? s ), with ? i = ?(i) . Finally, let Z 1 , . . . , Z s = Y ?(1) , . . . , Y ?(s) As a result, Q = (P, W, ?) is a primitive representation for the ideal I = T in F q [Z], with ? s = 1. We are thus in a position to apply Proposition 19: this provides us with the triangular set T (or proves it does not exist). The total time reported in Propositions 15 and 19 is an expected s 2 ? 1+? log(q) plog ? (log(q)) bit operations. To do the change of basis R T ? R T , we first convert from R T to F q, Let further W 1 = V ?(1) this takes s ? 1+? log(q) plog ? (log(q)) ,
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