As a part of my GSoC project, I would also like to work on computing limits of sequences. This is what I have come up wiith so far.
Implementing this algorithm will allow computing limits of some summations, which is not currently computed by sympy. This will improve the range of admissible functions of which limit can be computed. Algorithm for computing limits of sequences is explained in the paper "Computing Limits of Sequences" by Manuel Kauers. Applicability Criteria: This algorithm can be applied if the following conditions are fulfilled * Applies on expressions of the form pn/qn where pn, qn tends to oo when n tends to oo * qn should be asymptotically strictly monotonous. * terms are built from rational functions, indefinite sums and indefinite products over an indeterminate n, called Pi Sigma - expressions. Algorithm Details: Difference operator, is defined as D(an) = a(n+1) - a(n) Also, if limit (n -> oo) pn/qn = 0, then qn is the dominant term * Check for the applicability criteria's as described in the above section. * Use the difference operator on the numerator and denominator. * Find the dominant term of the numerator and the denominator. Drop all other terms. * Keep on doing recursively, until limit converges to a value. However I have some questions regarding the implementation: * Is there any implementation of difference operator presently in Sympy, I did not find any. I might have missed. * What would be the best possible way for finding the most dominant term. Is there a suitable implementation already implemented in gruntz module? * One way to implement, is to implement it as a new function and integrate it inside limit. Any other approach? -- 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 sympy+unsubscr...@googlegroups.com. To post to this group, send email to sympy@googlegroups.com. 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/a54b4611-7da7-4668-b7e1-56007a01aa2d%40googlegroups.com. For more options, visit https://groups.google.com/d/optout.
