# Question about sum and diff

Why this code :

```
f(x)=sum(diff(sin(x),x,n),n,1,10)
f(x)
```

does not work?

Question about sum and diff

Why this code :

```
f(x)=sum(diff(sin(x),x,n),n,1,10)
f(x)
```

does not work?

add a comment

1

When you write `sum(diff(sin(x),x,n),n,1,10)`

, you try to do a symbolic sum, hence the Python name `n`

should be defined as a symbolic variable (an element of the `Symbolic Ring`

). However, in Sage, the name `n`

corresponds to the function that makes numerical_approx:

```
sage: n
<function numerical_approx at 0xb3f63684>
sage: n(pi)
3.14159265358979
```

This explains why you got the error `TypeError: no canonical coercion from <type 'function'> to Symbolic Ring`

, this is because Sage try (without success) to transform the `numerical_approx`

function into an element of the `Symbolic Ring`

.

So you may try to overwrite the name `n`

to correspond to the symbolic variable `"n"`

:

```
sage: n = SR.var('n')
sage: sum(diff(sin(x),x,n),n,1,10)
0
```

But then the result is unexpected ! The problem is that now, when you write `diff(sin(x),x,n)`

, Sage does not understands "differentiate n times relative to x", but "differentiate relative to x and then to n", so you get `0`

since a function of `x`

has a zero derivative relative to `n`

.

For Sage to understand "differentiate n times relative to x", `n`

needs to be an integer, not a symbol. So, instead you can do a non-symbolic sum of a list that contains all derivatives:

```
sage: f(x) = sum([diff(sin(x),x,n) for n in range(1,11)])
sage: f(x)
cos(x) - sin(x)
```

Which seems correct.

Asked: **
2015-02-06 11:57:46 -0500
**

Seen: **388 times**

Last updated: **Feb 06 '15**

How to stop Sage from finding erroneous complex roots?

Bug in computing sum (of binomials)

Generic Symbolic function as input in actual funciton

Noob question about lists in sum()

Taylor expansion twice for a general function cause problem?

derivative of multivariate equation with nested sum

Variable Not Found while Plotting Finite Sum

Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.