The <> notation creates Python variables of the same name, so you shouldn't
use it together with the PolynomialRing(..., "e") constructor. Basically,
you need to be aware that the the string label "a" can be attached to
multiple Python variable names (its OK to do so for the computer but you
will get confused):
sage: p.parent()
Multivariate Polynomial Ring in a, b, c, d, e over Multivariate Polynomial
Ring in a, b, c, d over Rational Field
sage: preparse("R.<a,b,c,d,e> =
PolynomialRing(PolynomialRing(QQ,'a,b,c,d'),'e',sparse=True)")
"R = PolynomialRing(PolynomialRing(QQ,'a,b,c,d'),'e',sparse=True,
names=('a', 'b', 'c', 'd', 'e',)); (a, b, c, d, e,) = R._first_ngens(5)"
As for the second part, searching solutions over floating-point numbers
should be avoided. You probably want to first figure out if your system is
over/underdetermined and compute a lexicographic order Groebner basis:
http://ask.sagemath.org/question/403/method-for-solving-a-large-system-of-under
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