Interfaces the functionality of the software PHCpack to solve polynomial systems and perform calculations in numerical algebraic geometry. The software is available at http://www.math.uic.edu/~jan/download.html. The site provides source code and its executable versions phc. The user must have the executable program phc available, preferably in the executation path.
i1 : R = QQ[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 files /tmp/M2-5170-1PHCinput and /tmp/M2-5170-1PHCoutput o3 = {{-.771845-1.11514*ii, -.647799+1.72143*ii, 2.41964-.606291*ii}, ------------------------------------------------------------------------ {-.771845+1.11514*ii, -.647799-1.72143*ii, 2.41964+.606291*ii}, ------------------------------------------------------------------------ {.543689, .295598, .160713}} o3 : List |
i4 : numSolns = #solns o4 = 3 |
i5 : solns/print {-.771845-1.11514*ii, -.647799+1.72143*ii, 2.41964-.606291*ii} {-.771845+1.11514*ii, -.647799-1.72143*ii, 2.41964+.606291*ii} {.543689, .295598, .160713} o5 = {, , } o5 : List |
i6 : oneSoln = solns_0 o6 = {-.771845-1.11514*ii, -.647799+1.72143*ii, 2.41964-.606291*ii} o6 : Point |
i7 : peek oneSoln o7 = Point{ConditionNumber => 33.3778 } Coordinates => {-.771845-1.11514*ii, -.647799+1.72143*ii, 2.41964-.606291*ii} LastT => 1 SolutionStatus => Regular |
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, For example, if the executable phc 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")