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PHC OX server Manual

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

Table of Contents

Short Table of Contents

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