Try these computations directly in Maxima, and see whether it's still a
discrepancy there.
On Saturday, April 9, 2016 at 1:31:44 PM UTC+1, Sergey V Kozlukov wrote:
>
> x, y, r, phi = var('x y r phi')
> f(x, y) = sign(x^2 + y^2 - 4)
> T(r, phi) = [r*cos(phi), r*sin(phi)]
> J = diff(T).det().simplify_full()
> T_f = f.substitute(x=T[0], y=T[1])
> int_f = integral(integral(T_f*abs(J), r, 0, 3), phi, 0, 2*pi).
> simplify_full()
> show(r"$\iint\limits_\Omega%s = %s$"%(latex(f(x)), latex(int_f)))
> Returns correct answer: $\pi$, while
> x, y, r, phi = var('x y r phi')
> f(x, y) = sign(x^2 + y^2 - 4)
> T(r, phi) = [r*cos(phi), r*sin(phi)]
> J = diff(T).det() #.simplify_full()
> T_f = f.substitute(x=T[0], y=T[1])
> int_f = integral(integral(T_f*abs(J), r, 0, 3), phi, 0, 2*pi).
> simplify_full()
> show(r"$\iint\limits_\Omega%s = %s$"%(latex(f(x)), latex(int_f)))
> Yields $-9\pi$
> The only thing simplify_full() changes here is it applies identity $\sin^2
> + \cos^2 = 1$
>
> Code was executed in SMC worksheet
>
--
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.
