On Mon, Mar 20, 2017 at 7:51 AM, Jaume Aguade <ja...@jaumeaguade.cat> wrote: > Let r > a > 0 be real numbers. Let c = a + r, d = sqrt(r^2-a^2). Then, it is > obvious that 2*a*c=c^2-d^2. However, sage crashes when trying to check this > with a and r rather "simple" algebraic numbers. > > I've found this while using sage to solve elementary geometric problems > involving circles and intersection of circles, i. e. algebraic numbers which > can be written using only square roots. > > The capacity of working over the field AA is one of my favourite features of > sage, so I was disappointed when I found this easy example which > (apparently) cannot be worked out by sage. I would like to know if I'm > missing something or there is some other way to deal with these > computations. > > (The trouble persists in QQbar) > > Here is the code: > > a=AA(sqrt(sqrt(5))) > r=AA(sqrt((AA(sqrt(13))-a)^2+3)) > c=a+r > > d= AA(sqrt(r^2-a^2)) > > 2*a*c == c^2 - d^2 >
A possible work-around: It seems to work using SR: sage: r = SR(sqrt((SR(sqrt(13))-a)^2+3)) sage: a = SR(sqrt(sqrt(5))) sage: r = SR(sqrt((SR(sqrt(13))-a)^2+3)) sage: c = a+r sage: d = SR(sqrt(r^2-a^2)) sage: bool(2*a*c == c^2 - d^2) True > -- > You received this message because you are subscribed to the Google Groups > "sage-devel" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-devel+unsubscr...@googlegroups.com. > To post to this group, send email to sage-devel@googlegroups.com. > Visit this group at https://groups.google.com/group/sage-devel. > For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
