#14305: bug in simplify_radical
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       Reporter:  zimmerma  |        Owner:  burcin
           Type:  defect    |       Status:  new
       Priority:  critical  |    Milestone:  sage-5.12
      Component:  calculus  |   Resolution:
       Keywords:            |    Merged in:
        Authors:            |    Reviewers:
Report Upstream:  N/A       |  Work issues:
         Branch:            |       Commit:
   Dependencies:            |     Stopgaps:
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Comment (by mjo):

 I remember the first example, from #12845. This is the full test:

 {{{
 sage: a, b, c = var("a, b, c")
 sage: assume((a, 'real'), (b, 'real'), (c, 'real'))
 sage: z = a + b*I
 sage: bool(norm(z).simplify() == a^2 + b^2)
 True
 sage: norm(a + b).simplify()
 a^2 + 2*a*b + b^2
 sage: v = vector([a, b, c])
 sage: bool(norm(v).simplify() == sqrt(a^2 + b^2 + c^2))
 True
 sage: forget()
 }}}

 The assumptions aren't needed for the first result, but they are for the
 last one (the norm of the vector).

 The `rectform()` test is also mine, but the reasoning I've forgotten.

--
Ticket URL: <http://trac.sagemath.org/ticket/14305#comment:19>
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