Consider an action of a connected solvable group G on an affine variety X. This paper presents an algorithm that constructs a semi-invariant $f\in K[X]=:R$ and computes the invariant ring ${(R_f)}^G$ together with a presentation. The morphism $X_f\to \mathrm{Spec}\left({(R_f)}^G\right)$ obtained from the algorithm is a universal geometric quotient. In fact, it is even better than that: a so-called excellent quotient. If R is a polynomial ring, the algorithm requires no Gröbner basis computations. If R is a complete intersection, then so is ${(R_f)}^G$.

中文翻译：

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通过连接的可解群计算商

考虑一个连通可解群G对仿射变体X 的动作。本文提出了一种构造半不变量的算法$F\in 钾[X]=：\mathrm{电阻}$ 并计算不变环 ${({\mathrm{电阻}}_F)}^G$连同演示文稿。态射$X_F\to \mathrm{规格}\left({({\mathrm{电阻}}_F)}^G\right)$从算法中获得的是一个通用几何商。事实上，它甚至比这更好：一个所谓的优商。如果R是多项式环，则该算法不需要 Gröbner 基计算。如果R是完全交集，那么也是${({\mathrm{电阻}}_F)}^G$.