def isVersor(self) -> bool:
"""Returns true if multivector is a versor.
From :cite:`ga4cs` section 21.5, definition from 7.6.4
"""
Vhat = self.gradeInvol()
Vrev = ~self
Vinv = Vrev / (self * Vrev)[()]
# Test if the versor inverse (~V)/(V * ~V) is truly the inverse of the
# multivector V
if (Vhat * Vinv).grades(eps=0.000001) != {0}:
return False
if not np.sum(np.abs((Vhat * Vinv).value -
(Vinv * Vhat).value)) < 0.0001:
return False
# applying a versor (and hence an invertible blade) to a vector should
# not change the grade
if not all((Vhat * e * Vrev).grades(eps=0.000001) == {1}
for e in cf.basis_vectors(self.layout).values()):
return False
return True
def basis_vectors(self):
return cf.basis_vectors(self)
