examples/tensors.py

   1 #!/usr/bin/env python
   2 import iam_sympy_example
   3
   4 """
   5 http://www.lncc.br/~portugal/Canon.html
   6 http://www.lncc.br/~portugal/Invar.html
   7 http://www.ginac.de/tutorial/Indexed-objects.html
   8 http://grtensor.phy.queensu.ca/
   9
  10 """
  11
  12 from sympy import exp, Symbol, sin, Rational, Derivative, dsolve
  13
  14 from sympy.core import Basic, Function
  15 from sympy.matrices import Matrix
  16
  17 class Indexed(Basic):
  18     def __init__(self, A, idxlist):
  19         self._args = [A, idxlist]
  20
  21     def __str__(self):
  22         r = str(self[0])
  23         for idx in self[1]:
  24             r+=str(idx)
  25         return r
  26
  27 class Idx(Symbol):
  28     def __init__(self, name, dim = 4, up = True):
  29         Symbol.__init__(self, name)
  30         #self._args.extend([dim,up])
  31         self._name = name
  32         self._dim = dim
  33         self._up = up
  34
  35     def __str__(self):
  36         if self._up:
  37             r = "^"
  38         else:
  39             r = "_"
  40         return r+self._name
  41
  42     @property
  43     def up(self):
  44         return Idx(self._name, self._dim, True)
  45
  46     @property
  47     def dn(self):
  48         return Idx(self._name, self._dim, False)
  49
  50     def values(self):
  51         return range(self._dim)
  52
  53 t=Symbol("t")
  54 r=Symbol("r")
  55 theta=Symbol(r"\theta")
  56 phi=Symbol(r"\phi")
  57
  58 class nu(Function):
  59     pass
  60 class lam(Function):
  61     pass
  62
  63 gdd=Matrix((
  64     (-exp(nu(r)),0,0,0),
  65     (0, exp(lam(r)), 0, 0),
  66     (0, 0, r**2, 0),
  67     (0, 0, 0, r**2*sin(theta)**2)
  68     ))
  69
  70 mu = Idx("mu")
  71 nu = Idx("mu")
  72 i = Idx("i")
  73 m = Idx("m")
  74 k = Idx("k")
  75 l = Idx("l")
  76 g = Indexed(Symbol("A"), [mu,nu])
  77 Chr = g[i.up, m.up]/2 * (g[m.dn, k.dn].diff(l.up) + g[m.dn,l.dn].diff(k.up) \
  78         - g[k.dn, l.dn].diff(m.up))
  79 #G = g.uu(i,m)/2 * (g.dd(m,k).diff(x[l])+g.dd(m,l).diff(x[k]) \
  80 #                    - g.dd(k,l).diff(x[m]))
  81
  82 print g
  83 print Chr