Here is a example of Maxwell's equation using the galgebra module from github
import sys
from sympy import symbols,sin,cos,exp,I,Matrix,simplify,Eq,S
from sympy.solvers import solve
from printer import Format,xpdf,Get_Program,Print_Function,Fmt
from ga import Ga
from metric import linear_expand
def Maxwell_in_Geom_Calculus():
Print_Function()
X = (t,x,y,z) = symbols('t x y z',real=True)
(st4d,g0,g1,g2,g3) = Ga.build('gamma*t|x|y|z',g=[1,-1,-1,-1],coords=X)
i = st4d.I()
B = st4d.mv('B','vector',f=True)
B = B.proj([g1,g2,g3]) # Make vector from spatial components of B
print 'B =',B
E = st4d.mv('E','vector',f=True)
E = E.proj([g1,g2,g3]) # Make vector from spatial components of E
print 'E =',E
F = g0*E+i*g0*B
print 'F =', F
J = st4d.mv('J','vector',f=True)
print 'J =', J
gradF = st4d.grad*F
print 'grad*F =', gradF.Fmt(2)
W = gradF-J
print 'grad*F - J = 0 =', W.Fmt(2)
return
def dummy():
return
def main():
Get_Program()
Format()
Maxwell_in_Geom_Calculus()
xpdf()
return
if __name__ == "__main__":
main()
Attached is the pdf output of the above code.
On Wed, Feb 15, 2017 at 7:47 AM, Alan Bromborsky <[email protected]>
wrote:
> When you get galgebra from git in the galgebra/doc directory is
> galgebra.pdf. In section 1.3 of the document are instructions of how to
> install galgebra including how to set the python path so that other python
> programs can find galgebra.
>
> On Wed, Feb 15, 2017 at 5:35 AM, Henri Girard <[email protected]>
> wrote:
>
>> Hi,
>> I am new to sympy and I wanted to try it on maxwell's equations examples
>> so I installed galgebra from git but it doesn't work ? the import is not
>> found... ANy help ?
>> regards
>> Henri
>>
>> import sys
>> import sympy.galgebra.GAsympy 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')
>> print ('E = Evec gamma_0 =',E)
>> F = E+I*B
>> print ('$E+IB$ Electo-Magnetic Field Bi-Vector')
>> print ('F = E+IB =',F)
>> print ('$J$ Four Current')
>> print ('J =',J)
>> gradF = F.grad()
>> gradF.convert_to_blades()
>> print ('Geometric Derivative of EM Bi-Vector')
>> tex.MV_format(3)
>> print ('\\nabla F =',gradF)
>> print ('All Maxwell Equations are')
>> print ('\\nabla F = J')
>> print ('Div $E$ and Curl $H$ Equations')
>> print ('<\\nabla F>_1 -J =',gradF.project(1)-J,' = 0')
>> print ('Curl $E$ and Div $B$ equations')
>> print ('<\\nabla F>_3 =',gradF.project(3),' = 0')
>> tex.xdvi(filename='Maxwell.tex')
>>
>> ---------------------------------------------------------------------------ImportError
>> Traceback (most recent call
>> last)<ipython-input-1-45c89331d82f> in <module>() 1 import sys----> 2
>> import sympy.galgebra.GAsympy as GA 3 import sympy.galgebra.latex_ex as
>> tex 4 5 GA.set_main(sys.modules[__name__])
>> /home/pi/git/sage/local/lib/python2.7/site-packages/sympy/galgebra.py in
>> <module>()----> 1 raise ImportError("""As of SymPy 1.0 the galgebra module
>> is maintained separately at https://github.com/brombo/galgebra""";)
>> ImportError: As of SymPy 1.0 the galgebra module is maintained separately at
>> https://github.com/brombo/galgebra
>>
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maxwell.pdf
Description: Adobe PDF document
