Armand. "The Rank of Jo(N)," Asterisque 228 (1995) p. 41-68.

Yuen, David S. Siegel modular cusp forms (2004). personal communication.

Lewis, Robert H. and Stephen Bridgett, "Conic Tangency Equations and Apollonius Problems in Biochemistry and Pharmacology," Mathematics and Computers in Simulation 61(2) (2003) p. 101-114.download pdf version.

Lewis, Robert H. and Peter F. Stiller, "Solving the recognition problem for six lines using the Dixon resultant," Mathematics and Computers in Simulation 49 (1999) p. 205-219. download pdf version.

Lewis, Robert H. and George Nakos, "Solving the Six Line Problem with Resultants," presented to the "Grand Challenges" session at IMACS, Prague, August 1998.

Lewis, Robert H. "The Six Line Problem and Resultants," presented to the "Grand Challenges" session at IMACS, Hawaii, July 1997.

Lewis, Robert H. and Guy D. Moore. "Computer Search for Nilpotent Complexes," Experimental Mathematics6:3 (1997) p. 239-246.

Lewis, Robert H. and Sal Liriano. "Isomorphism Classes and Derived Series of Almost-Free Groups," Experimental Mathematics 3 (1994) p.255-258.

Some more papers that reference Fermat. In January 2024, this search found 250. No doubt there is overlap with the above list.

List of 250 papers.

ball Jenks Prize Nomination Form

The 2008 nomination form for Fermat for the Jenks Prize can be read here.

ball Older Update History

June 7, 2016. Features and bug fixes to 64 bit versions. Bug fix only to 32 bit versions, now considered obsolete. Small revisions to manual.

November 25, 2015. 64 bit version 5.21: Significant revision of some heuristics for multivariate polynomial GCD. New interface features upon invoking Fermat.

October 20, 2014: 64 bit version 5.17. Bug fix in both Mac and Linux 64 bit versions. There was another small bug in monomial multiply involving constants. Also, the imperative command &(_o = ...) now works.

June 24, 2014: 5.15 or 5.16. Bug fix in both Mac and Linux 64 bit versions. A small bug introduced last August when monomial multiply was implemented could crash Fermat.

November 9, 2013. Minor improvements in the 64 bit versions; version 5.1.

October 25, 2013. New fast monomial-oriented multiplication for multivariate polynomials in the 64 bit versions; version 5.0. See here.

March 25, 2013. Bug fix, all versions, involving large two-variable polynomial multiplication. Refined heuristics for multivariable polynomial gcd.

November 6, 2012. Bug fix, all versions, involving Pseudet.

June 12, 2012. Bug fix, all versions.

January 3, 2012. Three float versions created. See here. Also, minor revisions of Mac OS X, Linux, and Windows.

November 10, 2011. New Windows version, created with Cygwin. The old Windows version is obsolete and very inferior.

November 1, 2011. New versions for Linux and OS X, 32 bit and 64 bit.

July 25, 2011. New revised manuals for Linux and OS X.

July 23, 2011. 3.9.99 Several bug fixes, new functions, faster multivariate polynomial gcd, 64 bit versions. See here.

October 7, 8, 2010. Version 3.9.9x for OSX and Linux. New 64 bit versions 4.08. See above and here.

October 19, 2009. Version 3.9.9i for OSX and Linux. See here.

January 19, 2009. Source code for FFermat, float version, now available. See here.

January 8, 2009. Version 3.9.8f for OSX and Linux. See here.

August 6, 2008. Uploaded a documented set of functions to run the Dixon-EDF method. This is the method of choice for solving symbolic systems of multivariate polynomial equations over most ground rings. See here.

May 6, 2008. Version 3.9.7 for OSX and Linux. See here.

February 10, 2008. Version 3.9.2 for OSX and Linux. See here.

October 29, 2007. Version 3.8.8 for Mac OSX and Linux; 3.6.9 for Windows; 3.7.0 for Mac 0S9. See here.

September 26, 2007. Version 3.8.7 for Mac OSX and Linux. See here.

March 13, 2007. Version 3.8.1 for Mac OSX and Linux. 3.6.8 for Windows. See here.

August 10, 2006. Version 3.7.9 for Mac OSX and Linux. See here.

June 26, 2006. Version 3.7.8 for Mac OSX and Linux, 3.6.7 for Windows. See here.

June 11, 2006. Version 3.7.7 for Mac OSX and Linux. See here.

April 13, 2006. Version 3.7.5 for Mac OSX and Linux. See here.

March 10, 2006. Version 3.7.4 for Mac OSX and Linux. 3.6.6 for Windows. See here.

February 18, 2006. Version 3.7.2 for Mac OSX, Linux. Bug fixes and speed ups. See here.

December 30, 2005. Version 3.6.9 for Mac OSX, Linux, Unix; 3.6.5 for OS 9 and Windows. Bug fixes. See here.

November 30, 2005. Version 3.6.7 for Mac OSX. Bug fix. See here.

November 22, 2005. Version 3.6.4 for Windows. Bug fix. See here.

October 19, 2005. Version 3.6.7 for Linux. Various new features. See here.

July 27, 2005. Version 3.6.4 for all versions but Unix. Fixed a small memory leak. See here.

July 18, 2005. Version 3.6.3 for Mac OSX/Linux. Fixed a bug in the speedups of 3.5.8 - 3.6.0. See here.

June 27, 2005. Version 3.6.0 for Mac OSX/Linux/Windows/OS9. Additional speedup in multivariate polynomial gcd. See the Fermat Tests Page. Fixed memory leak.

June 10, 2005. Version 3.5.0 - 3.5.8 for Mac OSX/Linux/Unix. Significant speedups in multivariate polynomial gcd, 14% - 60% in various tests. See the Fermat Tests Page. Various bug fixes. Updated the manual for these versions, html and ps. See here.

January 1, 2005: Version 3.4.9 now available for Windows and Mac OS 9. This is a fix of a stupid trivial bug that got introduced in 3.4.8 in these two versions. It affected GCD of polynomials. Also see here.

November 3, 2004: Version 3.4.8 now available for Linux, Mac OS X, and Mac OS 9. Details are here.

October 20, 2004: New version 3.4.8 for Windows. Details are here.

September 1, 2004: New versions 3.4.7 for Linux and Mac OSX. Details are here.

July 12, 2004: Bug fix all versions but Unix. Multiplying a rational number by a rational function was flawed in some cases.

July 6, 2004: Version 3.4.6 for Linux. Minor bug fix. Details are here.

July 2, 2004: Version 3.4.5 for Linux. Minor bug fixes. Details are here.

June 27, 2004: Version 3.4.4 for Linux. Bug fix. Details are here.

June 9, 2004: Version 3.4.2 for Unix. See June 6 below. Details are here.

June 6, 2004: Versions 3.3.2 and 3.4.2. Quite a few bug fixes, especially in Linux. A few new features in Linux, bringing it up to the other versions. Details are here.

May 1, 2004: New version 3.3 for Mac and Windows. This version provides remarkable speedups in basic one variable polynomial arithmetic and g.c.d. Read the April 30, 2004 description below. This is not version 3.4 because the larger moduli have not been implemented here. The Mac MPW version has not been updated, and will no longer be maintained unless I hear from someone who cares about it.

April 30, 2004: New version 3.4 for Linux. This version provides remarkable speedups in basic one variable polynomial arithmetic and g.c.d. Since that is used by other parts of Fermat, the speedup propagates throughout the system to some extent. Problem 3 on the Fermat Tests Pagesaves 30%. Some computations over Z/p save 60%. Also a new implementation of LaGrange interpolation for determinant of sparse matrices, and Z/p is implemented for primes < 2^31. See the second ReadMe.

December 9, 2003: Added a version for Linux compiled with the -static option for gcc. This creates a very large application (5.5 meg), but fixes the problem some people had because they have old Linux libraries.

December 5, 2003: Version 3.3 for Linux and Windows; bug fix. A user reported a bug, which sometimes occurs when a rational number is multiplied or divided by a quolynomial. The same bug occurs in Mac and Unix, but those fixes are not ready yet.

September 25, 2003: Added Linux and Unix versions.

September 3, 2003: Version 3.2. Bug fixes. For Windows, Fermat would sometimes hang after hitting return. See the second ReadMe.

April 23, 2003: Version 3.1. Implemented builtin functions to return the number of polyvars and the nth prime. Content now has a second [optional] parameter, the name or ordinal of a poly var. The major improvement is yet another large gain in the speed of multivariate GCD. The time for one benchmark is cut by more than 64%. See the second ReadMe.