pygae/galgebra

import sys
from sympy import symbols, sin
from galgebra.printer import Format, xpdf
from galgebra.ga import Ga

Format()
X = (r, th, phi) = symbols('r theta phi')
s3d = Ga(
    'e_r e_theta e_phi', g=[
        1, r**2, r**2 * sin(th)**2], coords=X, norm=True)
(er, eth, ephi) = s3d.mv()
grad = s3d.grad

f = s3d.mv('f', 'scalar', f=True)
A = s3d.mv('A', 'vector', f=True)
B = s3d.mv('B', 'bivector', f=True)

print('f =', f)
print('A =', A)
print('B =', B)

# FIXME xxxx/r printed as \frac{xxxx}{r} instead of \frac{1}{r} xxxx
print('grad*f =', grad * f)
print('grad|A =', grad | A)
print('-I*(grad^A) =', (-s3d.i * (grad ^ A)).simplify())
print('grad^B =', grad ^ B)
print(r'%\nabla\cdot\lp\nabla f\rp =', s3d.grad | (s3d.grad * f))
xpdf(paper='letter', prog=True)