Estimating the number of solutions equation of N-point gravitational lenses algebraic geometry methods
Keywords:
gravitational lenses, algebraic geometry, Bézout’s theorem
Abstract
One of the main problems in the study of system of equations of the gravitational lens, is the computation of coordinates from the known position of the source.
In the process of computing finds the solution of equations with two unknowns. The difficulty lies in the fact that, in general, is not known constructive or analytical algorithm for solving systems of polynomial equations In this connection, use numerical methods like the method of tracing.
For the N-point gravitational lenses have a system of polynomial equations. Systems Research is advisable to start with an assessment of the number of solutions. This can be done by methods of algebraic geometry.
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References
P. V. Bliokh, A. A. Minakov, Gravitational Lenses, Naukova Dumka, Kiev 1989. P. 249.
Weinberg S. Gravitation and Cosmology, 1972. P 657.
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Zakharov A.F. Gravitacionnye linzy i mikrolinzy, 1997, P. 328.
Schneider P., Ehlers J., Falco E.E. Gravitational lenses. Springer-Verlag Berlin Heidelberg 1999 P. 560.
Kotvytskiy A.T., Bronza S.D. // Odessa Astronomical Publications, vol. 29 (2016), P.31-33.
Lang S. Algebra. Columbia University. New York, 1965. P.564.
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Van Der Waerden B.L. Algebra I,II. Achte auflage der modernen algebra Springer-Verlag Berlin Heidelberg New York 1971 P. 456.
Reid M. Undergraduate Algebraic Geometry. Math Inst., University of Warwick, Cambridge 1988, P. 136.
Garner, Lynn E. An Outline of Projective Geometry, North Holland, 1981, P.220.
Bocher, Maxime. Introduction to Higher Algebra. Macmillan, 1907, P.292.
Weinberg S. Gravitation and Cosmology, 1972. P 657.
Landau L.D., Lifshitz E.M. The classical Theory of Fields, 1988, V.2 P. 512.
Zakharov A.F. Gravitacionnye linzy i mikrolinzy, 1997, P. 328.
Schneider P., Ehlers J., Falco E.E. Gravitational lenses. Springer-Verlag Berlin Heidelberg 1999 P. 560.
Kotvytskiy A.T., Bronza S.D. // Odessa Astronomical Publications, vol. 29 (2016), P.31-33.
Lang S. Algebra. Columbia University. New York, 1965. P.564.
Walker R.J. Algebraic curves. Pringeton. New Jersey. 1950, P. 236.
Van Der Waerden B.L. Algebra I,II. Achte auflage der modernen algebra Springer-Verlag Berlin Heidelberg New York 1971 P. 456.
Reid M. Undergraduate Algebraic Geometry. Math Inst., University of Warwick, Cambridge 1988, P. 136.
Garner, Lynn E. An Outline of Projective Geometry, North Holland, 1981, P.220.
Bocher, Maxime. Introduction to Higher Algebra. Macmillan, 1907, P.292.
Published
2017-01-23
How to Cite
Kotvytskiy, A. T., Bronza, S. D., & Vovk, S. R. (2017). Estimating the number of solutions equation of N-point gravitational lenses algebraic geometry methods. Journal of V. N. Karazin Kharkiv National University. Series Physics, (24), 54-58. Retrieved from https://periodicals.karazin.ua/physics/article/view/9208
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