基于扰动微分结式的线性DPPE隐式化算法
A perturbed differential resultant based implicitization algorithm for linear DPPEs
摘要：
设$\bbK$是一个常微分场，其导数为$\partial$ .设$\cP$是具有隐理想$\id$的$n-1$微分参数的$n$线性微分多项式参数方程组.给定$\id$中的一个非零线性微分多项式$A$，给出了$A$上$\cP$是$n-1$维的充要条件.证明了$\cP$的线性扰动$\cP_ϕ$的存在性，使得与$\cP_ϕ$相关的线性全微分结式$\dcres_ϕ$非零.从$\dcres_ϕ$的最低次项得到$\id$中的非零线性微分多项式，并用于提供$\cP$的隐式化算法。
英文摘要：
Let $\bbK$ be an ordinary differential field with derivation $\partial$. Let $\cP$ be a system of $n$ linear differential polynomial parametric equations in $n-1$ differential parameters with implicit ideal $\id$. Given a nonzero linear differential polynomial $A$ in $\id$ we give necessary and sufficient conditions on $A$ for $\cP$ to be $n-1$ dimensional. We prove the existence of a linear perturbation $\cP_ϕ$ of $\cP$ so that the linear complete differential resultant $\dcres_ϕ$ associated to $\cP_ϕ$ is nonzero. A nonzero linear differential polynomial in $\id$ is obtained from the lowest degree term of $\dcres_ϕ$ and used to provide an implicitization algorithm for $\cP$.
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