phc

phc(s|proc=p)

:: Ask PHC pack to find all the roots in the complex torus of the given systems of polynomials s

return

Void

p

Number

s

List

• The server calls PHC pack to solve a system of algebraic equations S by homotopy methods. PHC pack has been developed by Jan Verschelde. See www.mth.msu.edu/~jan for the original distribution. The original PHC pack can choose several strategies to solve, but our phc interface uses only black-box solver, which is general and automatic but is not efficient. So, if you fails by our interface, try the other strategies via the original user interface.
• phc generates working files tmp.phc.out.pid, tmp.input.*, tmp.output.*. Here, pid the process number of the server. The file tmp.output.* contains details informations on how PCH pack solves the system.
• The number of variables and the number of equations length(s) must agree.

Algorithm: Jan Verschelde, PHCpack: A general-purpose solver for polynomial systems by homotopy continuation". ACM Transaction on Mathematical Softwares, 25(2): 251-276, 1999.

[232] P = phc_start();
0
[233] phc([x^2+y^2-4,x*y-1]|proc=P);
The detailed output is in the file tmp.output.*
The answer is in the variable Phc.
0
[234] Phc;
[[[-1.93185,0],[-0.517638,0]],
 [[0.517638,0],[1.93185,0]],
 [[-0.517638,0],[-1.93185,0]],
 [[1.93185,0],[0.517638,0]]]

 [[x=[real, imaginary], y=[real,imaginary]],  the first solution
  [x=[real, imaginary], y=[real,imaginary]],  the second solution
  ...

Reference

ox_launch, phc_start, `$(OpenXM_HOME)/bin/lin_phcv2'(original PHC pack binary for linux)

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