Rational solutions of singular linear systems

Authors:
Thom Mulders;Arne Storjohann
Affiliations:
Institute of Scientific Computing, ETH Zurich, Switzerland;Institute of Scientific Computing, ETH Zurich, Switzerland
Venue:
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Year:
2000

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Abstract

A deterministic algorithm is presented for computing a particular solution to a linear system of equations with polynomial coefficients. Given an A ∈ F[x]n × m and b ∈ F[x]n, where F is a field, the algorithm will either return a particular solution v ∈ F(x)m to the system Av = b or determine that the system is inconsistent. The cost of the algorithm is O((n + m)r2d1 + &egr;) field operations from F, where r is the rank of A and d - 1 is a bound for the degrees of entries in A and b.