We have to respect a strict processing order when applying homotopy continuation. Therefore, an interactive program with (hopefully) self-explanatory menus guides the user in the solving process. This menu-driven approach also enables some kind of batch processing. Enumerating all isolated solutions can easily lead to a computationally lengthy job (ranging from one hour, a night, several days...). So after we have chosen the algorithms from the menus, the program can run quietly in the background, writing the results to a file.
There are three modes to run the program. The first one is the full mode, where we pass through all the different stages. If we want to deal with only one specific stage of the solving procedure, we can invoke the program via the tool mode. The third mode is the black-box/batch processing mode. We will next give a more elaborate description of the last two modes.
Often only a part of the solver is needed. For example, first we want to focus on estimating the number of roots to get an idea about the complexity of the problem before attempting to solve it. So, in this first stage, we want to try several root counting methods before starting the continuation. Once an efficient homotopy is constructed, there is no need to go through all the menus of the root counting methods and the corresponding homotopy constructors. Therefore, the different components in the stages of the solver can be invoked separately. The hierarchy of the interactive drivers is displayed in Figure 4.
Figure 4: Schematic overview of the tools offered by the package PHC.
The program PHC is the main interactive driver and gives access to the tools. The two most important ones are RoCo (Root Counting) and PoCo (Polynomial Continuation). They are activated by calling PHC with the options `-r', for doing root counting only, and `-p', for polynomial continuation if we have already a homotopy at our disposal. The program MVC is a subdriver of RoCo and can be invoked directly by calling PHC with the option `-m'. Table 1 summarizes the options.
Table 1: Overview of tools, acronyms and options of PHC.
The third mode to invoke the program is the black-box/batch processing mode, by calling phc with the option `-b'. This mode avoids the usage of menus and applies the methods either with the values of the parameters provided in the input file, or otherwise with the default settings of the parameters. Small examples (to get a quick and dirty run) can be treated just by typing
phc -b test.in test.out
with test.in as input file containing the polynomial system and where test.out is the log file to put all results. Alternatively, this mode can be used if we want to redo the computations, with small modifications of the specific settings of the parameters we have made. These settings of the parameters have to be provided as part of the input file, according to the format of the log file.
The tools produce several intermediate results, such as a mixed subdivision, a start system and solution sets. These permanent objects are stored as files, so that they survive after the program has ended. The careful design of file formats enables different programs to communicate.