Collect

Collect[var1, var2] collects together terms involving the same powers of specified vars.

Collect[var1, var2, …, transformations] or Collect[var1, var2, ..., [Simplifications: transformations]] additionally applies specified transformations to the expression that forms the coefficient of each term obtained.

In the case of tensorial vars, Collect will insert Kronecker deltas or metric tensors in order to “uncontract” indices and factor out tensorial parts.

In the case of scalar vars, the behaviour of Collect is similar to other CASs.

To prevent expand of symbolic terms when collecting tensors one can use option Collect[[var1, var2, ..., [ExpandSymbolic: false]]

Collect terms involving x:

println Collect['x'] >> 'a*x + b*x + с*x**2 + d*x**2 + f*e'.t

> (a + b)*x + (c + d)*x**2 + f*e

Collect powers of x and factor coefficients:

println Collect['x', Factor] >> '(1 + a + x)**4'.t

> x**4 + 4*x**3*(a+1) + 6*x**2*(a+1)**2 + 4*(a+1)**3*x + (a+1)**4

Collect terms involving tensor A_i:

println Collect['A_i'] >> 'A_m*B_n + A_n*C_m + B_n*C_m'.t

> A_{a}*(C_{m}*d_{n}^{a} + B_{n}*d_{m}^{a}) + B_{n}*C_{m}

Collect terms involving same tensorial function F_ij[x_ab]:

def t = 'F_ij[t_ab]*t^ij + F_ab[t_pq]*f^ba + F_ij[f_ij]*t^ij + F_ij[f_ij]*f^ji'.t

println Collect['F_ij[a_ij]'] >> t

> (t^{ij}+f^{ji})*F_{ij}[t_{ab}]+(t^{ij}+f^{ji})*F_{ij}[f_{ij}]

Collect with respect to two variables:

def t = 'A_a * B^b + A^b * B_a + A_a * C^b + A^b * D_a'.t

println Collect['A_m', 'B_m'] >> t

> A_c*B^d*(d_a^c*d^b_d+g_ad*g^bc)+(C^b*d_a^c+g^bc*D_a)*A_c

By default Collect will expand all expressions:

1 2	`def` `t` `=` `'(a+b)*2 A_a * B^b + A^b * B_a'.t` `println` `Collect['B_m']` `>>` `t`

> B_{c}*((b**2+a**2+2*b*a)*A_{a}*g^{bc}+A^{b}*d_{a}^{c})

To prevent this overhead one can use:

3	`println` `Collect['B_m', [ExpandSymbolic:` `false]]` `>>` `t`

> B_{c}*((a+b)**2*A_{a}*g^{bc}+A^{b}*d_{a}^{c})