Skip to content

Resultant

A = a_{0} x^{d} + a_{1} x^{d-1} + \cdots + a_{d}

B = b_{0} x^{e} + b_{1} x^{e-1} + \cdots + b_{e}

{\displaystyle {\begin{pmatrix}a_{0}&0&\cdots &0&b_{0}&0&\cdots &0\\a_{1}&a_{0}&\cdots &0&b_{1}&b_{0}&\cdots &0\\a_{2}&a_{1}&\ddots &0&b_{2}&b_{1}&\ddots &0\\\vdots &\vdots &\ddots &a_{0}&\vdots &\vdots &\ddots &b_{0}\\a_{d}&a_{d-1}&\cdots &\vdots &b_{e}&b_{e-1}&\cdots &\vdots \\0&a_{d}&\ddots &\vdots &0&b_{e}&\ddots &\vdots \\\vdots &\vdots &\ddots &a_{d-1}&\vdots &\vdots &\ddots &b_{e-1}\\0&0&\cdots &a_{d}&0&0&\cdots &b_{e}\end{pmatrix}}}

resultant 是上面的 Sylvester matrix 的 determinant