10

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So, I'm working on a project where the number of independent variables is not fixed.

Consider a problem of $N$ independent variables, $\boldsymbol{r}$.

I want to perform different things with them. Amongst them, I want to consider (multidimensional) integration, etc.

## Variables definition

My first question regarding this topic, is the definition of the variables to perform algebraic manipulation. My first though was to use

```
variables[N_]:=Table[x[i],{i,1,N}]
```

However, in some situations, (e.g. with Block), I cannot use these variables as I use x1,x2,.... e.g.

```
Block[{x[1]=2},x[1]^2]
```

gives an error.

(my current naive solution is to use):

```
variables[N_] := Table[ToExpression["x" <> ToString[i]], {i, 1, N}];
```

Is there any more standard solution?

### Sums, integrals

This question also holds for the problem of computing integrals for arbitrary dimensions.

How can I tell *Mathematica* to compute

```
Integrate[f[{r1,r2,...,rn}], {r1, 0, 1}, {r2, 0, g[r1]},...,{rN, 0, h[{r1,r2,...,"rN-1"}]}]
```

Most of the times I will be interested in numerically compute the integral, but nevertheless, how do I tell *Mathematica*? I tried the simple "naive"

```
Integrate[1, Table[{i, 0, 1}, {i, variables[3]}]]
```

but it gives an error.

2Try

`Integrate[1, Sequence @@ Table[{i, 0, 1}, {i, variables[3]}]]`

. – b.gates.you.know.what – 2013-02-25T10:53:13.7431You can use something like

`Table[Unique["x"], {5}]`

to create variables. – Silvia – 2013-02-25T11:06:50.933You might find some useful ideas in this previous question and its answers. Also, in this one.

– m_goldberg – 2013-02-25T11:57:11.513Thank you all for the suggestions. @b.gatessucks: The Sequence works for Integrals, but not for sums. – Jorge Leitao – 2013-02-25T18:08:08.553

@J.C.Leitão: dump: because it has an holdall attribute – Jorge Leitao – 2013-02-25T18:09:48.693