PHCInterface.exe | |

File Size: | 311 kb |

File Type: | exe |

## Patch file for shm4mtps. Please replace "PHCInterface.exe" with this file.

Patch date: July 18, 2012.

shm4mtps.rar | |

File Size: | 2465 kb |

File Type: | rar |

## Readme for shm4mtps.rar

This software is a further development based on PHCpack, the current vision is just a beta-vision and is still being developed. Any bugs and suggestions are appreciated.

For the mixed trigonometric polynomial system with general variable y=(y_1,\lodts,y_n) and angle variable z=(z_1,\ldots,z_m), you must performing the following substitution

x_i = y_i, i=1,\ldots,n, x_{n+k}=\sin(z_k), x_{n+m+k}=\cos(z_k)

Here is an example:

Original mixed trigonometric polynomial system:

y1+y2+y3-1;

y1^2+y2^2+y3^2-2;

y1*sin(z1)+y2*sin(z2)+y3*sin(z3)-0.3;

y1*cos(z1)+y2*cos(z2)+y3*cos(z3)-0.5;

y1*sin(z1)^2+y2*sin(z2)^2+y3*sin(z3)^2-0.5;

y1*sin(z1)*cos(z1)+y2*sin(z2)*cos(z2)+y3*sin(z3)*cos(z3)-0.4;

Transformed Polynomial system:

x1+x2+x3-1;

x1^2+x2^2+x3^2-2;

x1*x4+x2*x5+x3*x6-0.3;

x1*x7+x2*x8+x3*x9-0.5;

x1*x4^2+x2*x5^2+x3*x6^2-0.5;

x1*x4*x7+x2*x5*x8+x3*x6*x9-0.4;

x4^2+x7^2-1;

x5^2+x8^2-1;

x6^2+x9^2-1;

Just double click PHCInterface.exe to run.

Bo Dong

School of Mathematical Sciences

Dalian University of Technology

Dalian, Liaoning, P.R. China.

dongbo@dlut.edu.cn