1
$\begingroup$

I know that I can wrote something like $a_1 + \cdots + a_n$ without the dots as $\sum_{i=1}^n a_i$ which seems clearer to me. As a programmer, I'd rather have a rule set with variables than something with dots where I have to extract the pattern from.

Is there some notation to do this for the parameters of a function? Say a Lagrangian like so: $L\left(q_1, \ldots, q_n, \dot q_1, \ldots, \dot q_n, t\right)$

The thought in the back of my head is the following. In Python, I could have a function like so:

f(x, y, z) 

When I call that function, I could either to f(1, 2, 3) or I could do the following:

parameters = [1, 2, 3] f(*parameters) 

Where I basically “dump” that list of parameters into the parenteses of the function. Is there some math notation for the same thing?

  • 0
    I think it's worth noting that even with $\sum_{i=1}^n$, there is a standard interpretation that is not really any more explicit than $a_1+\cdots+a_n$.2012-10-13

3 Answers 3

5

I don't know if that's what you're looking for, but we do that last thing in $\mathbb R^n$ usually ; the vectors in $\mathbb R^n$ are defined as vectors of the form $ (x_1, \dots, x_n), \qquad x_i \in \mathbb R $ but if we write $x = (x_1, \dots, x_n)$, when defining a function $f : \mathbb R^n \to \mathbb R$ for instance, we can just write $f(x)$ instead of $f(x_1, \dots,x_n)$. Is that what you were looking for?

For your Lagrangian for instance, you could define $q = (q_1, \dots, q_n)$, $\dot q = (\dot q_1, \dots, \dot q_n)$, and write $ L(q,\dot q, t) $ instead of $ L(q_1, \dots, q_n, \dot q_1, \dots, \dot q_n, t). $

Hope that helps,

  • 0
    @queueoverflow : When one does measure theory he also often writes $\int_X f$. So yeah, arrows for children. Did I answer your question?2012-10-13
0

According to one professor of mine, $\underline{x} = x_1, \dots , x_n$.

  • 0
    One professor of mine used the underscore for matrices.2012-10-14
0

You can write $\{x_i\}_{i\leq n}$ instead of $\{x_1, \dots, x_n\}$.

  • 0
    $n$-tuples $\neq$ sets. The order of the elements matters in $n$-tuples.2014-11-20