We have implemented two different types of scaling, following [15, Chapter 5,]. By equation scaling, each polynomial is divided by a constant. In the second type of scaling, so-called variable scaling, we scale each variable by a constant. This tool combines both to scale a polynomial system. Afterward it can be used to de-scale the computed solutions back into the original coordinates.
To compute the factors to scale the variables, a minimization problem has to be solved. The program returns the estimate for the inverse condition number of the linear system that determines the factors. This estimate measures how extreme the values of the original coefficients are. Scaling helps to bring the extreme values to a more acceptable range. However, as pre-processing facility, it cannot handle clusters of solutions effectively, because such transformations require information on the distribution of the solutions.
Related to the issue of scaling, we could also center the unknowns to lie inside a box of meaningful bounds for the expected solutions. The current version of PHC does not provide centering. The package has also no facilities to deal with multi-precision arithmetic, so it could very well be that a lot of precision is lost by transforming from one coordinate system into the other.