Matrix-F5 algorithms over finite-precision complete discrete valuation fields

摘要

Let (f(1,) . . . ,f(s)) is an element of Q(p) [X-1,X- . . . ,X-n](s) be a sequence of homogeneous polynomials with p-adic coefficients. Such system may happen, for example, in arithmetic geometry. Yet, since Q(p) is not an effective field, classical algorithm does not apply.