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#!/usr/bin/env python
from __future__ import print_function
from sympy import symbols
from sympy.galgebra import MV, ReciprocalFrame
from sympy.galgebra import enhance_print
from sympy.galgebra import oprint
from sympy.galgebra import define_precedence, GAeval
def main():
enhance_print()
coords = symbols('x y z')
(ex, ey, ez, grad) = MV.setup('ex ey ez', metric='[1,1,1]', coords=coords)
mfvar = (u, v) = symbols('u v')
eu = ex + ey
ev = ex - ey
(eu_r, ev_r) = ReciprocalFrame([eu, ev])
oprint('Frame', (eu, ev), 'Reciprocal Frame', (eu_r, ev_r))
print('eu.eu_r =', eu | eu_r)
print('eu.ev_r =', eu | ev_r)
print('ev.eu_r =', ev | eu_r)
print('ev.ev_r =', ev | ev_r)
eu = ex + ey + ez
ev = ex - ey
(eu_r, ev_r) = ReciprocalFrame([eu, ev])
oprint('Frame', (eu, ev), 'Reciprocal Frame', (eu_r, ev_r))
print('eu.eu_r =', eu | eu_r)
print('eu.ev_r =', eu | ev_r)
print('ev.eu_r =', ev | eu_r)
print('ev.ev_r =', ev | ev_r)
print('eu =', eu)
print('ev =', ev)
define_precedence(locals())
print(GAeval('eu^ev|ex', True))
print(GAeval('eu^ev|ex*eu', True))
return
if __name__ == "__main__":
main()
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