Changes between Initial Version and Version 1 of Ticket #17601, comment 83


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Timestamp:
10/30/15 19:51:15 (4 years ago)
Author:
vdelecroix
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  • Ticket #17601, comment 83

    initial v1  
    55Yes, 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.
    66
    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.
     7For asymptotic expansions you have x+O(x^(1/2)^) = O(x^(1/2)^), which is consistent with Puiseux series in t=1/x.
    88
    99The usual implementation for Puiseux series is as
     
    1717For arithmetic you just first bring series in common denominator "d" and then do power series arithmetic.
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    19 For multivariate series, the appropriate behaviour is caught by "local term orders". SingularLib might offer some useful things already.
     19For multivariate series, the appropriate behaviour is caught by "local term orders". !SingularLib might offer some useful things already.
    2020
    2121Note 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).
     
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    2525Searching the literature for these terms will probably also make it easier to find relevant algorithms.
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