GA.set_main(sys.modules[__name__])
if __name__ == '__main__':
metric = '1 0 0 0,'+\
'0 -1 0 0,'+\
'0 0 -1 0,'+\
'0 0 0 -1'
vars = GA.make_symbols('t x y z')
GA.MV.setup('gamma_t gamma_x gamma_y gamma_z', metric, True, vars)
parms = GA.make_symbols('m e')
tex.Format()
I = GA.MV(GA.ONE, 'pseudo')
nvars = len(vars)
psi = GA.MV('psi', 'spinor', fct=True)
psi.convert_to_blades()
A = GA.MV('A', 'vector', fct=True)
sig_x = gamma_x * gamma_t
sig_y = gamma_y * gamma_t
sig_z = gamma_z * gamma_t
print '$A$ is 4-vector potential'
print A
print r'$\bm{\psi}$ is 8-component real spinor (even multi-vector)'
print psi
dirac_eq = psi.grad() * I * sig_z - e * A * psi - m * psi * gamma_t
dirac_eq.simplify()
dirac_eq.convert_to_blades()
print 'Dirac equation in terms of real geometric algebra/calculus '+\
metric = '1 0 0,' \
'0 1 0,' \
'0 0 1'
gamma_x, gamma_y, gamma_z = GA.MV.setup('gamma_x gamma_y gamma_z', metric,
True)
tex.Format()
coords = r, theta, phi = sympy.symbols('r theta phi')
x = r * (sympy.cos(theta) * gamma_z + sympy.sin(theta) *
(sympy.cos(phi) * gamma_x + sympy.sin(phi) * gamma_y))
x.set_name('x')
GA.MV.rebase(x, coords, 'e', True)
psi = GA.MV('psi', 'scalar', fct=True)
dpsi = psi.grad()
print 'Gradient of Scalar Function $\\psi$'
print '\\nabla\\psi =', dpsi
A = GA.MV('A', 'vector', fct=True)
print 'Div and Curl of Vector Function $A$'
print A
gradA = A.grad()
I = GA.MV(GA.ONE, 'pseudo')
divA = A.grad_int()
curlA = -I * A.grad_ext()
print '\\nabla \\cdot A =', divA
import sympy.galgebra.GA as GA
import sympy.galgebra.latex_ex as tex
GA.set_main(sys.modules[__name__])
if __name__ == '__main__':
metric = '1 0 0 0,'+\
'0 -1 0 0,'+\
'0 0 -1 0,'+\
'0 0 0 -1'
vars = GA.make_symbols('t x y z')
GA.MV.setup('gamma_t gamma_x gamma_y gamma_z',metric,True,vars)
tex.Format()
I = GA.MV(1,'pseudo')
I.convert_to_blades()
print '$I$ Pseudo-Scalar'
print 'I =',I
B = GA.MV('B','vector',fct=True)
E = GA.MV('E','vector',fct=True)
B.set_coef(1,0,0)
E.set_coef(1,0,0)
B *= gamma_t
E *= gamma_t
B.convert_to_blades()
E.convert_to_blades()
J = GA.MV('J','vector',fct=True)
print '$B$ Magnetic Field Bi-Vector'
print 'B = Bvec gamma_0 =',B
print '$E$ Electric Field Bi-Vector'
