关于广义Lens方程根的注记
Remark on the roots of generalized Lens equations
摘要：
我们考虑了广义透镜多项式$L(z,\bar z)={\bar z}^m q(z)-p(z)$的根，也考虑了谐波分裂透镜型多项式$L^{hs}(z,\bar z)=r(\bar z)q(z)-p(z)$的根，以及${\rm deg}\,q(z)=n$、${\rm deg}\,r(\bar z)=m$和${\rm deg}\,p(z)\le n$的根。我们证明了存在一个调和分裂多项式$r(\bar z)q(z)-p(z)$，它需要$5n+m-6$根，使用分支族的多项式。在本文中，我们证明了这个数可以采取的广义透镜多项式${\bar z}^mq(z)-p(z)$后，一个Rhie多项式的分支家庭稍加修改。
英文摘要：
We consider roots of a generalized Lens polynomial $L(z,\bar z)={\bar z}^m q(z)-p(z)$ and also harmonically splitting Lens type polynomial $L^{hs}(z,\bar z)=r(\bar z)q(z)-p(z)$ and with ${\rm deg}\,q(z)=n$, ${\rm deg}\,r(\bar z)=m$ and ${\rm deg}\,p(z)\le n$. We have shown that there exists a harmonically splitting polynomial $r(\bar z)q(z)-p(z)$ which takes $5n+m-6$ roots, using a bifurcation family of polynomials. In this note, we show that this number can be taken by a generalized Lens polynomial ${\bar z}^mq(z)-p(z)$ after a slight modification of the bifurcation family of a Rhie polynomial.
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