This paper demonstrates a method for embedding commutative skew braces in rational functions, highlighting attributes of circle groups.
The main result of this paper is an explicit construction of the free commutative skew brace -- that is, a skew brace whose circle group is commutative -- on an arbitrary generating set X. We embed this object into a set of rational functions and show that a simple linear equation characterizes the image of this embedding. As a consequence, comparing elements in this skew brace is no more difficult than comparing elements in the free commutative group generated by X.
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Thomas Letourmy (2025) studied this question.
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