# retrieving word for free group with custom set of generators

I would like to define a free group on a custom ordered list of symbols, like say

```
Frgp=Groups().free([f'a{j}' for j in range (5,10)])
```

i.e. `a5`

up to `a9`

(say). It's important that the list be defined programmatically as above, as the number of generators changes throughout the program run (their labels also need to change).

I would then like to recover elements of the group by evaluating at numbered lists, as in `Frgp([1,2])`

to get back `a5*a6`

, say, as suggested in the docs. This syntax of `Frgp(<numerical list>)`

, however, only works when I define the group via one of the methods

```
Frgp.<x,y,z> = Groups().free()
```

or

```
Frgp=Groups().free(3,'t')
```

which are not flexible enough to allow me to interpolate strings in variable names (or are they? I have tried all sorts of `eval`

/`exec`

trickery to no avail).

If I define the group in my preferred style (first code display above), then

```
sage: Frgp=Groups().free([f'a{j}' for j in range (5,10)])
sage: Frgp([1,2])
```

results in an error:

```
TypeError: 'sage.rings.integer.Integer' object is not iterable
```

**Edit:**

To clarify, I am aware that the goal I alluded to above can be achieved by other means. For instance, I can do

```
sage: Frgp=Groups().free(5,'t')
sage: Frgp([1,2])([var(f'a{j}') for j in range (5,10)])
a5*a6
```

So in other words, I can create a list of symbolic variables and apply a free-group word to that. But this seems like a clumsy workaround. It would be preferable to work in the free group on the desired set of symbolic variables to begin with.