Hi Johannes,

On 2017-07-14, Johannes Schwab <goo...@jschwab.org> wrote:
> Here is the code:
> R.<x,y> = PolynomialRing(QQ, 'lex')

That's not what you want.
  sage: R.term_order()
  Degree reverse lexicographic term order

Instead you have to do
  sage: R.<x,y> = PolynomialRing(QQ, order='lex')
(i.e., specify what parameter is 'lex' being assigned to)

And then you'll get the correct result:
  sage: f = x^2 + 2*y
  sage: g = x*y - y^2 + 1
  sage: I = [f,g]*R
  sage: I.groebner_basis()
  [x - y^3 - 2*y^2 + y, y^4 + 2*y^3 - 2*y^2 + 1]

Best regards,
Simon

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