Changes between Version 4 and Version 12 of Ticket #17671


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Timestamp:
01/26/15 15:41:34 (5 years ago)
Author:
vdelecroix
Comment:

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  • Ticket #17671

    • Property Summary changed from Implement gcd for fraction fields to gcd and xgcd over fields, PID and UFD
    • Property Commit changed from d8a03d7fa1dd0e401adbae8e2a16ccbfb1902392 to 1d84c4a9160533338cb19a8df2351cd0fc9d79d0
  • Ticket #17671 – Description

    v4 v12  
    77}}}
    88
    9 We implement a `xgcd` for the `QuotientFields` category in order to fix that (there was a `gcd` here without a `xgcd`). We also check that for PID the `gcd` and `xgcd` agree by implementing a `_test_gcd_vs_xgcd`. With that branch
    10 {{{
    11 sage: xgcd(6/1,2/1)
    12 (2, 0, 1)
    13 sage: xgcd(5/2, 3/4)
    14 (1/4, -1/2, 2)
    15 }}}
    16 which is consistent with `gcd`.
     9In this ticket we:
     101. Ensure that `gcd` and `xgcd` are compatible over quotient fields by implementing the `xgcd` in the appropriate place. In particular, with that branch we have
     11  {{{
     12  sage: xgcd(6/1,2/1)
     13  (2, 0, 1)
     14  sage: xgcd(5/2, 3/4)
     15  (1/4, -1/2, 2)
     16  }}}
     172. We fix the `xgcd` for trivial cases in `rings.polynomial.polynomial_element_generic.Polynomial_generic_field` in order that `gcd` and `xgcd` agree for them.
     183. We introduce a generic test `_test_gcd_vs_xgcd` in the category `PrincipalIdealDomains` to ensure the compatibility of `gcd` and `xgcd`.
    1719
    1820QUESTIONS:
     
    2729  For the moment, I propagated this to `lcm` and `xgcd`.
    2830
    29 2. There is a method `xgcd` implemented for univariate polynomial over ZZ. This is not a proper name since it has nothing to do with `gcd` (see [https://groups.google.com/forum/#!topic/sage-devel/JV8fCPUqTzo this sage-devel thread])
     312. There is a method `xgcd` implemented for univariate polynomial over ZZ. ~~This is not a proper name since it has nothing to do with `gcd`~~ This might not be the best name since the first term is not the gcd in general (see [https://groups.google.com/forum/#!topic/sage-devel/JV8fCPUqTzo this sage-devel thread])