︠e545c591-6078-4c2d-9694-3e6d94633506s︠ P. = PolynomialRing(RR, 3, order='lex'); P I = ideal(x^2+y^2+z^2-1, x^2-y+z^2, x-z); I B = I.groebner_basis(); B ︡53650fd7-1fdf-485a-b9b6-b8d83d1d4445︡{"stdout":"Multivariate Polynomial Ring in x, y, z over Real Field with 53 bits of precision"}︡{"stdout":"\n"}︡{"stdout":"Ideal (x^2 + y^2 + z^2 - 1.00000000000000, x^2 - y + z^2, x - z) of Multivariate Polynomial Ring in x, y, z over Real Field with 53 bits of precision\n"}︡{"stderr":"Error in lines 3-3\n"}︡{"stderr":"Traceback (most recent call last):\n File \"/projects/sage/sage-7.5/local/lib/python2.7/site-packages/smc_sagews/sage_server.py\", line 982, in execute\n exec compile(block+'\\n', '', 'single') in namespace, locals\n File \"\", line 1, in \n File \"sage/misc/cachefunc.pyx\", line 2038, in sage.misc.cachefunc.CachedMethodCaller.__call__ (/projects/sage/sage-7.5/src/build/cythonized/sage/misc/cachefunc.c:10792)\n w = self._instance_call(*args, **kwds)\n File \"sage/misc/cachefunc.pyx\", line 1914, in sage.misc.cachefunc.CachedMethodCaller._instance_call (/projects/sage/sage-7.5/src/build/cythonized/sage/misc/cachefunc.c:10238)\n return self.f(self._instance, *args, **kwds)\n File \"/projects/sage/sage-7.5/local/lib/python2.7/site-packages/sage/rings/polynomial/multi_polynomial_ideal.py\", line 3731, in groebner_basis\n gb = self._groebner_basis_singular(\"groebner\", deg_bound=deg_bound, mult_bound=mult_bound, *args, **kwds)\n File \"/projects/sage/sage-7.5/local/lib/python2.7/site-packages/sage/interfaces/singular.py\", line 2724, in wrapper\n return func(*args, **kwds)\n File \"/projects/sage/sage-7.5/local/lib/python2.7/site-packages/sage/rings/polynomial/multi_polynomial_ideal.py\", line 1366, in _groebner_basis_singular\n S = PolynomialSequence([R(S[i+1]) for i in range(len(S))], R, immutable=True)\n File \"/projects/sage/sage-7.5/local/lib/python2.7/site-packages/sage/rings/polynomial/multi_polynomial_ring.py\", line 481, in __call__\n return x.sage_poly(self)\n File \"/projects/sage/sage-7.5/local/lib/python2.7/site-packages/sage/interfaces/singular.py\", line 1776, in sage_poly\n exp[var_dict[var]]=power\nKeyError: '(1.000e+00)'\n"}︡{"done":true}︡ ︠2a20dca5-8c86-4a85-bc22-c21392f31c86s︠ P. = PolynomialRing(RDF, 3, order='lex'); P I = ideal(x^2+y^2+z^2-1, x^2-y+z^2, x-z); I B = I.groebner_basis(); B ︡6bfa967d-1fee-4e0e-8733-625f605d7cf9︡{"stdout":"Multivariate Polynomial Ring in x, y, z over Real Double Field\n"}︡{"stdout":"Ideal (x^2 + y^2 + z^2 - 1.0, x^2 - y + z^2, x - z) of Multivariate Polynomial Ring in x, y, z over Real Double Field\n"}︡{"stderr":"Error in lines 3-3\nTraceback (most recent call last):\n File \"/projects/sage/sage-7.5/local/lib/python2.7/site-packages/smc_sagews/sage_server.py\", line 982, in execute\n exec compile(block+'\\n', '', 'single') in namespace, locals\n File \"\", line 1, in \n File \"sage/misc/cachefunc.pyx\", line 2038, in sage.misc.cachefunc.CachedMethodCaller.__call__ (/projects/sage/sage-7.5/src/build/cythonized/sage/misc/cachefunc.c:10792)\n w = self._instance_call(*args, **kwds)\n File \"sage/misc/cachefunc.pyx\", line 1914, in sage.misc.cachefunc.CachedMethodCaller._instance_call (/projects/sage/sage-7.5/src/build/cythonized/sage/misc/cachefunc.c:10238)\n return self.f(self._instance, *args, **kwds)\n File \"/projects/sage/sage-7.5/local/lib/python2.7/site-packages/sage/rings/polynomial/multi_polynomial_ideal.py\", line 3731, in groebner_basis\n gb = self._groebner_basis_singular(\"groebner\", deg_bound=deg_bound, mult_bound=mult_bound, *args, **kwds)\n File \"/projects/sage/sage-7.5/local/lib/python2.7/site-packages/sage/interfaces/singular.py\", line 2724, in wrapper\n return func(*args, **kwds)\n File \"/projects/sage/sage-7.5/local/lib/python2.7/site-packages/sage/rings/polynomial/multi_polynomial_ideal.py\", line 1366, in _groebner_basis_singular\n S = PolynomialSequence([R(S[i+1]) for i in range(len(S))], R, immutable=True)\n File \"/projects/sage/sage-7.5/local/lib/python2.7/site-packages/sage/rings/polynomial/multi_polynomial_ring.py\", line 481, in __call__\n return x.sage_poly(self)\n File \"/projects/sage/sage-7.5/local/lib/python2.7/site-packages/sage/interfaces/singular.py\", line 1776, in sage_poly\n exp[var_dict[var]]=power\nKeyError: '(1.000e+00)'\n"}︡{"done":true}︡ ︠9fa89469-ae60-4215-ade6-1941ecd7d376︠