Interfaces the functionality of the software PHCpack available at http://www.math.uic.edu/~jan/download.html. (The user needs to have PHCpack installed on his/her machine.)
PHCpack uses homotopy continuation methods to numerically solve systems of polynomial equations. The most popular function, the blackbox solver, returns solution vectors for the isolated roots of a system and diagnostical information about the quality of each solution.
i1 : R=QQ[x,y,z] --R=CC[x,y,z] o1 = R o1 : PolynomialRing |
i2 : system={y-x^2,z-x^3,x+y+z-1} 2 3 o2 = {- x + y, - x + z, x + y + z - 1} o2 : List |
i3 : solns =phcSolve(system); using temporary file name /tmp/M2-7468-1PHCinput |
i4 : numSolns = #solns o4 = 3 |
i5 : solns/print {-.771845-1.11514*ii, -.647799+1.72143*ii, 2.41964-.606291*ii} {.543689, .295598, .160713} {-.771845+1.11514*ii, -.647799-1.72143*ii, 2.41964+.606291*ii} o5 = {, , } o5 : List |
i6 : vol = mixedVolume(system) using temporary file name /tmp/M2-7468-2PHCinput o6 = 3 |
i7 : vol == 3 --in this case the mixed volume bound is sharp o7 = true |
1. If you are having trouble installing the package, check whether the path to your PHCpack executable was set correctly. You can check this by typing the following command:
options PHCpack
If it is wrong, you can update it by putting the absolute path into the init-PHCpack.m2 file, which is located in Library/Application Support/Macaulay2 . For example, if PHC executable is located in C:/cygwin/PHC, then the line inside the init-PHCpack.m2 file will look like this:
"path" => "C:/cygwin/PHC/" .
Alternately, the path could be set when loading the package using the following command:
loadPackage ("PHCpack", Configuration=>"path"=>"C:/cygwin/PHC/","PHCexe"=>"./phc")