from sympy.abc import x, y, z

from sympy.abc import i, j, k

#from sympy.abc import rho, phi, theta

from sympy.abc import r, n

from sympy.abc import alpha, beta, gamma

from sympy.abc import omega, mu, epsilon

from sympy import var, symbols, sin, cos, exp, zeros, Matrix, Symbol, Function, I, eye, simplify, latex

from sympy.galgebra.printing import xdvi

############### Geometric Algebra & Format of out pdf file ##############

#from sympy.galgebra.ga import *

#from printer import Eprint , Format , xpdf

#from ga import Ga

#Format(ipy=True)

#Format()

########################################################################

F, Psi = symbols('F, Psi', cls=Function)

G = symbols('G', integer=True)

var("rho theta phi")

var("t")

n = i * sin(theta) * cos(phi) + j * sin(theta) * sin (phi) + k * cos (theta)

r = i * x + j * y + k * z

g1 = expand(n * r)

# Square is equal to one unit vectors and the product of pairs of unit vectors is zero

oneii = i * i

onejj = j * j

onekk = k * k

oneij = i * j

oneik = i * k

onejk = j * k

# Simplifying

g1=g1.subs(oneii,1).expand().simplify()

g1=g1.subs(onejj,1).expand().simplify()

g1=g1.subs(onekk,1).expand().simplify()

g1=g1.subs(oneij,0).expand().simplify()

g1=g1.subs(oneik,0).expand().simplify()

g1=g1.subs(onejk,0).expand().simplify()

# Multiply by the propagation constant in the direction of wave

g2 = expand(G(mu, epsilon) * g1)

g2 = expand(g2)

# Propagation constants along the axes

#alpha1 = G(mu, epsilon) * sin(theta) * cos(phi)

#beta1 = G(mu, epsilon) * sin(theta) * sin(phi)

#gamma1 = G(mu, epsilon) * cos(theta)

alpha1 = G * sin(theta) * cos(phi)

beta1 = G * sin(theta) * sin(phi)

gamma1 = G * cos(theta)

# Simplifying

g2=g2.subs(alpha1,alpha).expand().simplify()

g2=g2.subs(beta1,beta).expand().simplify()

g2=g2.subs(gamma1,gamma).expand().simplify()

print "r =", g2

#Propagation constants along the axes are related

g3 = alpha1**2 + beta1**2 + gamma1**2

# Simplifying

g3=g3.subs(sin(phi)**2, 1-cos(phi)**2).expand().simplify()

print r'%\alpha^{2} + \beta^{2} + \gamma^{2} = ', latex(g3)

x_hat = Matrix([

rho * sin(theta) * cos(phi),

rho * sin(theta) * sin(phi),

rho * cos(theta)])

psi = Function("psi")

psi =exp(I*omega*t) * exp(-I*g2)

print "\Psi =", latex(psi)

#Derivatives of the wave function of the coordinates

dpsidx=psi.diff(x)

dpsidx=dpsidx.subs(psi,'Psi').expand().simplify()

print "d \Psi / dx =", latex(dpsidx)

dpsidy=psi.diff(y)

dpsidy=dpsidy.subs(psi,'Psi').expand().simplify()

print "d \Psi / dy =", latex(dpsidy)

dpsidz=psi.diff(z)

dpsidz=dpsidz.subs(psi,'Psi').expand().simplify()

print "d \Psi / dz =", latex(dpsidz)

########### Maxwell's Equations ###################

#A,B,C1,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R = symbols('A B C1 D E F G H I J K L M N O P Q R', cls=Function)

omega, mu, epsilon, muz, epsilonz = symbols('omega mu epsilon mu_z epsilon_z', integer=True)

# Vertical indexs: Hx Hy Hz Ex Ey Ez

# Gorizontal indexs: Hx Hy Hz Ex Ey Ez

Z = Matrix(([omega*mu,0,0,0,0,0],[0,omega*mu,0,0,0,0],[0,0,omega*muz,0,0,0],[0,0,0,omega*epsilon,0,0],[0,0,0,0,omega*epsilon,0],[0,0,0,0,0,omega*epsilonz]))

Z

# Vertical indexs: Hx Hy Hz Ex Ey Ez

# Gorizontal indexs: JEx JEy JEz JMx JMy JMz

# Сoefficient K of exp(KX) : alpha1 beta1 gamma1

C = Matrix((\

))

C

Z1=Z + C.transpose()

Z2=Z1.det()

Z3=Z2.simplify()

Z3=Z3/omega**2/mu/epsilon

Z4=solve(Z3,G)

for id in range(len(Z4)):

Z4[id]=Z4[id].subs(sin(theta)**2, 1-cos(theta)**2).expand().simplify()

Z4

vars = symbols('t x y z')

(g0,g1,g2,g3,grad) = MV.setup('gamma*t|x|y|z',metric='[1,-1,-1,-1]',coords=vars)

I = MV.I

E = MV('E','vector',fct=True)

H = MV('H','vector',fct=True)

E.set_coef(1,0,0)

H.set_coef(1,0,0)

#E *= g0

#H *= g0

E = E * g0

H = H * g0

#E.expand().simplify()

#H.simplify()

#J = MV('J','vector',fct=True)

F = E+I*H

print 'E = \\bm{E\\gamma_{t}} =',E

print 'H = \\bm{H\\gamma_{t}} =',H

print 'F = E+IH =',F

xpdf(paper=(6,7))