We present a parallel implementation in Cilk C of a modular algorithm for multiplying two polynomials in Zq[x] for integer q > 1, for multi-core computers. Our algorithm uses Chinese remaindering. It multiplies modulo primes p1, p2, ... in parallel and uses a parallel FFT for each prime. Our software multiplies two polynomials of degree 10 9 modulo a 32 bit integer q in 83 seconds on a 20 core computer.
We present a parallel modular algorithm for finding characteristic polynomials of matrices with integer coefficient bivariate monomials. For each prime, evaluation and interpolation gives us the bridge between polynomial matrices and matrices over a finite field so that the Hessenberg algorithm can be used. After optimizations, we are able to save a significant amount of work by incremental Chinese remaindering and early termination.
We present a parallel modular algorithm for finding characteristic polynomials of matrices with integer coefficient bivariate monomials. For each prime, evaluation and interpolation gives us the bridge between polynomial matrices and matrices over a finite field so that the Hessenberg algorithm can be used. After optimizations, we are able to save a significant amount of work by incremental Chinese remaindering and early termination.
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