In English, we can move some of the words around in the clause 'My computer is there' changing it to 'There is my computer' to alter the focus.
In Hungarian, it looks like 'Ott van a számítógépem' translates to 'my computer is there'. If I said something like 'A számítógépem ott van', would that be a loose translation of 'there is my computer'? Or am I completely off base here?
Both of your Hungarian sentences could work for either English ones. The focus in Hungarian is the spot preceding the verb, but in this case putting van after ott is also the most natural order.
I think the creators want to avoid saying there is/are in English when it doesn't refer to existence.
- Ott van egy kutya.
- A dog is there.
- Ein Hund ist da. (I see you're learning German, so it might help here.)
- Van egy kutya.
- There is a dog.
- Es gibt einen Hund.
"van after ott is also the most natural word order"
Isn't this because ott-ahol form some sort of important pair, so it is natural/important to put it, the place, in the focus right away?