Re: Branch cuts. Some efforts..
Michel Talon <[email protected]>
| Newsgroups | gmane.comp.mathematics.maxima.general |
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Le 22/08/2026 à 16:07, Richard Fateman a écrit : > https://scholar.google.com/citations?view_op=view_citation&hl=en&user=MKANuc0AAAAJ&citation_for_view=MKANuc0AAAAJ:ufrVoPGSRksC > <https://scholar.google.com/citations?view_op=view_citation&hl=en&user=MKANuc0AAAAJ&citation_for_view=MKANuc0AAAAJ:ufrVoPGSRksC> > I see you have worked on that!!! Anyways in the paper in question i see mostly square root branch cuts and logarithmic coverings. Maybe i have taken a too cursory look, but i have not seen anything which could be appropriate for the situation of an equation P(x,y)=0 (P polynomial) even on low degrees.For example if P is of degree 3 in y, you will have horribly complicated formulas for y=y(x), with cubic roots inside square roots. If the degree is >=5 you have nothing. In general you need to do analytic continuation around branch points, which themselves are roots of a high degree equation (the resultant of P and P'x.) All this is fine in theory (see "analytic elements" in Springer's book) but dubious how to do in practice. However it was the genius of Riemann to discover many remarkable properties for functions on such Riemann's surfaces, the most basic ones being described in Springer's book, but he did more sophisticated ones (see Griffith and Harris for example). -- Michel Talon _______________________________________________ Maxima-discuss mailing list [email protected] https://lists.sourceforge.net/lists/listinfo/maxima-discuss