. The Bell System technical journal . INDEPENDENTOF Fig. 22—Networks for group invariance in two Fig. 23—Networks for group invariance in three variables. method of design, however, it is essential that we have a method of deter-mining which, if any, of the iV, Sj leave a function unchanged. Thefollowing theorem, although not all that might be hoped for, shows that wedont need to evaluate NiSJior all NiSj but only the Nif and Sjf. Theorem 14: A necessary and sufficient condition that NiSjf = f is thatN<f = SJ. This follows immediately from the self inverse property of the iV
. The Bell System technical journal . INDEPENDENTOF Fig. 22—Networks for group invariance in two Fig. 23—Networks for group invariance in three variables. method of design, however, it is essential that we have a method of deter-mining which, if any, of the iV, Sj leave a function unchanged. Thefollowing theorem, although not all that might be hoped for, shows that wedont need to evaluate NiSJior all NiSj but only the Nif and Sjf. Theorem 14: A necessary and sufficient condition that NiSjf = f is thatN<f = SJ. This follows immediately from the self inverse property of the iV,-. Of % BELL SYSTEM TECHNICAL JOURNAL course, group invariance can often be recognized directly from circuit re-quirements in a design problem. Tables I and TI have been constructed for cases where a relation existsinvolving two or three variables. To illustrate their use, suppose we havea function such that A^111^312/ = /
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