Abstract
A. BLOCH1 recently extended to complex coefficients Lucas's method2 of the solution of polynomial equations with the aid of an electrolytic tank. Points of the tank represent complex numbers either directly or after a conformal transformation. In the extended method, sinusoidal currents, in complex vector notation proportional to the residues of a certain rational function with simple poles, are impressed at points corresponding to these poles. Then the points at which the electric field is circularly polarized correspond to the roots of the polynomial equation. The root-points can be found by exploring the tank systematically.
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References
Bloch, A., VIIth International Congress of Applied Mechanics, 4, Paper No. 28, 324 (London, 1948).
Lucas, F., C.R. Acad. Sci., Paris, 106, 645 and 1072 (1888).
Hansen, W. W., and Lundstrom, O. C., Proc. Inst. Rad. Eng., 33, 528 (1945).
Boothroyd, A. R., Cherry, E. C., and Makar, R., Proc. Inst. Elec. Eng., Pt. 1, 96, No. 99 (May 1949).
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TASNY-TSCHIASSNY, L., DOE, A. Solution of Polynomial Equations with the Aid of the Electrolytic Tank. Nature 168, 702–703 (1951). https://doi.org/10.1038/168702b0
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DOI: https://doi.org/10.1038/168702b0
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