#11549: Arithmetic with symbolic vectors always creates a new
FreeModuleElement_generic_dense
-------------------------+--------------------------------------------------
   Reporter:  jvkersch   |          Owner:  burcin                      
       Type:  defect     |         Status:  needs_review                
   Priority:  major      |      Milestone:  sage-4.7.2                  
  Component:  symbolics  |       Keywords:  vector, symbolic, arithmetic
Work_issues:             |       Upstream:  N/A                         
   Reviewer:             |         Author:                              
     Merged:             |   Dependencies:                              
-------------------------+--------------------------------------------------
Changes (by jvkersch):

 * cc: jason (added)
  * status:  new => needs_review


Comment:

 The current patch implements the modification in `_new_c` proposed in
 sage-devel, and adds an extra doctest to `Vector_symbolic_dense`.
 Interestingly, this change also affects the formatting of
 `Vector_callable_symbolic_dense`: instead of

 {{{
 sage: f(r, theta, z) = (r*cos(theta), r*sin(theta), z), f
 (r, theta, z) |--> (r*cos(theta), r*sin(theta), z)
 sage: f+f
 ((r, theta, z) |--> 2*r*cos(theta), (r, theta, z) |--> 2*r*sin(theta), (r,
 theta, z) |--> 2*z)
 sage: 3*f
 ((r, theta, z) |--> 3*r*cos(theta), (r, theta, z) |--> 3*r*sin(theta), (r,
 theta, z) |--> 3*z)
 }}}

 we now have

 {{{
 sage: f(r, theta, z) = (r*cos(theta), r*sin(theta), z), f
 (r, theta, z) |--> (r*cos(theta), r*sin(theta), z)
 sage: f+f
 (r, theta, z) |--> (2*r*cos(theta), 2*r*sin(theta), 2*z)
 sage: 3*f
 (r, theta, z) |--> (3*r*cos(theta), 3*r*sin(theta), 3*z)
 }}}

 As far as I can tell, this is a purely cosmetic change, so I've taken the
 liberty of going ahead and adapting the doctests in
 `Vector_callable_symbolic_dense`.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11549#comment:1>
Sage <http://www.sagemath.org>
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