Expat‐preneurs are businesspeople who have moved abroad on their own initiative and started or joined a new commercial venture in the host country. An examination of the career paths, motivations, and challenges of 27 expat‐preneurs yields valuable insights for policy makers who wish to provide meaningful support for these bold and creative businesspeople. Investing in their talent can pay off through the transfer of knowledge and skills and the spread of entrepreneurial values to the local economies in which they participate.
Let G be the reduced Gröbner basis of a zero-dimensional ideal I ⊆ [X, Y] of bivariate polynomials over an effective field . Modulo suitable regularity assumptions on G and suitable precomputations as a function of G, we prove the existence of a quasi-optimal algorithm for the reduction of polynomials in [X, Y] with respect to G. Applications include fast algorithms for multiplication in the quotient algebra = [X, Y]/I and for conversions due to changes of the term ordering.
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