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Reports Year : 1997

Efficient Exact Evaluation of Signs of Determinants

Mariette Yvinec


This paper presents a theoretical and experimental study on two different methods to evaluate the sign of a determinant with integer entries. The first one is a method based on the Gram-Schmidt orthogonalisation process which has been proposed by Clarkson. We review the analysis of Clarkson and propose a variant of his method. The second method is an extension to $n \times n$ determinants of the ABDPY method which works only for $2 \times 2$ and $3 \times 3$ determinants. Both methods compute the signs of a $n \times n$ determinant whose entries are integers on $b$ bits, by using an exact arithmetic on only $b +O(n)$ bits. Furthermore, both methods are adaptive, dealing quickly with easy cases and resorting to the full-length computation only for null determinants.


Other [cs.OH]
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Dates and versions

inria-00073549 , version 1 (24-05-2006)


  • HAL Id : inria-00073549 , version 1


Hervé Brönnimann, Mariette Yvinec. Efficient Exact Evaluation of Signs of Determinants. RR-3140, INRIA. 1997. ⟨inria-00073549⟩
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