Hello John thank you for this. I tried the same thing on mathematica, which managed to simplify 'c' back to 'a'.
I don't quite understand the culture of sage-support yet. Is commenting on mathematica's ability to do a particular task a useful thing to say? Or does it just annoy everyone? best wishes Robin On Thu, Jul 7, 2011 at 8:55 PM, John Cremona <john.crem...@gmail.com> wrote: > 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 > -- 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
