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5. Running the program in toolbox mode

To avoid the preconditioning stage (scaling and reduction) we can compute root counts and construct start systems via the option -r, thus calling the progam as phc -r. One important submenu is the mixed-volume computation, invoked via phc -m.

Once we created an appropriate start system, we can call the path trackers via the option -p. Calling the program as phc -p is useful if we have to solve a slightly modified problem. For instance, suppose we change the coefficients of the system in multilin, then we can still use multilin_start to solve the system with modified coefficients, using the -p option. In this way we use a cheater's homotopy, performing a kind of coefficient-parameter polynomial continuation.



Jan Verschelde
2002-05-23