Jupyter notebook Ask+sage.ipynb
%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
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()
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
set(res_coef)
uniq(res_coef)
v=[a1,a2,a1]
w=[i**2 for i in v]
w
uniq(w)
list(set(w))