Output

The output is rather long and depends on the mode you run phc. So here we will only explain the basics that will help you understand what you read. For a quick start read the two remarks at the end of this section.

Initial system:
In the first lines of the output file you will find your initial system of polynomial equations.

Root counting:
The following paragraphs describe the performed root counting. Of course this depends on which methods you chose for that. The description of the root counting is quite complete. E.g. if you compute the mixed volume you will find the lifting vectors used and all mixed cells etc.. Note that if the program runs into problems and has to perform some operation twice or more you will find the results of evry approach and not just the successful one in the output file. After that you find some timing information of the root counting.

Start system:
If you perfom polynomial continuation you will find all the information concerning the start system in the following paragraphs. (This information is usually stored in a separate file as well so you can use it for further computations.) The solutions of the start system are written in the same format as the solutions to your initial system which can be found later in the output-file. DON'T CONFUSE these two sets of solutions. Again you find the information about the time it took to compute the start system.

Parameters for continuation:
After that you find a list of the parameters used to perform the continuation. This will only be of interest to you if something went wrong and you want to find out why.

Solutions:
Now finally you are given a complete list of all isolated solutions to the initial system. All solutions are written in the following format:

solution : 4  :         start residual :  1.921E-14
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
x :  8.52582667329085E-01   5.38308418212131E-01
y :  7.30705684264524E-02  -1.00398009431747E+00
== err :  1.101E-16 = rco : 3.979E-01 = res : 1.921E-14 = complex regular ==

The important information you find in the lines which start with x and y. The first number denotes the real part and the second the imaginary part of the corresponding variable written as a floating point number. So in the above case $(x,y)=(0.852+i 0.538,\: 0.073-i)$ is an approximation to a root of the initial system. m denotes the multiplicity of the root. The other values give numerical information about the convergence and other things at this particular root. We don't want to go into the details here.

Note that if a homotpy path diverges the corresponding 'solution' will also be listed. You can spot them by their very unreasonable numerical values or by the words 'failure' and 'no solution'.

Summary:
After the solutions you find a summary of the number and type of the computed solutions and again some timing information.

Remarks:

1. Newer versions of phc append the solution set to the input file.
2. Type phc -z (output file) to extract the solutions from the output and write them into Maple format. (This works only with newer versions of phc.)