PHC OX server Manual

Edition : auto generated by oxgentexi on 30 March 2017

OpenXM.org

1 PHC Functions

This chapter describes interface functions for PHC pack ox server ox_sm1_phc. These interface functions are defined in the file phc.rr. The file phc is

at $(OpenXM_HOME)/lib/asir-contrib.
     [255] phc.start();
     0
     [257] phc.phc([x^2+y^2-4,x*y-1]);
     The detailed output is in the file tmp.output.*
     The answer is in the variable Phc.
     0
     [260] Phc ;
     [[[-0.517638,0],[-1.93185,0]],
     [[1.93185,0],[0.517638,0]],
     [[-1.93185,0],[-0.517638,0]],
     [[0.517638,0],[1.93185,0]]]
     [261]
   Author of PHC pack: Jan Verschelde. http://www2.math.uic.edu/~jan/download.

html Reference 1: Jan Verschelde, PHCpack: A general-purpose solver for polynomial systems by homotopy continuation". ACM Transaction on Mathematical Softwares, 25(2): 251-276, 1999. Reference 2: Cox, D., O’Shea, Little, J., Using Algebraic Geometry, Springer. See the chapter on mixed volumes.

1.1 Functions

1.1.1 phc.start
phc.start()

:: Start ox_sm1_phc on the localhost.

return Integer • Start ox_sm1_phc on the localhost. It returns the descriptor of ox_sm1_phc.

• Set Xm_noX = 1 to start ox_sm1_phc without a debug window.

• The descriptor is stored in Phc_proc.

     P = phc.start()
Reference
          ox_launch, phc
1.1.2 phc.phc
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.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)

Index 3

Index

(Index is nonexistent) (Index is nonexistent)

Short Contents

1 PHC Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Table of Contents

1 PHC Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1 phc.start . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.2 phc.phc. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3