Is your question related to series somehow? What kind of compositions > do you have in mind?
Yes, Ondrej. Since, we have already implemented many elementary functions in ring_series, it will be nice if we have faster methods to invert them and their compositions (eg sin(sin(x))) The general idea is that computing logarithmic and inverse trigonometric > functions of formal power series is just algebraic operations on power > series followed by formal (term by term) integration, e.g. log(f(x)) = int > f'(x) / f(x) dx. From there, Newton iteration allows you to compute > exponential and forward trigonometric functions. Right! We have attempted something similar in `ring_series`. Formula based expansion as `_atan_series` and this method as `rs_atan` are implemented here <https://github.com/sympy/sympy/blob/master/sympy/polys/ring_series.py#L627>. `_atan_series` seems to be much faster than `rs_atan`. As of now, we expand `tan` from `atan` using Newton iterations and sin/cos from `tan` using half angle formula. What do you suggest? The Brent-Kung paper is probably the best place to start. As further > reading, see the other references in my reversion paper (there's also a > little more content in section 4 of my PhD thesis). Thanks a lot Fredrik! These references are extremely helpful :) Regards Shivam Vats -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/d34a6877-c6ae-4945-ad73-955f30d77493%40googlegroups.com. For more options, visit https://groups.google.com/d/optout.
