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Several times, we have run into problems where analytical methods are no longer sufficient to analyze a GL system. Our “standard” problem is the inversion of the lens equation, i.e., to find all the images x for a given source position y. Only in the simplest cases can this be done analytically; in general, one must find all the roots of a two-dimensional system of equations. This is not trivial, in particular because the number of solutions is not known a priori. There are other problems where numerical analysis must be applied, e.g., if one wants to determine the total magnification for an extended source, as a function of its position. This problem is computationally simpler than the standard problem.
KeywordsDeflection Angle Surface Brightness Source Position Source Plane Image Position
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