2023-07-30 21:11:03 +0100 commented answer Trouble transforming a groebner basis Thank you so much Ricardo. Regarding your note about using libSingular: Am I interpreting the situation correctly if I'm 2023-07-30 21:08:40 +0100 commented answer Trouble transforming a groebner basis @rburing, just FYI, I opened an issue relating to converting back the polynomias to Sage using ._sage_() here: https://g 2023-07-30 18:23:18 +0100 commented answer Trouble transforming a groebner basis Thank you so much Ricardo. Regarding your note about using libSingular: I'm I interpreting the situation correctly if I' 2023-07-30 18:20:55 +0100 marked best answer Trouble transforming a groebner basis I'm using sage to compute Gröbner bases (in lexicographic order) over a fractional field. This has been working out well so far. For computational efficiency I've read that degrevlex order is often preferred for the initial basis calculation, followed by a transformation (using the FGLM algorithm) to the desired order (lex in my case). However, I'm facing a problem when I try to transform the basis, my invocation might be wrong, but currently this is yielding me a TypeError: no conversion to a Singular ring defined. This is the .sage file: P. = PolynomialRing(QQ) F = Frac(P) R = PolynomialRing(F, order='degrevlex', names=('z0', 'z1', 'z2', 'z3', 'z4', 'z5', 'z6', 'z7')) (z0, z1, z2, z3, z4, z5, z6, z7,) = R._first_ngens(8) I = R.ideal(p0*z0*z1 - z2*z3, p1*z4 - z3*z5, p2*z1*z5 - z6, -p3 - p4 - p5 + z4 + z5 + z6, -p5 - p6 - p7 + z0 + z3 + z4, -p3 - p8 - p9 + z1 + z2 + z6, -p7 - p8 + z0 + z2, -z6 + z7) gb = I.groebner_basis() print('So far so good...') S = PolynomialRing(F, order='lex', names=('z0', 'z1', 'z2', 'z3', 'z4', 'z5', 'z6', 'z7')) gbasis = Ideal(gb).transformed_basis('fglm', S) print([{k: str(v) for k, v in _.dict().items()} for _ in gbasis])  and this is my backtrace: So far so good... Traceback (most recent call last): File "sage/rings/polynomial/multi_polynomial_libsingular.pyx", line 1222, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._singular_ (build/cythonized/sage/rings/polynomial/multi_polynomial_libsingular.cpp:13949) ValueError During handling of the above exception, another exception occurred: Traceback (most recent call last): File "/tmp/tmp8h3xz_3s.sage.py", line 16, in gbasis = Ideal(gb).transformed_basis('fglm', S) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ File "/usr/lib/python3/dist-packages/sage/rings/polynomial/multi_polynomial_ideal.py", line 297, in __call__ return self.f(self._instance, *args, **kwds) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ File "/usr/lib/python3/dist-packages/sage/rings/qqbar_decorators.py", line 96, in wrapper return func(*args, **kwds) ^^^^^^^^^^^^^^^^^^^ File "/usr/lib/python3/dist-packages/sage/interfaces/singular.py", line 2763, in wrapper return func(*args, **kwds) ^^^^^^^^^^^^^^^^^^^ File "/usr/lib/python3/dist-packages/sage/libs/singular/standard_options.py", line 142, in wrapper return func(*args, **kwds) ^^^^^^^^^^^^^^^^^^^ File "/usr/lib/python3/dist-packages/sage/rings/polynomial/multi_polynomial_ideal.py", line 2055, in transformed_basis Rs = singular(R) ^^^^^^^^^^^ File "/usr/lib/python3/dist-packages/sage/interfaces/singular.py", line 766, in __call__ return x._singular_(self) ^^^^^^^^^^^^^^^^^^ File "sage/rings/polynomial/multi_polynomial_libsingular.pyx", line 1236, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._singular_ (build/cythonized/sage/rings/polynomial/multi_polynomial_libsingular.cpp:14457) File "sage/rings/polynomial/multi_polynomial_libsingular.pyx", line 1433, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._singular_init_ (build/cythonized/sage/rings/polynomial/multi_polynomial_libsingular.cpp:16290) TypeError: no conversion to a Singular ring defined  Any clue as to what I might be doing wrong? I'm using sage 9.5, provided by Debian 12 (bookworm) 2023-07-30 18:20:55 +0100 received badge ● Scholar (source) 2023-07-30 18:20:54 +0100 received badge ● Supporter (source) 2023-07-30 11:33:00 +0100 received badge ● Student (source) 2023-07-30 08:52:14 +0100 asked a question Trouble transforming a groebner basis Trouble transforming a groebner basis I'm using sage to compute Gröbner bases (in lexicographic order) over a fractional