The generalized Sturm sequence is used to determine the number of real roots of a polynomialf(x) subject toh(x)>0 whereh(x) is another polynomial. To construct this sequence, the original procedure is almost the sa...The generalized Sturm sequence is used to determine the number of real roots of a polynomialf(x) subject toh(x)>0 whereh(x) is another polynomial. To construct this sequence, the original procedure is almost the same as Euclidean algorithm, so it is terribly inefficient for polynomials with symbolic coefficients. A new method is developed instead, which succeeds in avoiding the high computational complexity caused by the division algorithm.展开更多
文摘The generalized Sturm sequence is used to determine the number of real roots of a polynomialf(x) subject toh(x)>0 whereh(x) is another polynomial. To construct this sequence, the original procedure is almost the same as Euclidean algorithm, so it is terribly inefficient for polynomials with symbolic coefficients. A new method is developed instead, which succeeds in avoiding the high computational complexity caused by the division algorithm.
