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#!/usr/bin/env python
from __future__ import print_function
from sympy import symbols
from sympy.galgebra import MV, Format
from sympy.galgebra import xdvi
def main():
Format()
coords = (x, y, z) = symbols('x y z')
(ex, ey, ez, grad) = MV.setup('e*x|y|z', '[1,1,1]', coords=coords)
s = MV('s', 'scalar')
v = MV('v', 'vector')
b = MV('b', 'bivector')
print(r'#3D Orthogonal Metric\newline')
print('#Multvectors:')
print('s =', s)
print('v =', v)
print('b =', b)
print('#Products:')
X = ((s, 's'), (v, 'v'), (b, 'b'))
for xi in X:
print('')
for yi in X:
print(xi[1] + '*' + yi[1] + ' =', xi[0]*yi[0])
print(xi[1] + '^' + yi[1] + ' =', xi[0] ^ yi[0])
print(xi[1] + '|' + yi[1] + ' =', xi[0] | yi[0])
print(xi[1] + '<' + yi[1] + ' =', xi[0] < yi[0])
print(xi[1] + '>' + yi[1] + ' =', xi[0] > yi[0])
fs = MV('s', 'scalar', fct=True)
fv = MV('v', 'vector', fct=True)
fb = MV('b', 'bivector', fct=True)
print('#Multivector Functions:')
print('s(X) =', fs)
print('v(X) =', fv)
print('b(X) =', fb)
print('#Products:')
fX = ((grad, 'grad'), (fs, 's'), (fv, 'v'), (fb, 'b'))
for xi in fX:
print('')
for yi in fX:
if xi[1] == 'grad' and yi[1] == 'grad':
pass
else:
print(xi[1] + '*' + yi[1] + ' =', xi[0]*yi[0])
print(xi[1] + '^' + yi[1] + ' =', xi[0] ^ yi[0])
print(xi[1] + '|' + yi[1] + ' =', xi[0] | yi[0])
print(xi[1] + '<' + yi[1] + ' =', xi[0] < yi[0])
print(xi[1] + '>' + yi[1] + ' =', xi[0] > yi[0])
(ex, ey, grad) = MV.setup('e', coords=(x, y))
print(r'#General 2D Metric\newline')
print('#Multivector Functions:')
s = MV('s', 'scalar', fct=True)
v = MV('v', 'vector', fct=True)
b = MV('v', 'bivector', fct=True)
print('s(X) =', s)
print('v(X) =', v)
print('b(X) =', b)
X = ((grad, 'grad'), (s, 's'), (v, 'v'))
print('#Products:')
for xi in X:
print('')
for yi in X:
if xi[1] == 'grad' and yi[1] == 'grad':
pass
else:
print(xi[1] + '*' + yi[1] + ' =', xi[0]*yi[0])
print(xi[1] + '^' + yi[1] + ' =', xi[0] ^ yi[0])
print(xi[1] + '|' + yi[1] + ' =', xi[0] | yi[0])
print(xi[1] + '<' + yi[1] + ' =', xi[0] < yi[0])
print(xi[1] + '>' + yi[1] + ' =', xi[0] > yi[0])
xdvi(paper='letter')
return
if __name__ == "__main__":
main()
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