I am looking for a way of expressing something like:
$\sum{a_k} \sum{b_k}, \, a_k \in \mathbb{R}, \, b_k \in \mathbb{R} \tag{1}$
with the caveat that I would like the result to be negative in the case in which $\sum{a_k} < 0$ and $\sum{b_k} < 0$ .
In summary, I would like a function/operator that behaves like multiplication sans the case where - * - = + but rather when both are negative then I expect a negative answer.
I can see a way of doing this with binary numbers represented in sign-magnitude, by doing the usual multiplication of the magnitude bits and the NAND of the sign bits. However, I am failing in finding a way of extending this to decimal numbers.
Is there some way I could add something to $(1)$ so it behaves like this?