def testlorentz(self):
mu=g.varidx(g.symbol("mu"),4)
e=g.delta_tensor(g.varidx(0,4),mu.toggle_variance())*\
g.lorentz_g(mu,g.varidx(0,4))
self.assertEqual(e.simplify_indexed(),1)
e=g.delta_tensor(g.varidx(0,4),mu.toggle_variance())*\
g.lorentz_g(mu,g.varidx(0,4),True)
self.assertEqual(e.simplify_indexed(),-1)
def testdelta(self):
i=g.idx(g.symbol("i"),3)
j=g.idx(g.symbol("j"),3)
k=g.idx(g.symbol("k"),3)
l=g.idx(g.symbol("l"),3)
A=g.symbol("A")
B=g.symbol("B")
e=g.indexed(A,i,j)*g.indexed(B,k,l)*g.delta_tensor(i,k)*\
g.delta_tensor(j,l)
self.assertEqual((e-g.indexed(A,k,l)*g.indexed(B,k,l)).
simplify_indexed(),0)
self.assertEqual((e-g.indexed(B,k,l)*g.indexed(A,k,l)).
simplify_indexed(),0)
self.assertEqual((e-g.indexed(A,i,l)*g.indexed(B,i,l)).
simplify_indexed(),0)
self.assertEqual((e-g.indexed(A,i,j)*g.indexed(B,i,j)).
simplify_indexed(),0)
self.assertNotEqual((e-g.indexed(A,i,i)*g.indexed(B,k,k)).
simplify_indexed(),0)
self.assertEqual(g.delta_tensor(i,i),3)
self.assertNotEqual(g.delta_tensor(i,i),4)
def testmetric(self):
mu=g.varidx(g.symbol("mu"),4)
nu=g.varidx(g.symbol("nu"),4)
rho=g.varidx(g.symbol("rho"),4)
A=g.symbol("A")
e=g.metric_tensor(mu,nu)*g.indexed(A,nu.toggle_variance(),rho)
self.assertEqual(e.simplify_indexed(),g.indexed(A,mu,rho))
self.assertNotEqual(e.simplify_indexed(),g.indexed(A,nu,rho))
e=g.delta_tensor(mu,nu.toggle_variance())*g.metric_tensor(nu,rho)
self.assertEqual(e.simplify_indexed(),g.metric_tensor(mu,rho))
e=g.metric_tensor(mu.toggle_variance(),nu.toggle_variance())*\
g.metric_tensor(nu,rho)
self.assertEqual(e.simplify_indexed(),
g.delta_tensor(mu.toggle_variance(),rho))
e=g.metric_tensor(nu.toggle_variance(),rho.toggle_variance())*\
g.metric_tensor(mu,nu)*(g.delta_tensor(mu.toggle_variance(),rho)+\
g.indexed(A,mu.toggle_variance(),rho))
self.assertEqual((e-(4+g.indexed(A,rho.toggle_variance(),rho))).
simplify_indexed(),0)