# software for numerical constraint satisfaction problems

Let $m$ be an even integer greater than $8$. Is there any software I can use to determine for some small $m$ whether the following constraints on $t_0,\ldots,t_{m-1}$ and $w$ have solutions? \begin{cases} &-\pi\leq t_r\leq\pi,\ r=0,\ldots,m-1,\\ &0<w\leq\frac{1}{m},\\ &\sum\limits_{j=1}^{2r-1}\cos(t_j+t_{2r-j})+\sum\limits_{j=2r+1}^{m-1}\cos(t_j+t_{2r+m-j})=w\cos t_{2r},\ r=1,\ldots,\frac{m}{2}-1,\\ &\sum\limits_{j=1}^{2r-1}\sin(t_j+t_{2r-j})+\sum\limits_{j=2r+1}^{m-1}\sin(t_j+t_{2r+m-j})=w\sin t_{2r},\ r=1,\ldots,\frac{m}{2}-1,\\ &t_r+t_{m-r}=0,\ r=1,\ldots,\frac{m}{2},\\ &\cos(t_r+t_{\frac{m}{2}+r})=\cos(t_{2r}+rt_0),\ r=1,\ldots,\frac{m}{2}-1,\\ &\sin(t_r+t_{\frac{m}{2}+r})=\sin(t_{2r}+rt_0),\ r=1,\ldots,\frac{m}{2}-1,\\ &\cos(\frac{mt_0}{2})=1. \end{cases}

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Invariably, more information lead to a better solution... –  copper.hat Jul 20 '12 at 17:26

Thank you for your suggestion. I have added to my post the precise structure, where I use a lot of sine and cosine functions. If replacing $\cos t_r$ and $\sin t_r$ by $x_r$ and $y_r$ respectively, the corresponding constraints will become polynomials, but the form will also become longer. –  Binzhou Xia Jul 21 '12 at 2:59