#10364: Vector constructor improvements
------------------------------+---------------------------------------------
   Reporter:  rbeezer         |       Owner:  jason, was
       Type:  enhancement     |      Status:  new       
   Priority:  minor           |   Milestone:            
  Component:  linear algebra  |    Keywords:            
     Author:  Rob Beezer      |    Upstream:  N/A       
   Reviewer:                  |      Merged:            
Work_issues:                  |  
------------------------------+---------------------------------------------
 Patch creates a `zero_vector` constructor, mirroring the `zero_matrix`
 constructor.  It adds error-checking to the `vector` constructor for the
 case of a negative degree.

 Finally, it adds a new, more informative error message when a dictionary
 is used for the entries of a (sparse) vector and a degree is given.
 Presently, the following syntax executes without an error, though the
 result would not be what we should expect.  This "works" since the
 dictionary has "length" 3.

 {{{
 sage: vector(QQ, 3, {0:0, 2:5, 12:-1})
 (0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1)
 }}}

 This could be improved further by adjusting the `prepare_dict` method to
 accept an optional integer degree for the number of entries.  Then instead
 of an error we could have the (fictional) behavior:

 {{{
 sage: vector(QQ, 6, {1:2, 4:-3})
 (0, 2, 0, 0, -3, 0)
 }}}

 This depends on #10362 since one doctest there has changed in this patch.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10364>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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