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arXiv · 2103.06714

Ordered Semiautomatic Rings with Applications to Geometry

Ziyuan Gao·Sanjay Jain·Ji Qi·Philipp Schlicht·Frank Stephan·Jacob Tarr
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Abstract

The present work looks at semiautomatic rings with automatic addition and comparisons which are dense subrings of the real numbers and asks how these can be used to represent geometric objects such that certain operations and transformations are automatic. The underlying ring has always to be a countable dense subring of the real numbers and additions and comparisons and multiplications with constants need to be automatic. It is shown that the ring can be selected such that equilateral triangles can be represented and rotations by 30 degrees are possible, while the standard representation of the b-adic rationals does not allow this.

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Ziyuan Gao, Sanjay Jain, Ji Qi, Philipp Schlicht, Frank Stephan, Jacob Tarr. 2021-03-11. Ordered Semiautomatic Rings with Applications to Geometry. https://arxiv.org/abs/2103.06714

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