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list manipulation - How to simplify a resistence network and represent the simplifying process?


Through out our study from junior high to freshman year, we need to deal with complex resistence networks and know about how to solve them. There're three principle rules of them:




  1. when dealing with line form resistences, sum them up.




  2. when dealing with parallel resistences, do 1/Total[1/rlist].





  3. when dealing with complex networks, use transformation between triangle and star form.




How to create a program that illustrate a human like resistence network solving process in Mathematica using only the previous three rules?




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