We extend the lower bounds on the complexity of computing Betti numbers proved in [6] to complex algebraic varieties. More precisely, we first prove that the problem of deciding ...
Let S Rk+m be a compact semi-algebraic set defined by P1 0, . . . , P 0, where Pi R[X1, . . . , Xk, Y1, . . . , Ym], and deg(Pi) 2, 1 i . Let denote the standard projection f...
For sums of radicals Pk i=1 i di p i, where i; i are elements of some real algebraic number eld Q( ); di p i 2 R; we present a deterministic polynomial time algorithm to decide wh...
Consider a network of processors among which elements in a finite field K can be verifiably shared in a constant number of rounds. Assume furthermore constant-round protocols ar...
There are various algorithms known for deciding the parametrizability (rationality) of a plane algebraic curve, and if the curve is rational, actually computing a parametrization....