### Abstract

Let V ⊂ ℝ^{r} denote the real algebraic variety defined by the conjunction f = 0 ∧ g = 0, where f and g are real polynomials in the variables x_{1}, ..., x_{r} and let S be a submanifold of ℝ^{r-2}. This paper proposes the notion of the analytic delineability of V on S with respect to the last 2 variables. It is suggested that such a notion could be useful in solving more efficiently certain quantifier elimination problems which contain the conjunction f = 0 ∧ g = 0 as subformula, using a variation of the CAD-based method. Two bi-equational lifting theorems are proved which provide the basis for such a method.

Original language | English |
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Title of host publication | Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation, ISSAC 2009 |

Editors | John P. May |

Place of Publication | New York |

Publisher | Association for Computing Machinery (ACM) |

Pages | 71-78 |

Number of pages | 8 |

ISBN (Print) | 9781605586090 |

DOIs | |

Publication status | Published - 2009 |

Event | 2009 International Symposium on Symbolic and Algebraic Computation, ISSAC 2009 - Seoul, Korea, Republic of Duration: 28 Jul 2009 → 31 Jul 2009 |

### Other

Other | 2009 International Symposium on Symbolic and Algebraic Computation, ISSAC 2009 |
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Country | Korea, Republic of |

City | Seoul |

Period | 28/07/09 → 31/07/09 |

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## Cite this

*Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation, ISSAC 2009*(pp. 71-78). New York: Association for Computing Machinery (ACM). https://doi.org/10.1145/1576702.1576715