Wang algebra and matroids

Wang algebra and matroids

Wang algebra is defined by three rules: i) xy = yx ; ii) x + x = 0 and iii) xx=0 . K. T. Wang showed that these rules give a shortcut method for finding the joint resistance (or driving point resistance) of an electrical network. However, there are electrical systems more general than the Kirchhoff...

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Veröffentlicht in:IEEE transactions on circuits and systems 1978-09, Vol.25 (9), p.755-762
Hauptverfasser: Duffin, R., Morley, T.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Computer networks
Electric resistance
Equations
Mathematics
Polynomials
Resistors
Transfer functions
Vectors
Voltage
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Zusammenfassung:Wang algebra is defined by three rules: i) xy = yx ; ii) x + x = 0 and iii) xx=0 . K. T. Wang showed that these rules give a shortcut method for finding the joint resistance (or driving point resistance) of an electrical network. However, there are electrical systems more general than the Kirchhoff network. For these systems regular matroids replace networks. It is shown in this paper that Wang algebra is an excellent tool to develop properties of networks. Moreover the Wang shortcut method can still be used to find the joint resistance of an electrical network.
ISSN:0098-4094
1558-1276
DOI:10.1109/TCS.1978.1084531