Resultant for polynomials over RDF and CDF not implemented #10978
Description
Calling the resultant method for a polynomial defined over RDF or CDF returns a NotImplementedError. It would appear that this results from it not being implemented in Singular.
sage: R.<x> = PolynomialRing(CDF)
sage: f = R(1 - I*x + (0.5)*x^2 + (1.7)*x^3)
sage: g = f.derivative()
sage: f.resultant(g)
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
/Users/simonspicer/<ipython console> in <module>()
/Users/simonspicer/sage/local/lib/python2.6/site-packages/sage/rings/polynomial/polynomial_singular_interface.pyc in resultant(self, other, variable)
351 return lcm_func(self, singular, have_ring)
352 def resultant(self, other, variable=None):
--> 353 return resultant_func(self, other, variable)
354
355 def _singular_func(self, singular=singular_default, have_ring=False):
/Users/simonspicer/sage/local/lib/python2.6/site-packages/sage/rings/polynomial/polynomial_singular_interface.pyc in resultant_func(self, other, variable)
499 if variable is None:
500 variable = self.parent().gen(0)
--> 501 rt = self._singular_().resultant(other._singular_(), variable._singular_())
502 r = rt.sage_poly(self.parent())
503 if self.parent().ngens() <= 1 and r.degree() <= 0:
/Users/simonspicer/sage/local/lib/python2.6/site-packages/sage/interfaces/expect.pyc in __call__(self, *args, **kwds)
1481
1482 def __call__(self, *args, **kwds):
-> 1483 return self._obj.parent().function_call(self._name, [self._obj] + list(args), kwds)
1484
1485 def help(self):
/Users/simonspicer/sage/local/lib/python2.6/site-packages/sage/interfaces/expect.pyc in function_call(self, function, args, kwds)
1380 [s.name() for s in args],
1381 ['%s=%s'%(key,value.name()) for key, value in kwds.items()])
-> 1382 return self.new(s)
1383
1384 def _function_call_string(self, function, args, kwds):
/Users/simonspicer/sage/local/lib/python2.6/site-packages/sage/interfaces/expect.pyc in new(self, code)
1161
1162 def new(self, code):
-> 1163 return self(code)
1164
1165 ###################################################################
/Users/simonspicer/sage/local/lib/python2.6/site-packages/sage/interfaces/singular.pyc in __call__(self, x, type)
659 x = str(x)[1:-1]
660
--> 661 return SingularElement(self, type, x, False)
662
663 def has_coerce_map_from_impl(self, S):
/Users/simonspicer/sage/local/lib/python2.6/site-packages/sage/interfaces/singular.pyc in __init__(self, parent, type, value, is_name)
1122 except (RuntimeError, TypeError, KeyboardInterrupt), x:
1123 self._session_number = -1
-> 1124 raise TypeError, x
1125 else:
1126 self._name = value
TypeError: Singular error:
? not implemented
? error occurred in or before STDIN line 94: `def sage19=resultant(sage17,sage18,sage15);`
Component: algebra
Keywords: polynomial, resultant
Reviewer: Bruno Grenet
Issue created by migration from https://trac.sagemath.org/ticket/10978