#!/usr/bin/env python

from __future__ import print_function

from sympy import symbols, sin, cos, simplify
from sympy.galgebra.ga import MV
from sympy.galgebra.printing import enhance_print

def main():
    enhance_print()

    (ex, ey, ez) = MV.setup('e*x|y|z', metric='[1,1,1]')

    u = MV('u', 'vector')
    v = MV('v', 'vector')
    w = MV('w', 'vector')
    print(u)
    print(v)
    print(w)

    uv = u ^ v
    print(uv)
    print(uv.is_blade())
    uvw = u ^ v ^ w
    print(uvw)
    print(uvw.is_blade())

    print(simplify((uv*uv).scalar()))
    return

if __name__ == "__main__":
    main()