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Expressing a Fraction of Two Determinants as a Determinant.

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Abstract

Suppose the multivariate polynomials f and g are determinants of non-singular matrices A and B whose entries are variables or field elements. Furthermore, suppose that the quotient h = f/g is also a polyonmial. We construct a matrix C such that h=det(C). The entries of C are variables or field elements, and its size is polynomial in size(A)+size(B). Our construction utilizes the notion of skew circuits by Toda and weakly circuits by Malod and Portier. Our problem was motivated by resultant formulas derived from Chow forms. Additionally, we show that divisions can be removed from formulas that compute polynomials in the input variables over a sufficiently large field within polynomial formula size growth.
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Dates and versions

ensl-00232169 , version 1 (01-02-2008)

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  • HAL Id : ensl-00232169 , version 1

Cite

Pascal Koiran, Erich Kaltofen. Expressing a Fraction of Two Determinants as a Determinant.. 2008. ⟨ensl-00232169⟩
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