Test the second polarization identity from my notes or from
Baes (2.4)::
- sage: x,y,z = random_eja().random_elements(3)
- sage: Lx = x.operator()
- sage: Ly = y.operator()
- sage: Lz = z.operator()
- sage: Lzy = (z*y).operator()
- sage: Lxy = (x*y).operator()
- sage: Lxz = (x*z).operator()
- sage: bool(Lx*Lzy + Lz*Lxy + Ly*Lxz == Lzy*Lx + Lxy*Lz + Lxz*Ly)
+ sage: x,y,z = random_eja().random_elements(3) # long time
+ sage: Lx = x.operator() # long time
+ sage: Ly = y.operator() # long time
+ sage: Lz = z.operator() # long time
+ sage: Lzy = (z*y).operator() # long time
+ sage: Lxy = (x*y).operator() # long time
+ sage: Lxz = (x*z).operator() # long time
+ sage: lhs = Lx*Lzy + Lz*Lxy + Ly*Lxz # long time
+ sage: rhs = Lzy*Lx + Lxy*Lz + Lxz*Ly # long time
+ sage: bool(lhs == rhs) # long time
True
Test the third polarization identity from my notes or from
Baes (2.5)::
- sage: u,y,z = random_eja().random_elements(3)
- sage: Lu = u.operator()
- sage: Ly = y.operator()
- sage: Lz = z.operator()
- sage: Lzy = (z*y).operator()
- sage: Luy = (u*y).operator()
- sage: Luz = (u*z).operator()
- sage: Luyz = (u*(y*z)).operator()
- sage: lhs = Lu*Lzy + Lz*Luy + Ly*Luz
- sage: rhs = Luyz + Ly*Lu*Lz + Lz*Lu*Ly
- sage: bool(lhs == rhs)
+ sage: u,y,z = random_eja().random_elements(3) # long time
+ sage: Lu = u.operator() # long time
+ sage: Ly = y.operator() # long time
+ sage: Lz = z.operator() # long time
+ sage: Lzy = (z*y).operator() # long time
+ sage: Luy = (u*y).operator() # long time
+ sage: Luz = (u*z).operator() # long time
+ sage: Luyz = (u*(y*z)).operator() # long time
+ sage: lhs = Lu*Lzy + Lz*Luy + Ly*Luz # long time
+ sage: rhs = Luyz + Ly*Lu*Lz + Lz*Lu*Ly # long time
+ sage: bool(lhs == rhs) # long time
True
"""