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HomotopyContinuation.jl: A Package for Homotopy Continuation in Julia

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Mathematical Software – ICMS 2018 (ICMS 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10931))

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Abstract

We present the Julia package HomotopyContinuation.jl, which provides an algorithmic framework for solving polynomial systems by numerical homotopy continuation. We introduce the basic capabilities of the package and demonstrate the software on an illustrative example. We motivate our choice of Julia and how its features allow us to improve upon existing software packages with respect to usability, modularity and performance. Furthermore, we compare the performance of HomotopyContinuation.jl to the existing packages Bertini and PHCpack.

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Notes

  1. 1.

    www.JuliaHomotopyContinuation.org.

  2. 2.

    The authors discovered the examples in the excellent database of Jan Verschelde available at http://homepages.math.uic.edu/~jan/.

References

  1. Alizadeh, F.: Interior point methods in semidefinite programming with applications to combinatorial optimization. SIAM J. Optim. 5(1), 13–51 (1995)

    Article  MathSciNet  Google Scholar 

  2. Bates, D.J., Hauenstein, J.D., Sommese, A.J., Wampler, C.W.: Adaptive multiprecision path tracking. SIAM J. Numer. Anal. 46(2), 722–746 (2008)

    Article  MathSciNet  Google Scholar 

  3. Bates, D.J., Hauenstein, J.D., Sommese, A.J., Wampler, C.W.: Bertini: Software for Numerical Algebraic Geometry. bertini.nd.edu, https://doi.org/10.7274/R0H41PB5

  4. Bezanson, J., Edelman, A., Karpinski, S., Shah, V.B.: Julia: a fresh approach to numerical computing. SIAM Rev. 59(1), 65–98 (2017)

    Article  MathSciNet  Google Scholar 

  5. Björck, G., Fröberg, R.: A faster way to count the solutions of inhomogeneous systems of algebraic equations, with applications to cyclic n-roots. J. Symbolic Comput. 12(3), 329–336 (1991)

    Article  MathSciNet  Google Scholar 

  6. Cayley, A.: A memoir on quartic surfaces. Proc. London Math. Soc. 3, 19–69 (1869/1871). (Collected Papers, VII, 133–181; see also the sequels on pages 256–260, 264–297)

    Google Scholar 

  7. Degtyarev, A., Itenberg, I.: On real determinantal quartics. In: Proceedings of the Gökova Geometry Topology Conference 2010 (2011)

    Google Scholar 

  8. Huber, B., Verschelde, J.: Polyhedral end games for polynomial continuation. Numer. Algorithms 18(1), 91–108 (1998)

    Article  MathSciNet  Google Scholar 

  9. Katsura, S.: Spin glass problem by the method of integral equation of the effective field. In: New Trends in Magnetism, pp. 110–121 (1990)

    Google Scholar 

  10. Knuth, D.E.: The Art of Computer Programming, 3rd edn. Seminumerical Algorithms, vol. 2. Addison-Wesley Longman Publishing Co. (1997)

    Google Scholar 

  11. Nelson, C.V., Hodgkin, B.C.: Determination of magnitudes, directions, and locations of two independent dipoles in a circular conducting region from boundary potential measurements. IEEE Trans. Biomed. Eng. 12, 817–823 (1981)

    Article  Google Scholar 

  12. Ramana, M., Goldman, A.J.: Some geometric results in semidefinite programming. J. Global Optim. 7, 33–50 (1995)

    Article  MathSciNet  Google Scholar 

  13. Sanyal, R.: On the derivative cones of polyhedral cones. Adv. Geometry 13(2), 315–321 (2011)

    MathSciNet  MATH  Google Scholar 

  14. Sturmfels, B.: Spectrahedra and their shadows. Talk at the Simons Institute Workshop on Semidefinite Optimization, Approximation and Applications (2014). https://simons.berkeley.edu/sites/default/files/docs/2039/slidessturmfels.pdf

  15. Verschelde, J.: Algorithm 795: PHCpack: a general-purpose solver for polynomial systems by homotopy continuation. ACM Trans. Math. Software (TOMS) 25(2), 251–276 (1999)

    Article  Google Scholar 

  16. Vinzant, C.: What is... a Spectrahedron? Not. AMS 61(5), 492–494 (2014)

    MathSciNet  MATH  Google Scholar 

  17. Wampler, C., Morgan, A.: Solving the 6R inverse position problem using a generic-case solution methodology. Mech. Mach. Theory 26(1), 91–106 (1991)

    Article  Google Scholar 

  18. Wampler, I.C.W.: The Numerical Solution of Systems of Polynomials Arising in Engineering and Science. World Scientific (2005)

    Google Scholar 

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Correspondence to Paul Breiding or Sascha Timme .

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Breiding, P., Timme, S. (2018). HomotopyContinuation.jl: A Package for Homotopy Continuation in Julia. In: Davenport, J., Kauers, M., Labahn, G., Urban, J. (eds) Mathematical Software – ICMS 2018. ICMS 2018. Lecture Notes in Computer Science(), vol 10931. Springer, Cham. https://doi.org/10.1007/978-3-319-96418-8_54

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  • DOI: https://doi.org/10.1007/978-3-319-96418-8_54

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