prob_not_solenoidal.py

from __future__ import print_function

from sympy import symbols,sin,cos,factor_terms,simplify
from galgebra.printer import enhance_print
from galgebra.deprecated import MV

def main():
    enhance_print()

    X = (x,y,z) = symbols('x y z')
    (ex,ey,ez,grad) = MV.setup('e_x e_y e_z',metric='[1,1,1]',coords=(x,y,z))

    A = x*(ey^ez) + y*(ez^ex) + z*(ex^ey)
    print('A =', A)
    print('grad^A =',(grad^A).simplify())
    print()

    f = MV('f','scalar',fct=True)
    f = (x**2 + y**2 + z**2)**(-1.5)
    print('f =', f)
    print('grad*f =',(grad*f).expand())
    print()

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

    Curl_B = grad^B

    print('grad^B =', Curl_B.simplify())

    def Symplify(A):
        return(factor_terms(simplify(A)))

    print(Curl_B.func(Symplify))
    return

if __name__ == "__main__":
    main()