def testvaridx3(self):
mu=g.varidx(g.symbol("mu"),4)
nu=g.varidx(g.symbol("nu"),4)
A=g.symbol("A")
self.assertEqual(str(g.indexed(A,mu,nu)),"A~mu~nu")
self.assertEqual(str(g.indexed(A,mu,nu.toggle_variance())),"A~mu.nu")
self.assertEqual(str(g.indexed(A,mu.toggle_variance(),nu)),"A.mu~nu")
self.failUnless(mu.is_contravariant())
self.failUnless(nu.is_contravariant())
def testsimplify(self):
mu=g.varidx(g.symbol("mu"),4)
nu=g.varidx(g.symbol("nu"),4)
A=g.symbol("A")
e1=g.indexed(A,mu,mu.toggle_variance())
e2=g.indexed(A,nu,nu.toggle_variance())
self.assertNotEqual(e1,e2)
self.assertEqual((e1-e2).simplify_indexed(),0)
def testsubs(self):
mu=g.varidx(g.symbol("mu"),4)
nu=g.varidx(g.symbol("nu"),4,True)
A=g.symbol("A")
e=g.indexed(A,mu)
self.assertEqual(str(e),"A~mu")
self.assertEqual(str(e.subs(mu==nu)),"A.nu")
self.assertEqual(str(e.subs(mu==0)),"A~0")
def testdummy(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")
C=g.symbol("C")
e=g.indexed(A,i,j)*g.indexed(B,j,k)+g.indexed(C,k,l,i,l)
#can vary from run to run
#self.assertEqual(str(e),"C.k.l.i.l+B.j.k*A.i.j")
f=e.get_free_indices()
self.failUnless(type(f)==list)
self.failUnless(f==[i,k] or f==[k,i])
self.failUnless(str(f)=="[.i, .k]" or str(f)=="[.k, .i]")
mu=g.varidx(g.symbol("mu"),4)
nu=g.varidx(g.symbol("nu"),4)
rho=g.varidx(g.symbol("rho"),4)
sigma=g.varidx(g.symbol("sigma"),4)
e=g.indexed(A,mu,nu)*g.indexed(B,nu.toggle_variance(),rho)+\
g.indexed(C,mu,sigma,rho,sigma.toggle_variance())
self.failUnless(e.get_free_indices()==[mu,rho] or
e.get_free_indices()==[rho,mu])
e=g.indexed(A,mu,mu)
self.assertEqual(e.get_free_indices(),[mu])
self.assertNotEqual(e.get_free_indices(),[mu.toggle_variance()])
def testeps(self):
mu=g.varidx(g.symbol("mu"),4)
nu=g.varidx(g.symbol("nu"),4)
rho=g.varidx(g.symbol("rho"),4)
sig=g.varidx(g.symbol("sig"),4)
lam=g.varidx(g.symbol("lam"),4)
bet=g.varidx(g.symbol("bet"),4)
e=g.lorentz_eps(mu,nu,rho,sig)*g.lorentz_eps(mu.toggle_variance(),
nu.toggle_variance(),lam,bet)
g.simplify_indexed(e)
i=g.idx(g.symbol("i"),3)
j=g.idx(g.symbol("j"),3)
k=g.idx(g.symbol("k"),3)
A=g.symbol("A")
B=g.symbol("B")
e=g.epsilon_tensor(i,j,k)*g.indexed(A,j)*g.indexed(B,k)
self.assertNotEqual(g.simplify_indexed(e),0)
e=g.epsilon_tensor(i,j,k)*g.indexed(A,j)*g.indexed(A,k)
self.assertEqual(g.simplify_indexed(e),0)
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)
def testsimplify(self):
i=g.idx(g.symbol("i"),3)
j=g.idx(g.symbol("i"),3)
A=g.symbol("A")
B=g.symbol("B")
C=g.symbol("C")
sp=g.scalar_products()
sp.add(A,B,0)
sp.add(A,C,0)
sp.add(A,A,4)
e=g.indexed(A+B,i)*g.indexed(A+C,i)
self.assertEqual(e.expand(g.expand_options.expand_indexed).
simplify_indexed(sp),4+g.indexed(C,i)*g.indexed(B,i))
self.assertEqual(g.simplify_indexed(e.expand(g.expand_options.
expand_indexed),sp),4+g.indexed(C,i)*g.indexed(B,i))
self.assertNotEqual(g.simplify_indexed(e.expand(g.expand_options.
expand_indexed)),4+g.indexed(C,i)*g.indexed(B,i))
self.assertNotEqual(g.simplify_indexed(e.expand(g.expand_options.
expand_indexed),sp),5+g.indexed(C,i)*g.indexed(B,i))
self.assertNotEqual(g.simplify_indexed(e.expand(g.expand_options.
expand_indexed),sp),4+g.indexed(C,i)*g.indexed(B,j))
def testvaridx1(self):
i=g.varidx(g.symbol("i"),3)
j=g.varidx(g.symbol("j"),3)
A=g.symbol("A")
self.assertEqual(str(g.indexed(A,i,j)),"A~i~j")
def testidx(self):
i=g.idx(g.symbol("i"),3)
j=g.idx(g.symbol("j"),3)
A=g.symbol("A")
self.assertEqual(str(g.indexed(A,i,j)),"A.i.j")
def testsymm(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")
e=g.indexed(A,i,j)
e=g.indexed(A,g.sy_none(), i,j)
e=g.indexed(A,g.sy_none(0, 1), i,j)
e=g.indexed(A,g.sy_none(g.symmetry(0), g.symmetry(1)), i,j)
e=g.indexed(A,g.sy_symm(), i,j,k)
e=g.indexed(A,g.sy_symm(0,1,2), i,j,k)
e=g.indexed(A,g.sy_symm(2,0,1), i,j,k)
e=g.indexed(A,g.sy_symm(0,1), i,j,k)
e=g.indexed(A,g.sy_none(g.sy_symm(0,1),2), i,j,k)
e=g.indexed(A,g.sy_anti(0,2), i,j,k)
e=g.indexed(A,g.sy_none(g.sy_anti(0,2),1), i,j,k)
e=g.indexed(A,g.sy_symm(g.sy_anti(0,1),g.sy_anti(2,3)), i,j,k,l)
e=g.indexed(A,g.sy_cycl(), i,j,k)
e=g.indexed(A,g.sy_cycl(0,1,2), i,j,k)
#this is a deadlock... bug in ginac?
#but nobody really needs that, so I don't care
#g.sy_symm(0,1,2,3).add(4).add(5)
e=g.indexed(A,g.sy_symm(),i,j)+g.indexed(A,g.sy_symm(),j,i)
self.assertEqual(e,2*g.indexed(A,g.sy_symm(), i,j))
e=g.indexed(A,g.sy_anti(),i,j)+g.indexed(A,g.sy_anti(),j,i)
self.assertEqual(e,0)
e=g.indexed(A,g.sy_anti(),i,j,k)+g.indexed(A,g.sy_anti(),j,i,k)
self.assertEqual(e,0)
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)