Changes between Initial Version and Version 1 of Ticket #17601, comment 83
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 10/30/15 19:51:15 (4 years ago)
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Ticket #17601, comment 83
initial v1 5 5 Yes, and you could get a lot of leverage out of making that link more prominent. In fact, the appropriate concept would be "Puiseux series", which are Laurent series (with negative exponents allowed) in fractional powers of your variables. 6 6 7 For asymptotic expansions you have x+O(x^(1/2) ) = O(x^(1/2)), which is consistent with Puiseux series in t=1/x.7 For asymptotic expansions you have x+O(x^(1/2)^) = O(x^(1/2)^), which is consistent with Puiseux series in t=1/x. 8 8 9 9 The usual implementation for Puiseux series is as … … 17 17 For arithmetic you just first bring series in common denominator "d" and then do power series arithmetic. 18 18 19 For multivariate series, the appropriate behaviour is caught by "local term orders". SingularLib might offer some useful things already.19 For multivariate series, the appropriate behaviour is caught by "local term orders". !SingularLib might offer some useful things already. 20 20 21 21 Note that a series in n and log(n) can be treated as a bivariate series, with an appropriate term order on the variables signifying "n" and "log(n)", for asymptotic series probably again modelling these with X=1/n and Y= 1/log(n). … … 24 24 25 25 Searching the literature for these terms will probably also make it easier to find relevant algorithms. 26 27 28 29