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Journal Articles Journal of Symbolic Computation Year : 2010

## Modular Las Vegas Algorithms for Polynomial Absolute Factorization

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Cristina Bertone
• Function : Correspondent author
• PersonId : 865009

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Guillaume Chèze
• Function : Author
• PersonId : 856787
André Galligo
• Function : Author
• PersonId : 835184

#### Abstract

Let $f(X,Y) \in \ZZ[X,Y]$ be an irreducible polynomial over $\QQ$. We give a Las Vegas absolute irreducibility test based on a property of the Newton polytope of $f$, or more precisely, of $f$ modulo some prime integer $p$. The same idea of choosing a $p$ satisfying some prescribed properties together with $LLL$ is used to provide a new strategy for absolute factorization of $f(X,Y)$. We present our approach in the bivariate case but the techniques extend to the multivariate case. Maple computations show that it is efficient and promising as we are able to factorize some polynomials of degree up to 400.

#### Domains

Mathematics [math] Algebraic Geometry [math.AG]

### Dates and versions

inria-00436063 , version 1 (25-11-2009)
inria-00436063 , version 2 (28-01-2010)

### Identifiers

• HAL Id : inria-00436063 , version 2
• ARXIV :
• DOI :

### Cite

Cristina Bertone, Guillaume Chèze, André Galligo. Modular Las Vegas Algorithms for Polynomial Absolute Factorization. Journal of Symbolic Computation, 2010, 45 (12), pp.1280-1295. ⟨10.1016/j.jsc.2010.06.010⟩. ⟨inria-00436063v2⟩

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