Software which writes long math expressions in short form by detecting the patterns?

Question

Is there any software which can detects the patterns in long math expression and collects them as sums and products in short form. I am working with some long expressions of the following forms. I have longer expressions than this. I was wondering if I can shorten them in some programme to save time.

$$\left(-a_0 a_1 a_2-a_0 a_1 a_3-a_0 a_2 a_3-a_1 a_2 a_3-a_0 a_1 a_4-a_0 a_2 a_4-a_1 a_2 a_4-a_0 a_3 a_4-a_1 a_3 a_4-a_2 a_3 a_4-a_0 a_1 a_5-a_0 a_2 a_5-a_1 a_2 a_5-a_0 a_3 a_5-a_1 a_3 a_5-a_2 a_3 a_5-a_0 a_4 a_5-a_1 a_4 a_5-a_2 a_4 a_5-a_3 a_4 a_5-a_0 a_1 a_6-a_0 a_2 a_6-a_1 a_2 a_6-a_0 a_3 a_6-a_1 a_3 a_6-a_2 a_3 a_6-a_0 a_4 a_6-a_1 a_4 a_6-a_2 a_4 a_6-a_3 a_4 a_6-a_0 a_5 a_6-a_1 a_5 a_6-a_2 a_5 a_6-a_3 a_5 a_6-a_4 a_5 a_6-a_0 a_1 a_7-a_0 a_2 a_7-a_1 a_2 a_7-a_0 a_3 a_7-a_1 a_3 a_7-a_2 a_3 a_7-a_0 a_4 a_7-a_1 a_4 a_7-a_2 a_4 a_7-a_3 a_4 a_7-a_0 a_5 a_7-a_1 a_5 a_7-a_2 a_5 a_7-a_3 a_5 a_7-a_4 a_5 a_7-a_0 a_6 a_7-a_1 a_6 a_7-a_2 a_6 a_7-a_3 a_6 a_7-a_4 a_6 a_7-a_5 a_6 a_7-a_0 a_1 a_8-a_0 a_2 a_8-a_1 a_2 a_8-a_0 a_3 a_8-a_1 a_3 a_8-a_2 a_3 a_8-a_0 a_4 a_8-a_1 a_4 a_8-a_2 a_4 a_8-a_3 a_4 a_8-a_0 a_5 a_8-a_1 a_5 a_8-a_2 a_5 a_8-a_3 a_5 a_8-a_4 a_5 a_8-a_0 a_6 a_8-a_1 a_6 a_8-a_2 a_6 a_8-a_3 a_6 a_8-a_4 a_6 a_8-a_5 a_6 a_8-a_0 a_7 a_8-a_1 a_7 a_8-a_2 a_7 a_8-a_3 a_7 a_8-a_4 a_7 a_8-a_5 a_7 a_8-a_6 a_7 a_8-a_0 a_1 a_9-a_0 a_2 a_9-a_1 a_2 a_9-a_0 a_3 a_9-a_1 a_3 a_9-a_2 a_3 a_9-a_0 a_4 a_9-a_1 a_4 a_9-a_2 a_4 a_9-a_3 a_4 a_9-a_0 a_5 a_9-a_1 a_5 a_9-a_2 a_5 a_9-a_3 a_5 a_9-a_4 a_5 a_9-a_0 a_6 a_9-a_1 a_6 a_9-a_2 a_6 a_9-a_3 a_6 a_9-a_4 a_6 a_9-a_5 a_6 a_9-a_0 a_7 a_9-a_1 a_7 a_9-a_2 a_7 a_9-a_3 a_7 a_9-a_4 a_7 a_9-a_5 a_7 a_9-a_6 a_7 a_9-a_0 a_8 a_9-a_1 a_8 a_9-a_2 a_8 a_9-a_3 a_8 a_9-a_4 a_8 a_9-a_5 a_8 a_9-a_6 a_8 a_9-a_7 a_8 a_9\right)$$

EDIT: $$\left(a_0 a_1 a_2 a_3+a_0 a_1 a_2 a_4+a_0 a_1 a_3 a_4+a_0 a_2 a_3 a_4+a_1 a_2 a_3 a_4+a_0 a_1 a_2 a_5+a_0 a_1 a_3 a_5+a_0 a_2 a_3 a_5+a_1 a_2 a_3 a_5+a_0 a_1 a_4 a_5+a_0 a_2 a_4 a_5+a_1 a_2 a_4 a_5+a_0 a_3 a_4 a_5+a_1 a_3 a_4 a_5+a_2 a_3 a_4 a_5+a_0 a_1 a_2 a_6+a_0 a_1 a_3 a_6+a_0 a_2 a_3 a_6+a_1 a_2 a_3 a_6+a_0 a_1 a_4 a_6+a_0 a_2 a_4 a_6+a_1 a_2 a_4 a_6+a_0 a_3 a_4 a_6+a_1 a_3 a_4 a_6+a_2 a_3 a_4 a_6+a_0 a_1 a_5 a_6+a_0 a_2 a_5 a_6+a_1 a_2 a_5 a_6+a_0 a_3 a_5 a_6+a_1 a_3 a_5 a_6+a_2 a_3 a_5 a_6+a_0 a_4 a_5 a_6+a_1 a_4 a_5 a_6+a_2 a_4 a_5 a_6+a_3 a_4 a_5 a_6+a_0 a_1 a_2 a_7+a_0 a_1 a_3 a_7+a_0 a_2 a_3 a_7+a_1 a_2 a_3 a_7+a_0 a_1 a_4 a_7+a_0 a_2 a_4 a_7+a_1 a_2 a_4 a_7+a_0 a_3 a_4 a_7+a_1 a_3 a_4 a_7+a_2 a_3 a_4 a_7+a_0 a_1 a_5 a_7+a_0 a_2 a_5 a_7+a_1 a_2 a_5 a_7+a_0 a_3 a_5 a_7+a_1 a_3 a_5 a_7+a_2 a_3 a_5 a_7+a_0 a_4 a_5 a_7+a_1 a_4 a_5 a_7+a_2 a_4 a_5 a_7+a_3 a_4 a_5 a_7+a_0 a_1 a_6 a_7+a_0 a_2 a_6 a_7+a_1 a_2 a_6 a_7+a_0 a_3 a_6 a_7+a_1 a_3 a_6 a_7+a_2 a_3 a_6 a_7+a_0 a_4 a_6 a_7+a_1 a_4 a_6 a_7+a_2 a_4 a_6 a_7+a_3 a_4 a_6 a_7+a_0 a_5 a_6 a_7+a_1 a_5 a_6 a_7+a_2 a_5 a_6 a_7+a_3 a_5 a_6 a_7+a_4 a_5 a_6 a_7+a_0 a_1 a_2 a_8+a_0 a_1 a_3 a_8+a_0 a_2 a_3 a_8+a_1 a_2 a_3 a_8+a_0 a_1 a_4 a_8+a_0 a_2 a_4 a_8+a_1 a_2 a_4 a_8+a_0 a_3 a_4 a_8+a_1 a_3 a_4 a_8+a_2 a_3 a_4 a_8+a_0 a_1 a_5 a_8+a_0 a_2 a_5 a_8+a_1 a_2 a_5 a_8+a_0 a_3 a_5 a_8+a_1 a_3 a_5 a_8+a_2 a_3 a_5 a_8+a_0 a_4 a_5 a_8+a_1 a_4 a_5 a_8+a_2 a_4 a_5 a_8+a_3 a_4 a_5 a_8+a_0 a_1 a_6 a_8+a_0 a_2 a_6 a_8+a_1 a_2 a_6 a_8+a_0 a_3 a_6 a_8+a_1 a_3 a_6 a_8+a_2 a_3 a_6 a_8+a_0 a_4 a_6 a_8+a_1 a_4 a_6 a_8+a_2 a_4 a_6 a_8+a_3 a_4 a_6 a_8+a_0 a_5 a_6 a_8+a_1 a_5 a_6 a_8+a_2 a_5 a_6 a_8+a_3 a_5 a_6 a_8+a_4 a_5 a_6 a_8+a_0 a_1 a_7 a_8+a_0 a_2 a_7 a_8+a_1 a_2 a_7 a_8+a_0 a_3 a_7 a_8+a_1 a_3 a_7 a_8+a_2 a_3 a_7 a_8+a_0 a_4 a_7 a_8+a_1 a_4 a_7 a_8+a_2 a_4 a_7 a_8+a_3 a_4 a_7 a_8+a_0 a_5 a_7 a_8+a_1 a_5 a_7 a_8+a_2 a_5 a_7 a_8+a_3 a_5 a_7 a_8+a_4 a_5 a_7 a_8+a_0 a_6 a_7 a_8+a_1 a_6 a_7 a_8+a_2 a_6 a_7 a_8+a_3 a_6 a_7 a_8+a_4 a_6 a_7 a_8+a_5 a_6 a_7 a_8+a_0 a_1 a_2 a_9+a_0 a_1 a_3 a_9+a_0 a_2 a_3 a_9+a_1 a_2 a_3 a_9+a_0 a_1 a_4 a_9+a_0 a_2 a_4 a_9+a_1 a_2 a_4 a_9+a_0 a_3 a_4 a_9+a_1 a_3 a_4 a_9+a_2 a_3 a_4 a_9+a_0 a_1 a_5 a_9+a_0 a_2 a_5 a_9+a_1 a_2 a_5 a_9+a_0 a_3 a_5 a_9+a_1 a_3 a_5 a_9+a_2 a_3 a_5 a_9+a_0 a_4 a_5 a_9+a_1 a_4 a_5 a_9+a_2 a_4 a_5 a_9+a_3 a_4 a_5 a_9+a_0 a_1 a_6 a_9+a_0 a_2 a_6 a_9+a_1 a_2 a_6 a_9+a_0 a_3 a_6 a_9+a_1 a_3 a_6 a_9+a_2 a_3 a_6 a_9+a_0 a_4 a_6 a_9+a_1 a_4 a_6 a_9+a_2 a_4 a_6 a_9+a_3 a_4 a_6 a_9+a_0 a_5 a_6 a_9+a_1 a_5 a_6 a_9+a_2 a_5 a_6 a_9+a_3 a_5 a_6 a_9+a_4 a_5 a_6 a_9+a_0 a_1 a_7 a_9+a_0 a_2 a_7 a_9+a_1 a_2 a_7 a_9+a_0 a_3 a_7 a_9+a_1 a_3 a_7 a_9+a_2 a_3 a_7 a_9+a_0 a_4 a_7 a_9+a_1 a_4 a_7 a_9+a_2 a_4 a_7 a_9+a_3 a_4 a_7 a_9+a_0 a_5 a_7 a_9+a_1 a_5 a_7 a_9+a_2 a_5 a_7 a_9+a_3 a_5 a_7 a_9+a_4 a_5 a_7 a_9+a_0 a_6 a_7 a_9+a_1 a_6 a_7 a_9+a_2 a_6 a_7 a_9+a_3 a_6 a_7 a_9+a_4 a_6 a_7 a_9+a_5 a_6 a_7 a_9+a_0 a_1 a_8 a_9+a_0 a_2 a_8 a_9+a_1 a_2 a_8 a_9+a_0 a_3 a_8 a_9+a_1 a_3 a_8 a_9+a_2 a_3 a_8 a_9+a_0 a_4 a_8 a_9+a_1 a_4 a_8 a_9+a_2 a_4 a_8 a_9+a_3 a_4 a_8 a_9+a_0 a_5 a_8 a_9+a_1 a_5 a_8 a_9+a_2 a_5 a_8 a_9+a_3 a_5 a_8 a_9+a_4 a_5 a_8 a_9+a_0 a_6 a_8 a_9+a_1 a_6 a_8 a_9+a_2 a_6 a_8 a_9+a_3 a_6 a_8 a_9+a_4 a_6 a_8 a_9+a_5 a_6 a_8 a_9+a_0 a_7 a_8 a_9+a_1 a_7 a_8 a_9+a_2 a_7 a_8 a_9+a_3 a_7 a_8 a_9+a_4 a_7 a_8 a_9+a_5 a_7 a_8 a_9+a_6 a_7 a_8 a_9\right)$$

Answer 1

I don't think this is a problem software can presently solve. Incidentally, your expression is $\binom{10}{3}=120$ terms, $-\sum_{ijk}a_ia_ja_k$ with the sum over size-$3$ sets $\{i,\,j,\,k\}\subseteq\{0,\,\cdots,\,9\}$.