Software Productions (Download)arrow_0055

1.       HOM4PS-2.0 : HOMotopy method for solving Polynomial Systems.

2.       MixedVol-2.0 : Computing the Mixed Volume of a polynomial system.

3.       RankRev : A Matlab package for computing numerical ranks.






[1] Allgower, E.L. and K. Georg (1993), “Continuation and path following”, Acta Numerica, 1-64.


[2] Bernshtein, D.N. (1975), “The number of roots of a system of equations”, Functional Analysis and Appl., 9(3), 183-185. Translated from Funktsional. Anal. I Ego Prilozhen., 9(3), 1-4.


[3] R.D. Fierro, P.C. Hansen, and P.S.K. Hansen (1999), “UTV tools: MATLAB templates for rank-revealing UTV decompositions”, Numer. Algorithms, 20, pp. 165-194.


[4] Gao, T. and T.Y. Li (2000), “Mixed volume computation via linear programming”, Taiwan J. of Math., 4(4), 599-619.


[5] Gao, T. and T.Y. Li (2000), “Mixed volume computation for semi-mixed polynomial systems”, Disc. & Comput. Geom., 29, pp. 257-277.


[6] Gao, T., T.Y. Li, J. Verschelde and M. Wu (2000), “Balancing the lifting values to improve the numerical stability of polyhedral homotopy continuation methods”, App. Math. & Comput., 114, 233-247.


[7] Huber, B. and B. Sturmfels (1995), “A polyhedral method for solving sparse polynomial systems”, Math. Comp., 64, 1541-1555.


[8] Li, T.Y., T. Sauer and J.A. Yorke (1989), “The cheater’s homotopy: an efficient procedure for solving systems of polynomial equations”, SIAM J. Numer. Anal., 26, 1241-1251.


[9] Li, T.Y. and X. Wang (1997), “The BKK root count incn”, Math. Comp., 65, 1477-1484.


[10] Li, T.Y. and Z. Zeng (2005), “A rank-revealing method with updating, downdating, and applications”, SIAM J. Matrix Analysis and Applications, 26(4), pp918-946.


[11] T.L. Lee and T.Y. Li, “Mixed Volume Computation in solving polynomial systems”, Contemporary Mathematics, 556:97-112, 2011.


[12] T.L. Lee, T.Y. Li and C.H. Tsai (2008), “HOM4PS-2.0, A software package for solving polynomial systems by the polyhedral homotopy continuation method”, Computing, 83, pp109-133.


[13] T.L. Lee, T.Y. Li and Z. Zeng (2009), “A rank-revealing method with updating, downdating, and applications, Part II”, SIAM J. Matrix Analysis and Applications, 31(2), pp503-525.


[14] Verschelde, J. (1999), “PHCPACK: A general-purpose solver for polynomial systems by homotopy continuation”, ACM Tran. Math. Softw., 25, 251-276.


[15] Watson, L.T., m. Sosonkina, R.C. Melville, A.P. Morgan and H.F. Walker (1997), “HOMPACK90: A suite of Fortran 90 codes for globally convergent homotopy algorithms”, ACM Trans. Math. Softw., 23(4), 514-549. Available at


[16] Z. Zeng (2005), “Computing multiple roots of inexact polynomials”, Mathematics of Computation, 74, pp. 869-903.


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