#13173: Multivariate polynomial rings do not respect custom registered 
coercions.
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   Reporter:  mderickx       |             Owner:  tbd     
       Type:  PLEASE CHANGE  |            Status:  new     
   Priority:  major          |         Milestone:  sage-5.2
  Component:  PLEASE CHANGE  |          Keywords:          
Work issues:                 |   Report Upstream:  N/A     
  Reviewers:                 |           Authors:          
  Merged in:                 |      Dependencies:          
   Stopgaps:                 |  
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 The following behavior is wrong.
 {{{
 sage: K=QQ['t,s']
 sage: L=QQ['t0,t1,s0,s1']
 sage: L.inject_variables()
 Defining t0, t1, s0, s1
 sage: Hom(K,L)([t0+t1,s0]).register_as_coercion()
 sage: L.coerce_map_from(K)
 Ring morphism:
   From: Multivariate Polynomial Ring in t, s over Rational Field
   To:   Multivariate Polynomial Ring in t0, t1, s0, s1 over Rational Field
   Defn: t |--> t0 + t1
         s |--> s0
 sage: K.0*L(1)
 t0 + t1   #GOOD
 sage: L(K.0)
 t0          #BAD
 }}}

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13173>
Sage <http://www.sagemath.org>
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