Since we have to respect a strict processing order and we may expect computationally lengthy jobs, PHC is organized as a menu-driven and file-oriented program.
The simplest way to solve systems by PHC is to type
phc -b input outputwhen input is the name of the input file that contains the system. This mode is the so-called black-box mode and requires no other input than the polynomial system. Results can be found in the file output. One particular choice for a black-box solver is outlined in section nine.
The second mode is the full mode where PHC runs through all stages of the solver and asks the user to confirm the default settings while giving the opportunity to modify the settings interactively. This mode is invoked by default, just by typing phc after the prompt.
Some stages may be skipped, whereas more than one root-counting method can be invoked before the construction of a homotopy. Therefore, the tool mode has been created, see Figure 5. Another advantage of working with tools is that intermediate results, such as a mixed subdivision and a random coefficient start system, can be valuable stepping stones in the resolution of a large and difficult system.
Table 1 gives an overview of the tools and the options of PHC to invoke them.
|stage||acronym||description of the tool||option|
|1||scal||coefficient scaling||phc -s|
|redu||reduction of degrees||phc -d|
|2||roco||root counts and start systems||phc -r|
|mvc||mixed-volume computation||phc -m|
|3||poco||polynomial continuation||phc -p|
|4||vali||validation of results||phc -v|
|x||enum||enumerative geometry||phc -e|