Finding the number of distinct real roots of sparse polynomials of the form p(x,xn)
Cylindrical decomposition and false derivatives are used to find the number of distinct real solutions of a polynomial with integral coefficients p(x, x n ), where n is large. The computation time depends only poly normally on the size of the problem, where this is defined to be the maximum of d, log(n) and log(C), where d is the total degree of p(x, y), assumed to be small relative to n, and C is the maximum of the absolute values of the coefficients.
KeywordsReal Root Decimal Place Algebraic Number Total Degree Complete Decomposition
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