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How to use sign[] for symbolic operations?

I use Mathematica 3.0. My question is how to solve the following
I define a < 0 and b < 0 (to intend that the sign is negative in both
cases). Now I like to
know the sign of the produkt of a*b, it should be positive by the hand.
But how can I express it
within mathematica 3.0? In general: how can I get the sign of an
expression in symbolic form?
In  1: Sign[a*b] ?
Out 1: > 0 or positive.

Many thanks for your help.

Lothar Dillinger

EMail: doellinger at

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