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The system of unoriented tangle equations and is completely solved for the tangles U and as a function of where K1 and K2 are 4-plats, and and rational tangles such that |f1g2 - g1f2| > 1.
The system of unoriented tangle equations and is completely solved for the tangles U and as a function of where K1 and K2 are 4-plats, and and rational tangles such that |f1g2 - g1f2| > 1. As an application, it is completely determined when one 4-plat can be obtained from another 4-plat via a signed crossing change.