Comment #7 on issue 1878 by asmeurer: For non-commutative symbols all
comparisons evaluate to False
http://code.google.com/p/sympy/issues/detail?id=1878
But once you say a > b, that implies that a - b > 0, or in other words, a -
b is "positive", at least in the sence
that it is in a positive subring. In that case, elements of the inverse
subring are usually called negative. See
http://en.wikipedia.org/wiki/Partially-ordered_ring.
So I guess it depends on what is meant by .is_negative. If that assumption
implies is_real, then of course we
don't want it here. But I think assuming negativity is key for
inequalities, so maybe it should be separate
somehow.
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