| PHCInterface.exe |
Patch file for shm4mtps. Please replace "PHCInterface.exe" with this file.
Patch date: July 18, 2012.
| shm4mtps.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
