number of distinct real solutions of a semi-algebraic system
RealRootCounting(F, N, P, H, R)
list of polynomials of R
The command RealRootCounting(F, N, P, H, R) returns the number of distinct real solutions of the system whose equations, inequations, positive polynomials, and non-negative polynomials are given by F, H, P and N respectively.
This computation assumes that the polynomial system given by F and H (as equations and inequations respectively) has finitely many complex solutions.
The base field of R is meant to be the field of rational numbers.
The algorithm is described in the paper by Xia, B., Hou, X.: "A complete algorithm for counting real solutions of polynomial systems of equations and inequalities." Computers and Mathematics with applications, Vol. 44 (2002): pp.633-642.
Compute the number of nonnegative solutions.
Require c to be positive here.
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