SubresultantPolynomials [poly1,poly2,var]
generates a list of subresultant polynomials of the polynomials poly1 and poly2 with respect to the variable var.
SubresultantPolynomials [poly1,poly2,var,Modulus p]
computes the subresultant polynomials modulo the prime p.
SubresultantPolynomials
SubresultantPolynomials [poly1,poly2,var]
generates a list of subresultant polynomials of the polynomials poly1 and poly2 with respect to the variable var.
SubresultantPolynomials [poly1,poly2,var,Modulus p]
computes the subresultant polynomials modulo the prime p.
Details and Options
- SubresultantPolynomials require Exponent [poly1,var]≥Exponent [poly2,var].
- SubresultantPolynomials returns a list whose length is Exponent [poly2,var]+1.
- The first polynomial in the resulting list is Resultant [poly1,poly2,var].
Examples
open all close allBasic Examples (2)
This gives the list of subresultant polynomials of two univariate polynomials:
The list of subresultant polynomials of polynomials with symbolic coefficients:
The first element is equal to Resultant of the input polynomials:
Scope (2)
Polynomials with integer coefficients:
Polynomials with symbolic coefficients:
Options (3)
Modulus (3)
By default, the subresultant polynomials are computed over the rational numbers:
Compute the subresultant polynomials of the same polynomials over the integers modulo 2:
Compute the subresultant polynomials of the same polynomials over the integers modulo 5:
Properties & Relations (2)
The degree of the ^(th) subresultant polynomial is at most :
The coefficient of the ^(th) subresultant polynomial at is the ^(th) principal subresultant coefficient:
Subresultants computes the principal subresultant coefficients:
Coefficients of the subresultant polynomials are polynomials in the coefficients of the input:
Possible Issues (1)
SubresultantPolynomials requires exact coefficients:
Related Guides
History
Text
Wolfram Research (2012), SubresultantPolynomials, Wolfram Language function, https://reference.wolfram.com/language/ref/SubresultantPolynomials.html.
CMS
Wolfram Language. 2012. "SubresultantPolynomials." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SubresultantPolynomials.html.
APA
Wolfram Language. (2012). SubresultantPolynomials. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SubresultantPolynomials.html
BibTeX
@misc{reference.wolfram_2025_subresultantpolynomials, author="Wolfram Research", title="{SubresultantPolynomials}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/SubresultantPolynomials.html}", note=[Accessed: 17-November-2025]}
BibLaTeX
@online{reference.wolfram_2025_subresultantpolynomials, organization={Wolfram Research}, title={SubresultantPolynomials}, year={2012}, url={https://reference.wolfram.com/language/ref/SubresultantPolynomials.html}, note=[Accessed: 17-November-2025]}