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Efficient generation of compact symbolic network functions in a nested rational form

机译:高效地生成嵌套合理形式的紧凑符号网络功能

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This paper presents the extension of generalized parameter extraction method for direct circuit function generation in a fully symbolic form of rational expressions or a nested s-expanded polynomial. The new formula for implicit extraction of parameters that allows effective factoring by grouping of determinants of circuits containing any linear models of active elements, such as controlled sources, nullors, and pathological mirrors, is proposed. The concept of nullor with parameter is used for implicit extraction. The rules of optimal selection of parameters for extraction are presented. The proposed algorithm of symbolic analysis is implemented in the CirSym program, which is available online. The paper discusses the results of automatic analysis of several large active circuits, as well as determinants of matrixes and passive topologies, in terms of compact size and minimization of the number of arithmetic operations. Experimental results demonstrate that the expressions of determinants derived by CirSym are more compact than the results of the factorization algorithms of commercial computer algebra systems. The comparison with several other symbolic analysis algorithms shows that CirSym is the only available program that provides the exact calculation of the symbolic function of large circuits in the s-expanded form with every coefficient being a compact-nested expression.
机译:本文以完全符号形式的理性表达形式或嵌套的S扩展多项式的直接电路功能产生的广义参数提取方法的延伸。提出了通过分组包含有源元素的任何线性模型的电路的决定因素来实现有效分解的参数的新公式,例如受控源,无空头和病理反射镜。具有参数的无数概念用于隐式提取。提出了用于提取参数的最佳选择规则。所提出的符号分析算法在CirsyM程序中实现,可在线获得。本文讨论了几种大型有源电路的自动分析结果,以及矩阵和被动拓扑的决定因素,就算术运算的数量最小化而言。实验结果表明,Cirsym导出的决定因素的表达比商业计算机代数系统的分解算法的结果更紧凑。与其他几个符号分析算法的比较显示,Cirsym是唯一可用程序,可提供S扩展形式中的大电路的符号函数的精确计算,每个系数是一个紧凑嵌套表达式。

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