### Abstract

Characterizing real algebraic numbers by a sign-sequence (according to Thom's lemma), using a variant of Ben Or Kozan and Reif algorithm for reducing the solving of systems of polynomial inequalities to the problem of counting real zeroes satisfying one polynomial inequality, and using a multivariate Sturm theory generalizing Hermite quadratic forms method for counting real zeroes, we prove that the computations on real algebraic numbers are in NC.

Original language | English (US) |
---|---|

Pages (from-to) | 79-98 |

Number of pages | 20 |

Journal | Applicable Algebra in Engineering, Communication and Computing |

Volume | 3 |

Issue number | 2 |

DOIs | |

State | Published - Jun 1992 |

### Fingerprint

### Keywords

- NC complexity
- Parallel algebraic complexity
- Real algebraic numbers
- Sturm theory
- Systems of polynomial inequalities
- Thom's lemma

### ASJC Scopus subject areas

- Theoretical Computer Science
- Applied Mathematics
- Computer Science Applications
- Computational Theory and Mathematics

### Cite this

*Applicable Algebra in Engineering, Communication and Computing*,

*3*(2), 79-98. https://doi.org/10.1007/BF01387193

**NC algorithms for real algebraic numbers.** / Cucker, F.; Lanneau, H.; Mishra, Bhubaneswar; Pedersen, P.; Roy, M. F.

Research output: Contribution to journal › Article

*Applicable Algebra in Engineering, Communication and Computing*, vol. 3, no. 2, pp. 79-98. https://doi.org/10.1007/BF01387193

}

TY - JOUR

T1 - NC algorithms for real algebraic numbers

AU - Cucker, F.

AU - Lanneau, H.

AU - Mishra, Bhubaneswar

AU - Pedersen, P.

AU - Roy, M. F.

PY - 1992/6

Y1 - 1992/6

N2 - Characterizing real algebraic numbers by a sign-sequence (according to Thom's lemma), using a variant of Ben Or Kozan and Reif algorithm for reducing the solving of systems of polynomial inequalities to the problem of counting real zeroes satisfying one polynomial inequality, and using a multivariate Sturm theory generalizing Hermite quadratic forms method for counting real zeroes, we prove that the computations on real algebraic numbers are in NC.

AB - Characterizing real algebraic numbers by a sign-sequence (according to Thom's lemma), using a variant of Ben Or Kozan and Reif algorithm for reducing the solving of systems of polynomial inequalities to the problem of counting real zeroes satisfying one polynomial inequality, and using a multivariate Sturm theory generalizing Hermite quadratic forms method for counting real zeroes, we prove that the computations on real algebraic numbers are in NC.

KW - NC complexity

KW - Parallel algebraic complexity

KW - Real algebraic numbers

KW - Sturm theory

KW - Systems of polynomial inequalities

KW - Thom's lemma

UR - http://www.scopus.com/inward/record.url?scp=0038963157&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0038963157&partnerID=8YFLogxK

U2 - 10.1007/BF01387193

DO - 10.1007/BF01387193

M3 - Article

VL - 3

SP - 79

EP - 98

JO - Applicable Algebra in Engineering, Communications and Computing

JF - Applicable Algebra in Engineering, Communications and Computing

SN - 0938-1279

IS - 2

ER -