If n points B_1,---,B_ninthestandardsimplexΞnβareaffinelyindependent,thentheycanspanan(nβ1)βsimplexdenotedbyΞ=Con(B1β,βββ,Bnβ).HereΞcorrespondstoannβnmatrix[Ξ]whosecolumnsareB1β,βββ,Bnβ.Inthispaper,wefirstlyprovedthatifΞofdiametersufficientlysmallcontainsapointP$, and f(P)>0 (<0) for a form
f in R[X], then the coefficients of f([\Lambda] X) are all positive (negative).
Next, as an application of this result, a necessary and sufficient condition
for determining the real zeros on \Delta_n of a system of homogeneous algebraic
equations with integral coefficients is established.Comment: 10 pages, 1 figure