1 | initial version |

`diff`

only works on symbolic expression (elements of the symbolic ring `SR`

), not on python objects like functions. But you are in luck because `f(*v)`

is precisely an element of `SR`

. So the correct syntax is `f(*v).diff(v[i])`

.

As a side remark, `f`

can be simplified a lot, by defining `f = (M*vector(v)).norm()`

. In this case, `f`

is a symbolic expression.

Here is a code that computes all the partial derivatives for some matrix M:

```
n = 3
v = list(var('v_%d' % i) for i in range(1, n+1))
M = Matrix([[1, 0, 0],
[0, 1, 0],
[0, 0, 1]])
f = (M*vector(v)).norm()
[diff(f, vi) for vi in v]
```

The output is:

```
[1/2*(v_1 + conjugate(v_1))/sqrt(abs(v_1)^2 + abs(v_2)^2 + abs(v_3)^2),
1/2*(v_2 + conjugate(v_2))/sqrt(abs(v_1)^2 + abs(v_2)^2 + abs(v_3)^2),
1/2*(v_3 + conjugate(v_3))/sqrt(abs(v_1)^2 + abs(v_2)^2 + abs(v_3)^2)]
```

Of course you can take the dot product of this list with any tangent vector.

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