spherial harmonic.sagews

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))

$\displaystyle -e^{\left(-x\right)}$

tan(-1).n()

-1.55740772465490

%var R, h, p, f
di = R == 20*log(p*h*f) - 47.5
show(solve(di, h))

[$\displaystyle h = \frac{e^{\left(\frac{1}{20} \, R + \frac{19}{8}\right)}}{f p}$]

d = solve(di, h)
show(d)

[$\displaystyle h = \frac{e^{\left(\frac{1}{20} \, R + \frac{19}{8}\right)}}{f p}$]