# Revision history [back]

You should use

sage: d[2][R] = 1


Indeed, when R is the list [eU, 0, 1], as in your example, the above is equivalent to

sage: d[2][eU, 0, 1] = 1


Side note: in your example, the line

sage: d = {(i): var("d_{}".format(i)) for i in range(2*p*q)}


is useless, because the elements of the dictionary d are redefined in the two lines that follow:

sage: for i in range(2*p*q):
sage:     d[i] = M.diff_form(i)


If you want to give names to the differential forms d[i], you could write simply

sage: d = {i: M.diff_form(i, name="d_{}".format(i)) for i in range(2*p*q)}


Then

sage: d[2]
2-form d_2 on the 4-dimensional complex manifold M
sage: R = [eU, 0, 1]
sage: d[2][R] = 1
sage: d[2].display()
d_2 = dx_0/\dx_1


You should usewrite

sage: d[2][R] = 1


Indeed, when R is the list [eU, 0, 1], as in your example, the above is equivalent to

sage: d[2][eU, 0, 1] = 1


Side note: in your example, the line

sage: d = {(i): var("d_{}".format(i)) for i in range(2*p*q)}


is useless, because the elements of the dictionary d are redefined in the two lines that follow:

sage: for i in range(2*p*q):
sage:     d[i] = M.diff_form(i)


If you want to give names to the differential forms d[i], you could write simply

sage: d = {i: M.diff_form(i, name="d_{}".format(i)) for i in range(2*p*q)}


Then

sage: d[2]
2-form d_2 on the 4-dimensional complex manifold M
sage: R = [eU, 0, 1]
sage: d[2][R] = 1
sage: d[2].display()
d_2 = dx_0/\dx_1


You should write

sage: d[2][R] = 1


Indeed, when R is the list [eU, 0, 1], as in your example, the above is equivalent to

sage: d[2][eU, 0, 1] = 1


Side note: in your example, the line

sage: d = {(i): var("d_{}".format(i)) for i in range(2*p*q)}


is useless, because the elements of the dictionary d are fully redefined in the two lines that follow:

sage: for i in range(2*p*q):
sage:     d[i] = M.diff_form(i)


If you want to give names to the differential forms d[i], you could write simply

sage: d = {i: M.diff_form(i, name="d_{}".format(i)) for i in range(2*p*q)}


Then

sage: d[2]
2-form d_2 on the 4-dimensional complex manifold M
sage: R = [eU, 0, 1]
sage: d[2][R] = 1
sage: d[2].display()
d_2 = dx_0/\dx_1