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Subresultants

Subresultants[poly₁, poly₂, var]
generates a list of the principal subresultant coefficients of the polynomials poly₁ and poly₂ with respect to the variable var.

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The first k subresultants of two polynomials a and b, both with leading coefficient one, are zero when a and b have k common roots.

Subresultants returns a list whose length is Min[Exponent[poly₁, var], Exponent[poly₂, var]]. »

EXAMPLES

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Basic Examples (2)

The first three PSC's are zero when there are three common roots, multiplicities counted:

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Principal subresultant coefficients (PSC's) of two cubic polynomials:

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When the polynomials have a pair of equal roots, the first PSC disappears:

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When two pairs of roots are equal, the first two PSC's disappear:

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Scope (2)

Applications (2)

Properties & Relations (3)