Changes between Initial Version and Version 1 of Ticket #9555, comment 2


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Timestamp:
07/15/20 02:08:00 (15 months ago)
Author:
slelievre
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  • Ticket #9555, comment 2

    initial v1  
    55Essentially, they don't claim to work with fractional power series.  Here's the reply:
    66
    7 GiNaC can only compute Taylor and Laurent series. Your's is a Puiseux
    8 series: a series not in integer powers of x but in rational powers of x.
    9 
    10 The Puiseux expansion of sqrt(x) is, well, x^(1/2).
    11 
    12 You may try to set x=y^q and compute the Laurent expansion in y. Setting
    13 q=2 in your case would give the desired result:
    14 
    15    series(sqrt(x),x,0,3)
    16      = series(sqrt(y^2),y,0,3*2)
    17      = y
    18      = x^(1/2).
    19 
    20 Note that the member functions degree() and ldegree() currently return
    21 int, so this would have to be generalized somehow, when implementing
    22 Puiseux series directly in GiNaC.
    23 
    24 Bye
    25    -richy.
     7> GiNaC can only compute Taylor and Laurent series. Yours is a Puiseux
     8> series: a series not in integer powers of x but in rational powers of x.
     9>
     10> The Puiseux expansion of sqrt(x) is, well, x^(1/2)^.
     11>
     12> You may try to set x=y^q^ and compute the Laurent expansion in y. Setting
     13> q=2 in your case would give the desired result:
     14>
     15> {{{
     16> series(sqrt(x), x, 0, 3)
     17>      = series(sqrt(y^2), y, 0, 3*2)
     18>      = y
     19>      = x^(1/2).
     20> }}}
     21>
     22> Note that the member functions degree() and ldegree() currently return
     23> int, so this would have to be generalized somehow, when implementing
     24> Puiseux series directly in GiNaC.
     25>
     26> Bye
     27>    -richy.
    2628
    2729
    28 Note that Richy's suggestion about using 'x=y^2' doesn't work either in ginsh.  Does anybody know how maxima resolves this issue?
     30Note that Richy's suggestion about using `x=y^2` doesn't work either in ginsh.
     31Does anybody know how maxima resolves this issue?