ExpandTensors

Description

  • ExpandTensors expands out products of tensors leaving unexpended all symbolic terms.
  • ExpandTensors[transformations] or ExpandTensors[[Simplifications: transformations]] applies transformations at each level of expand procedure.
  • ExpandTensors[[LeaveScalars: true]] will not expand expressions like (A_a^a + B_a^a)*(C_b^b + D_b^b).

Examples

Expand tensors in expressions: 

println ExpandTensors >> '(a+b)**10*(x_n + y_n)*(f_m - r_m)'.t

   > (a+b)**10*x_{n}*f_{m}+(a+b)**10*f_{m}*y_{n}-(a+b)**10*r_{m}*y_{n}-(a+b)**10*x_{n}*r_{m}


println ExpandTensors >> '(1 + x)**4*(A_a + B_a)'.t

   > (1 + x)**4 * A_a + (1 + x)**4 * B_a


println ExpandTensors >> '(1 + x)**4*(A_a + B_a)*(A^a + B^a)'.t

   > (x+1)**4*B^{a}*B_{a}+2*(x+1)**4*B^{a}*A_{a}+(x+1)**4*A^{a}*A_{a}

Symbolic parts will be kept on all levels: 

def t = '((a+b)*(c+d)*(f_a + (k+i)*t_a) + (a + c)*t_a)*(c+r)*((a+b)*f^a + (c+d)*t^a)'.t
println ExpandTensors >> t

   > (c+r)*(c+d)*(a+b)**2*f_a*f^a + (c+r)*((a+b)*(c+d)*(k+i) + 
          (a + c))*(a+b)*t_a*f^a + (c+r)*(a+b)*(c+d)*(c+d)*f_a*t^a 
          + (c+r)*((a+b)*(c+d)*(k+i) + (a + c))*(c+d)*t_a*t^a

Specify additional simplifications: 

def simplify = 'f_a*f^a = a'.t & 'f_a*t^a = b'.t & 't_a*t^a = c'.t
def t = '(2*(c+a)-164*a)*(f_{a}+t_{a})*f^{a}'.t
println ExpandTensors[simplify] >> t

   > a*(-164*a+2*(c+a))+b*(-164*a+2*(c+a))

See also