P.<x,y,z> = 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
Multivariate Polynomial Ring in x, y, z over Real Field with 53 bits of precision 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
Error in lines 3-3 Traceback (most recent call last): File "/projects/sage/sage-7.5/local/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 982, in execute exec compile(block+'\n', '', 'single') in namespace, locals File "", line 1, in <module> 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) w = self._instance_call(*args, **kwds) 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) return self.f(self._instance, *args, **kwds) File "/projects/sage/sage-7.5/local/lib/python2.7/site-packages/sage/rings/polynomial/multi_polynomial_ideal.py", line 3731, in groebner_basis gb = self._groebner_basis_singular("groebner", deg_bound=deg_bound, mult_bound=mult_bound, *args, **kwds) File "/projects/sage/sage-7.5/local/lib/python2.7/site-packages/sage/interfaces/singular.py", line 2724, in wrapper return func(*args, **kwds) 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 S = PolynomialSequence([R(S[i+1]) for i in range(len(S))], R, immutable=True) File "/projects/sage/sage-7.5/local/lib/python2.7/site-packages/sage/rings/polynomial/multi_polynomial_ring.py", line 481, in __call__ return x.sage_poly(self) File "/projects/sage/sage-7.5/local/lib/python2.7/site-packages/sage/interfaces/singular.py", line 1776, in sage_poly exp[var_dict[var]]=power KeyError: '(1.000e+00)'
P.<x,y,z> = 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
Multivariate Polynomial Ring in x, y, z over Real Double Field 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
Error in lines 3-3 Traceback (most recent call last): File "/projects/sage/sage-7.5/local/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 982, in execute exec compile(block+'\n', '', 'single') in namespace, locals File "", line 1, in <module> 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) w = self._instance_call(*args, **kwds) 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) return self.f(self._instance, *args, **kwds) File "/projects/sage/sage-7.5/local/lib/python2.7/site-packages/sage/rings/polynomial/multi_polynomial_ideal.py", line 3731, in groebner_basis gb = self._groebner_basis_singular("groebner", deg_bound=deg_bound, mult_bound=mult_bound, *args, **kwds) File "/projects/sage/sage-7.5/local/lib/python2.7/site-packages/sage/interfaces/singular.py", line 2724, in wrapper return func(*args, **kwds) 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 S = PolynomialSequence([R(S[i+1]) for i in range(len(S))], R, immutable=True) File "/projects/sage/sage-7.5/local/lib/python2.7/site-packages/sage/rings/polynomial/multi_polynomial_ring.py", line 481, in __call__ return x.sage_poly(self) File "/projects/sage/sage-7.5/local/lib/python2.7/site-packages/sage/interfaces/singular.py", line 1776, in sage_poly exp[var_dict[var]]=power KeyError: '(1.000e+00)'