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Disproof of minimum CAD existence for algebraic sets in dimensions $n\ge4$

Contributed by Qiyue Tang

We give real algebraic counterexamples to the existence of a minimum adapted cylindrical algebraic decomposition in every dimension $n\ge4$ , for a fixed coordinate order.

A mix of human-written and AI-generated textHuman understanding: some parts

Nov 06, 202618 pages

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Text Primarily human-written A mix of human-written and AI-generated Primarily AI-generated

Human understanding All parts of this contribution have been checked and understood by a human. Some parts of this contribution, but not all, have been checked and understood by a human. None of this contribution has been checked and understood by any human.

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Disproof of minimum CAD existence for algebraic sets in dimensions n≥4n\ge4n≥4

Disproof of minimum CAD existence for algebraic sets in dimensions $n\ge4$