# Symbolic accumulation

With Maple I can write

```
seq(add(a[i], i=0..n), n=0..3);
```

and get

```
a[0], a[0]+a[1], a[0]+a[1]+a[2], a[0]+a[1]+a[2]+a[3] (*)
```

If I write in Sage

```
for n in range(4):
add(a[i] for i in range(n))
```

I get the NameError: global name 'a' is not defined. If I first introduce the variable by a = var('a') then I get the TypeError: 'sage.symbolic.expression.Expression' object does not support indexing.

How can I get the line (*) with Sage?

Edit: This works:

```
f=function('f')
[add(f(i) for i in (0..n)) for n in (0..3)]
```

gives

```
[f(0), f(1) + f(0), f(2) + f(1) + f(0), f(3) + f(2) + f(1) + f(0)]
```

So what I want is an equivalent for lists.

```
a=list('a')
[add(a[i] for i in (0..n)) for n in (0..3)]
```

Is http://ask.sagemath.org/question/363/a-list-of-symbolic-variables helpful? This is unfortunately not implemented in the same way, see http://trac.sagemath.org/ticket/11576

Hmm, now I'm more confused about what you want. Lists are Python objects and of course the brackets are slicing.