ph, th = var('ph, th') Y = spherical_harmonic(4, 0, th, ph) rea = spherical_plot3d(abs(real(Y)), (ph,0,2*pi), (th,0,pi), color='blue', opacity=0.3) ima = spherical_plot3d(abs(imag(Y)), (ph,0,2*pi), (th,0,pi), color='red', opacity=0.6) (rea + ima).show(aspect_ratio=1) # long time (4s on sage.math, 2011)
3D rendering not yet implemented
ph, th = var('ph, th') Y = spherical_harmonic(3, 1, th, ph) rea = spherical_plot3d(abs(real(Y)), (ph,0,2*pi), (th,0,pi), color='blue', opacity=0.6) ima = spherical_plot3d(abs(imag(Y)), (ph,0,2*pi), (th,0,pi), color='red', opacity=0.6) (rea + ima).show(aspect_ratio=1) # long time (4s on sage.math, 2011)
3D rendering not yet implemented
ph, th = var('ph, th') Y = 2*pi*spherical_harmonic(1, 0, th, ph)*(4*pi*spherical_harmonic(0, 0, th, ph)^2 - 4*pi*spherical_harmonic(1, 0, th, ph)^2/3)*((spherical_harmonic(1, -1, th, ph))+I*(spherical_harmonic(1, -1, th, ph) + spherical_harmonic(1, 1, th, ph))) + (4*pi/3)^(5/2)*spherical_harmonic(1, 0, th, ph)*((spherical_harmonic(1, -1, th, ph) - spherical_harmonic(1, 1, th, ph))^3 +I*(spherical_harmonic(1, -1, th, ph) + spherical_harmonic(1, 1, th, ph))^3) rea = spherical_plot3d(abs(real(Y)), (ph,0,2*pi), (th,0,pi), color='blue', opacity=0.6) ima = spherical_plot3d(abs(imag(Y)), (ph,0,2*pi), (th,0,pi), color='red', opacity=0.6) (rea + ima).show(aspect_ratio=1) # long time (4s on sage.math, 2011)
3D rendering not yet implemented
show(integrate(e^-x,x))
−e(−x)
tan(-1).n()
-1.55740772465490
%var R, h, p, f di = R == 20*log(p*h*f) - 47.5 show(solve(di, h))
[h=fpe(201R+819)]
d = solve(di, h) show(d)
[h=fpe(201R+819)]