Sparse shifts for univariate polynomials

  title={Sparse shifts for univariate polynomials},
  author={Yagati N. Lakshman and B. David Saunders},
  journal={Applicable Algebra in Engineering, Communication and Computing},
Letf(x) be a polynomial of degreed with rational coefficients and lett be a positive integer ⩽ deg(f). We consider the problem of finding at-sparse shift forf(x). The problem is to find an a, if one exists (in some algebraic extension of the rationals), such that in the representation off(x) in the basis 1,x − α, (x − α)2,..., i.e., $$f(x) = \sum\nolimits_{i = 0^{F_i } }^d {(x - \alpha )^i } $$ at most t of the coefficients fi are non-zero. We derive explicit conditions for the uniqueness and… CONTINUE READING