#19299: product of elements of a cartesian products is very slow
---------------------------+-------------------------------------
   Reporter:  vdelecroix   |            Owner:
       Type:  enhancement  |           Status:  new
   Priority:  major        |        Milestone:  sage-6.9
  Component:  algebra      |         Keywords:
  Merged in:               |          Authors:  Vincent Delecroix
  Reviewers:               |  Report Upstream:  N/A
Work issues:               |           Branch:
     Commit:               |     Dependencies:
   Stopgaps:               |
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 As reported in [https://groups.google.com/forum/#!topic/sage-
 devel/hbF_0XVpq_k this sage-devel thread] the product of elements of a
 cartesian product are very slow
 {{{
 sage: X = cartesian_product([IntegerModRing(2)] * 8)
 sage: A = X.addition_table() # very very long
 }}}
 One problem is the default implementation of `cartesian_factors` for
 element of such product provided by `sage.categories.sets_cat`
 {{{
 def cartesian_factors(self):
    # TODO: optimize
    return tuple(self.cartesian_projection(i) for i in
 self.parent()._sets_keys())
 }}}

--
Ticket URL: <http://trac.sagemath.org/ticket/19299>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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