Hi -
I'm trying to calculate the resultant (with respect to one variable, say x) of a pair of 2-variable polynomials. Following some advice I found in this trac ticket, I tried entering something like this:
R.<x,y> = RR[]
P = 4*x^3*y^2 + 7*x^5*y - 3*x*y^4
Q = 5*x^3*y^3 - 9*y^2
P.polynomial(x).resultant(Q.polynomial(x))
However, P.polynomial(x) returns the error:
ValueError: max() arg is an empty sequence
(Full error message pasted below.) Same problem with P.polynomial(y), etc. It seems to work okay if the coefficient ring is ZZ or QQ instead of RR.
Does anyone know why this is happening, or of a different workaround for calculating these resultants?
Thanks!
Full error message:
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "_sage_input_28.py", line 10, in <module>
exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("Ui48eCx5PiA9IFJSW10KcCA9IHggKyB5CnEgPSB4KnkKcC5wb2x5bm9taWFsKHgpLnJlc3VsdGFudChxLnBvbHlub21pYWwoeCkp"),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))
File "", line 1, in <module>
File "/private/var/folders/5h/c6x89ch91fjgr43q99g8wbjw0000gn/T/tmpVUVLIc/___code___.py", line 5, in <module>
exec compile(u'p.polynomial(x).resultant(q.polynomial(x))
File "", line 1, in <module>
File "multi_polynomial.pyx", line 452, in sage.rings.polynomial.multi_polynomial.MPolynomial.polynomial (sage/rings/polynomial/multi_polynomial.c:5376)
File "parent.pyx", line 988, in sage.structure.parent.Parent.__call__ (sage/structure/parent.c:7355)
File "coerce_maps.pyx", line 82, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_ (sage/structure/coerce_maps.c:3311)
File "coerce_maps.pyx", line 77, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_ (sage/structure/coerce_maps.c:3214)
File "/Applications/Sage-4.8-OSX-64bit-10.6.app/Contents/Resources/sage/local/lib/python2.6/site-packages/sage/rings/polynomial/polynomial_ring.py", line 407, in _element_constructor_
return C(self, x, check, is_gen, construct=construct, **kwds)
File "polynomial_real_mpfr_dense.pyx", line 87, in sage.rings.polynomial.polynomial_real_mpfr_dense.PolynomialRealDense.__init__ (sage/rings/polynomial/polynomial_real_mpfr_dense.c:3418)
ValueError: max() arg is an empty sequence
