%display latex

R7 = Manifold(7, 'R^7', r'\mathbb{R}^7', start_index=1);
cart.<x_1,x_2,x_3,x_4,x_5,x_6,x_7> = R7.chart() ; cart

$$\newcommand{\Bold}[1]{\mathbf{#1}}\left(\mathbb{R}^7,(x_{1}, x_{2}, x_{3}, x_{4}, x_{5}, x_{6}, x_{7})\right)$$

phi1=R7.diff_form(3,name='phi1',latex_name='\phi_1');
phi1[1,2,3],phi1[1,4,5],phi1[1,6,7],phi1[2,4,6],phi1[2,5,7],phi1[3,4,7],phi1[3,5,6]=1,1,1,1,-1,-1,-1;
phi1.display()

$$\newcommand{\Bold}[1]{\mathbf{#1}}\phi_1 = \mathrm{d} x_{1}\wedge \mathrm{d} x_{2}\wedge \mathrm{d} x_{3}+\mathrm{d} x_{1}\wedge \mathrm{d} x_{4}\wedge \mathrm{d} x_{5}+\mathrm{d} x_{1}\wedge \mathrm{d} x_{6}\wedge \mathrm{d} x_{7}+\mathrm{d} x_{2}\wedge \mathrm{d} x_{4}\wedge \mathrm{d} x_{6}-\mathrm{d} x_{2}\wedge \mathrm{d} x_{5}\wedge \mathrm{d} x_{7}-\mathrm{d} x_{3}\wedge \mathrm{d} x_{4}\wedge \mathrm{d} x_{7}-\mathrm{d} x_{3}\wedge \mathrm{d} x_{5}\wedge \mathrm{d} x_{6}$$

var('a1,a2,a3,a4,a5,a6,a7');
va = R7.tensor_field(1,0,name='va',latex_name='v_a');
va[1],va[2],va[3],va[4],va[5],va[6],va[7]=a1,a2,a3,a4,a5,a6,a7;

form=phi1
vec=va
res=form['_ijk']*vec['^i']
res_coef=[]
for ind in res.comp().non_redundant_index_generator():
    if res[ind]!=0:
        res_coef.append(res[ind].expr()**2)

res_coef

$$\newcommand{\Bold}[1]{\mathbf{#1}}\left[a_{3}^{2}, a_{2}^{2}, a_{5}^{2}, a_{4}^{2}, a_{7}^{2}, a_{6}^{2}, a_{1}^{2}, a_{6}^{2}, a_{7}^{2}, a_{4}^{2}, a_{5}^{2}, a_{7}^{2}, a_{6}^{2}, a_{5}^{2}, a_{4}^{2}, a_{1}^{2}, a_{2}^{2}, a_{3}^{2}, a_{3}^{2}, a_{2}^{2}, a_{1}^{2}\right]$$

set(res_coef)

$$\newcommand{\Bold}[1]{\mathbf{#1}}\verb|set([a4^2,|\phantom{\verb!x!}\verb|a6^2,|\phantom{\verb!x!}\verb|a2^2,|\phantom{\verb!x!}\verb|a5^2,|\phantom{\verb!x!}\verb|a7^2,|\phantom{\verb!x!}\verb|a1^2,|\phantom{\verb!x!}\verb|a3^2])|$$

uniq(res_coef)

$$\newcommand{\Bold}[1]{\mathbf{#1}}\left[a_{4}^{2}, a_{6}^{2}, a_{2}^{2}, a_{5}^{2}, a_{7}^{2}, a_{1}^{2}, a_{3}^{2}\right]$$

v=[a1,a2,a1]

w=[i**2 for i in v]

w

$$\newcommand{\Bold}[1]{\mathbf{#1}}\left[a_{1}^{2}, a_{2}^{2}, a_{1}^{2}\right]$$

uniq(w)

$$\newcommand{\Bold}[1]{\mathbf{#1}}\left[a_{1}^{2}, a_{2}^{2}\right]$$

list(set(w))

$$\newcommand{\Bold}[1]{\mathbf{#1}}\left[a_{1}^{2}, a_{2}^{2}\right]$$