Input expressions, apply substitutions and other transformations and Redberry will automatically match and relabel indices, resolve dummy indices clashes etc.:
expr = 'F_mn*(F^ma + T^am)'.t println 'F_ij = A_i*A_j'.t >> expr
> A_m*A_n*(A^m*A^a + T^am)
subs = 'x = x_a^a'.t expr = '(x*f_a + y_a)*(x*f_b + z_b)'.t println subs >> expr
> (x_d^d*f_a+y_a)*(x_c^c*f_b+z_b)
Redberry provides a wide range of general-purpose and tensor-specific transformations:
println Expand >> '(a+b)**2'.t
> a**2 + 2*a*b + b**2
expr = 'g_mn*A^mn + g_ab*(g^ab + A^ab)'.t println EliminateMetrics >> expr
> 2*A^m_m + d^b_b
Define symmetries of tensors and Redberry will take them into account during any manipulation:
// Setting up Riemann symmetries addSymmetry 'R_abcd', [[0, 2], [1, 3]].p addSymmetry 'R_abcd', -[[1, 0]].p println 'R^abc_d*R_abc^m + R_rdqp*R^mrqp'.t
> 0
Calculate trace of Dirac, SU(N) matrices, simplify Levi-Civita tensors, calculate one-loop counterterms etc.:
// Set up gamma matrix defineMatrices 'G_a', Matrix1.matrix // DiracTrace transformation dTrace = DiracTrace['G_a'] expr = 'Tr[(p_a*G^a + m)*(q_a*G^a-m)*G_n]'.t println dTrace >> expr
> 4*m*q_n - 4*m*p_n
The underlying Redberry algorithms are largely based on computational graph and group theory:
perm1 = [[0, 7, 4, 2], [8, 5]].p perm2 = [[0, 3, 6], [1, 4, 2]].p group = Group(perm1, perm2) println group.setwiseStabilizer(0,4,2,5)
> Group( [[1, 7, 6]], [[1, 3, 7]],
[[1, 6], [2, 4]], [[0, 2], [1, 6]] )
Use all features of general-purpose programming language (looping, branching, functions, classes etc.) to implement custom functions and transformations:
//invert indices of expr
invert = { expr ->
indices = expr.indices
(indices % indices.inverted) >> expr
} as Transformation
println invert >> ['f_mn'.t, 't^ab'.t]
> [f^mn, t_ab]