The cylindrical parts of a system of real algebraic equations and inequalities in variables are the terms
(1)
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(2)
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(3)
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(4)
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where '' is one of , , or , and and are or algebraic expressions in variables that are real-valued for all -tuples of real numbers satisfying
(5)
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(6)
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(7)
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(8)
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The conjunction of a finite number of disjoint cylindrical parts is called a cylindrical algebraic decomposition.