Dear sage supporters,

a strange error occurs in sage 2.10.2 in the following way:

sage: R.<x> = QQ[]
sage: f = x^3 + x + 1;  g = x^3 - x - 1
sage: r = f.resultant(g)
sage: R.__dict__
{'_PolynomialRing_general__cyclopoly_cache': {},
 '_PolynomialRing_general__generator': x,
 '_PolynomialRing_general__is_sparse': False,
 '_PolynomialRing_general__polynomial_class': <class
'sage.rings.polynomial.polynomial_element_generic.Polynomial_rational_dense'>,
 '_PolynomialRing_singular_repr__singular': //   characteristic : 0
//   number of vars : 1
//        block   1 : ordering lp
//                  : names    x
//        block   2 : ordering C,
 '_has_singular': True}

Ok so far. Now we use the gap interface and experience a bad surprise:

sage: gap(R.base_ring())
Rationals
sage: R.__dict__
{'_PolynomialRing_general__cyclopoly_cache': {},
 '_PolynomialRing_general__generator': x,
 '_PolynomialRing_general__is_sparse': False,
 '_PolynomialRing_general__polynomial_class': <class
'sage.rings.polynomial.polynomial_element_generic.Polynomial_rational_dense'>,
 '_PolynomialRing_singular_repr__singular': print(sage0);
//   characteristic : 0
//   number of vars : 1
//        block   1 : ordering lp
//                  : names    x
//        block   2 : ordering C,
 '_has_singular': True}

See how R.__dict__['PolynomialRing_singular_repr__singular'] has
changed!
In the first part of the session, it contained a ring, but now it
contains print(sage0).

Even worse: Although sage0 used to be the identifier of the singular
ring associated with R, we now get
  sage: singular('sage0')
  print(sage8);
  sage:   sage: singular('sage0')
  print(sage9);
  sage:   sage: singular('sage0')
  print(sage10);
and so on!

So, the singular interface seems to be completely messed up. I have no
idea where this behaviour comes from.

Note that the line
  sage: r = f.resultant(g)
is essential. When this line is replaced by, e.g.,
  sage: singular(R)
the error does not occur. Also, when we first say gap(R.base_ring())
and then compute the resultant, everything is alright.

Perhaps this helps to detect the bug.

Any idea? Shall i open a ticket?

Yours
       Simon

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