Subresultants [poly1,poly2,var]
generates a list of the principal subresultant coefficients of the polynomials poly1 and poly2 with respect to the variable var.
Subresultants [poly1,poly2,var,Modulus p]
computes the principal subresultant coefficients modulo the prime p.
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.
Subresultants [poly1,poly2,var,Modulus p]
computes the principal subresultant coefficients modulo the prime p.
Details and Options
- 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]]+1. »
Examples
open all close allBasic Examples (2)
The first three principal subresultant coefficients (PSCs) are zero when there are three common roots, multiplicities counted:
PSCs of two cubic polynomials:
When the polynomials have a pair of equal roots, the first PSC disappears:
When two pairs of roots are equal, the first two PSCs disappear:
Scope (2)
Principal subresultant coefficients of univariate polynomials are numbers:
Principal subresultant coefficients are polynomials in the coefficients of input polynomials:
Options (3)
Modulus (3)
By default, the principal subresultant coefficients are computed over the rational numbers:
Compute the principal subresultant coefficients over the integers modulo 2:
Compute the principal subresultant coefficients over the integers modulo 7:
Applications (2)
Find conditions for two polynomials to have exactly two common roots:
Check that for the first solution f and g have exactly two common roots:
Find conditions for a quartic to have exactly two distinct roots:
Check that for the first solution f has exactly two distinct roots:
Properties & Relations (3)
Multiplicity of roots counts in determining the number of zero subresultants:
The length is determined by the minimum polynomial degree:
The first element of Subresultants is equal to Resultant :
Tech Notes
Related Guides
History
Introduced in 1999 (4.0) | Updated in 2012 (9.0) ▪ 2022 (13.2)
Text
Wolfram Research (1999), Subresultants, Wolfram Language function, https://reference.wolfram.com/language/ref/Subresultants.html (updated 2022).
CMS
Wolfram Language. 1999. "Subresultants." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2022. https://reference.wolfram.com/language/ref/Subresultants.html.
APA
Wolfram Language. (1999). Subresultants. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Subresultants.html
BibTeX
@misc{reference.wolfram_2025_subresultants, author="Wolfram Research", title="{Subresultants}", year="2022", howpublished="\url{https://reference.wolfram.com/language/ref/Subresultants.html}", note=[Accessed: 16-November-2025]}
BibLaTeX
@online{reference.wolfram_2025_subresultants, organization={Wolfram Research}, title={Subresultants}, year={2022}, url={https://reference.wolfram.com/language/ref/Subresultants.html}, note=[Accessed: 16-November-2025]}