#5679: fix a bug in solve and polynomial generators
----------------------+-----------------------------------------------------
 Reporter:  was       |       Owner:  burcin    
     Type:  defect    |      Status:  new       
 Priority:  major     |   Milestone:  sage-3.4.1
Component:  calculus  |    Keywords:            
----------------------+-----------------------------------------------------
 {{{
 Some code that used to work in sage-3.0.6 (or something close like
 3.0.3), now break with this error message:

 >>> R.<x0,x1,x2> = PolynomialRing(RR, 3)
 >>> solve([symbolic_expression(x0) == 0], x0, x1, x2)
 Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/Users/anakha/.sage/sage_notebook/worksheets/admin/12/code/30.py",
 line 8, in <module>
    solve(x0 == _sage_const_0 , x0, x1, x2)
  File "/Volumes/Place/anakha/Applications/sage/local/lib/python2.5/site-
 packages/SQLAlchemy-0.4.6-py2.5.egg/",
 line 1, in <module>

  File "/Volumes/Place/anakha/Applications/sage-3.4/local/lib/python2.5
 /site-packages/sage/calculus/equations.py",
 line 1563, in solve
    raise TypeError, "%s is not a valid variable."%v
 TypeError: not all arguments converted during string formatting

 The printing problem is due to the fact that Polynomials have an
 implicit conversion to sequence types triggered by this code:

        try:
            variables = tuple(args[0])
        except TypeError:
            variables = args

 near the start of solve(), (Hint: tuple(args[0]) works if the first
 variable is a PolynomialElement and thus the rest of the vars are
 ignored and you get the bogus ((1.0000000, x0),) tuple as variables)

 If that is fixed, then you get this message which does not help much more:

 >>> R.<x0,x1,x2> = PolynomialRing(RR, 3)
 >>> solve([symbolic_expression(x0) == 0], x0, x1, x2)
 Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/Users/anakha/.sage/sage_notebook/worksheets/admin/12/code/55.py",
 line 8, in <module>
    solve(x0 == _sage_const_0 , x0, x1, x2)
  File "/Volumes/Place/anakha/Applications/sage/local/lib/python2.5/site-
 packages/SQLAlchemy-0.4.6-py2.5.egg/",
 line 1, in <module>

  File "/Users/anakha/.sage/sage_notebook/worksheets/admin/12/code/54.py",
 line 22, in solve
    raise TypeError, "%s is not a valid variable."%v
 TypeError: x0 is not a valid variable.

 Furthermore, if you disable the type checking that is done on the
 input variables, then it works as before:

 >>> R.<x0,x1,x2> = PolynomialRing(RR, 3)
 >>> solve([symbolic_expression(x0) == 0], x0, x1, x2)
 [[x0 == 0, x1 == r10, x2 == r9]]

 I don't think killing the typecheck is the way to go, but maybe
 extending it to cover the polynomial elements.

 Or maybe another better way to do this has come up.

 Arnaud
 }}}

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5679>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of 
Reinventing the Wheel

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