#13609: symbolic arithmetic errors
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   Reporter:  llpamies       |             Owner:  tbd     
       Type:  defect         |            Status:  new     
   Priority:  major          |         Milestone:  sage-5.5
  Component:  PLEASE CHANGE  |          Keywords:          
Work issues:                 |   Report Upstream:  N/A     
  Reviewers:                 |           Authors:          
  Merged in:                 |      Dependencies:          
   Stopgaps:                 |  
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 Consider the following code:

 {{{
 ff.<z> = GF(2**8, 'z')
 poly.<c1,c2,c3> = PolynomialRing(ff, 3, 'c')
 r1,r2 = var('r1,r2')
 expression = -(c1*r2 - c2*r1)/c3
 print expression.substitute(r1=z, r2=z)
 }}}

 This produces a TypeError: unsupported operand parent(s) for '*': 'Finite
 Field in z of size 2pow8' and 'Rational Field'. I know that 'expression'
 is not an element of the ring 'poly', but using a PolynomialRing is the
 only way I found to achieve symbolic arithmetic on finite fields.

 However, the interesting story is that if I replace the expression by


 {{{
 expression = -(r2 - c2*r1)/c3
 }}}

 it work perfectly well, but if instead the expression is


 {{{
 expression = -(c1 + r2 - c2*r1)/c3
 }}}

 then I get a segmentation fault.


 To make things a little bit more interesting I can rename r1 and r2 to a
 and b:

 {{{
 ff.<z> = GF(2**8, 'z')
 poly.<c1,c2,c3> = PolynomialRing(ff, 3, 'c')
 a,b = var('a,b')
 expression = -(c1*b - c2*a)/c3
 print expression.substitute(a=z, b=z)
 }}}

 Then it works fine, but produces a segmentation fault for,


 {{{
 expression = -(c1 + b - c2*a)/c3
 }}}

 so you can think that it might be a problem with the use of the names r1
 and r2. But this is not the case, if I rename the PolynomialRing variables
 instead, from c's to x's:

 {{{
 ff.<z> = GF(2**8, 'z')
 poly.<x1,x2,x3> = PolynomialRing(ff, 3, 'x')
 r1,r2 = var('r1,r2')
 expression = -(x1*r2 - x2*r1)/x3
 print expression.substitute(r1=z, r2=z)
 }}}

 Then it works again for the first two expressions but produces a
 segmentation fault for the third too.

 Any idea of what is going wrong here?

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13609>
Sage <http://www.sagemath.org>
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