> My understanding was that 'x' was the indeterminate > of the ring of polynomials over QQ, i.e. the rationals. So how come > the polynomial > has coefficients which are not rational?
Because the polynomial isn't living where you think it does anymore: sage: R.<x> = QQ['x'] sage: R Univariate Polynomial Ring in x over Rational Field sage: parent(x) Univariate Polynomial Ring in x over Rational Field sage: sage: f = (x-sqrt(2))*(x+sqrt(2)) sage: f (x - sqrt(2))*(x + sqrt(2)) sage: parent(f) Symbolic Ring sage: R(f) --------------------------------------------------------------------------- TypeError Traceback (most recent call last) [...] TypeError: unable to convert -sqrt(2) to a rational sage: R(expand(f)) x^2 - 2 In this case, the introduction of the sqrt terms pushed the expression out of R and into SR. We can convert back, but only if the expression is in a form that Sage can recognize as belonging to R. Doug -- To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
