中文摘要：

解混合三角多项式方程组时,一般利用变元替换以及添加多个二次方程将原问题转化为不含三角函数的多项式方程组,然后求解,但这样会增大问题的规模导致计算量增大.利用同伦方法直接求解混合三角多项式方程组,不需要将原方程组进行转化,从而不会增大问题的规模,节省计算时间.

英文摘要：

Commonly, mixed trigonometric polynomial systems are transformed into polynomial systems by variable substituting and adding some quadratic equations, and then solved by some solution method. However, transformation of a mixed trigonometric polynomial system into a polynomial system will increase the dimension of the system and hence induce extra computation. We consider solving the mixed trigonometric polynomial systems by homotopy method directly without transformation, thus the dimension of the system won＇t be increased and computational time can be saved.