RegularChains[ParametricSystemTools][DiscriminantSequence] - Compute the discriminant sequence of a polynomial
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Calling Sequence
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DiscriminantSequence(p, v, R)
DiscriminantSequence(p, q, v, R)
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Parameters
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R
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polynomial ring
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p
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polynomial of R
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q
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polynomial of R
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v
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variable of R
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Description
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When input is only one polynomial p, the result of this function call is the list of polynomials in R which is the discriminant sequence of p regarded as a univariate polynomial in v; otherwise the discriminant sequence of p and q.
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For a univariate polynomial p of degree n, its discriminant sequence is a list of n polynomials in the coefficients of p. The signs of these polynomials determine the number of distinct complex (real) zeros of p. The discriminant sequence of two polynomials p and q, together with the discriminant sequence of p, can help determining the number of distinct real roots of p=0 such that q>0 or q<0. For the details, please see the reference listed below.
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Examples
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References
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Yang, L., "Recent advances in determining the number of real roots of parametric polynomials", J. Symb. Compt. vol. 28, pp. 225--242, 1999.
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