Changes between Version 9 and Version 30 of Ticket #4618


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Timestamp:
Dec 26, 2017, 4:12:37 PM (5 years ago)
Author:
Vincent Delecroix
Comment:

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  • Ticket #4618

    • Property Cc Marc Mezzarobba Vincent Delecroix added
    • Property Milestone changed from sage-6.2 to sage-8.2
    • Property Dependencies changed from to #24420, #24431
    • Property Summary changed from Request for Puiseux series in SAGE to Puiseux series
    • Property Branch changed from to public/4618
    • Property Commit changed from to 98afe229b00ae434a5a2bd4849bf94081ff39bca
  • Ticket #4618 – Description

    v9 v30  
    1 In MAGMA, one can have fractional exponents for power series (which it calls Puiseux series), but SAGE does not seem to support this:
    2 {{{
    3 sage: PSR.<q>=PowerSeriesRing(QQ)
    4 sage: q^(1/5)
    5 ---------------------------------------------------------------------------
    6 NotImplementedError                       Traceback (most recent call last)
     1We provide an implementation of Puiseux series, that is power series in `x^(1/n)` where `n` is an arbitrary integer.
    72
    8 /home/ljpk/.sage/temp/sage/2339/_home_ljpk_Eisenstein_sage_9.py in <module>()
    9 /home/was/s/local/lib/python2.5/site-packages/sage/structure/element.so in sage.structure.element.RingElement.__pow__ (sage/structure/element.c:8866)()
    10 /home/was/s/local/lib/python2.5/site-packages/sage/structure/element.so in sage.structure.element.generic_power_c (sage/structure/element.c:17789)()
    11 
    12 NotImplementedError: non-integral exponents not supported
    13 }}}
     3When the base ring is an algebraically closed field, this is an algebraically closed field. In other words, any polynomial in `QQ[X,Y]` has a solution in `Y` as a Puiseux series in `X` over `QQbar`.