[PPL-devel] How about normalizing the opposite way?

Elisa Ricci wrote:

    In function Row::normalize() if we normalize an equality or a line, we decide
    that the first element of the corresponding row is positive.

While this change is good for a number of reasons (cheap removal of repeated constraints/generators being the most important one), it has a problem with respect to the most natural output procedure we and the user tend to write. For instance, we now get things like

-X = -1

instead of the more natural

X = 1

While this could be easily fixed in the output procedures, it is also true that normalizing one way or the other has little cost for us. So why don't we normalize so that the first non-null coefficient of lines and equalities is _negative_?

    In function Matrix::back_substitute(), if we call linear_combine with an
    equality and an inequality, we must change the coefficients of the equality so
    that the coefficient of the inequality in the linear combination is
    non-negative.

I am confused here. What does that mean? Is this necessary due to the new normalization? Would this be solved by adopting the specular normalization I am suggesting?

Roberto