With d=c-a, not even d.simplify_radical() gives 0. Simplifying "nested radicals" is a notoriously hard problem in symbolic computer algebra. As this example shows (unless there are other tricks to try which I do not know about), Sage's symbolic system is not up to examples like this.
As an algebraist I would use a different approach. Note that sage: type(a) <type 'sage.symbolic.expression.Expression'> but as these quantities are all algebraic one can also use sage: QQbar Algebraic Field for example sage: QQbar(a) == QQbar(c) True Behind the scenes, this is checking first that a and c have the same minimal polynomial: sage: QQbar(a).minpoly() x^4 - 4*x^3 - 4*x^2 + 16*x - 8 sage: QQbar(c).minpoly() x^4 - 4*x^3 - 4*x^2 + 16*x - 8 and also (by using numerical approximations to whatever precision is necessary) that they are the same root of that poly. John Cremona On Jul 5, 11:38 pm, robin hankin <hankin.ro...@gmail.com> wrote: > Hi. I am having difficulty using sage to manipulate surds. > > Consider: > > a = 1 + sqrt(2) + sqrt(3) > b= (a^2).expand() > c = sqrt(b) > > Then 'y' should be equal to 'a'. > > But, given 'y' I cannot make sage return the simple form. > Trying > > y.simplify_full() > > doesn't do what I want. > > How do I make sage recognize that a=c, other than using n()? > > -- > Robin Hankin > Uncertainty Analyst > hankin.ro...@gmail.com -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
