# 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,Modulusp]

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

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## Basic 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 subresultant polynomial is at most :

The coefficient of the subresultant polynomial at is the 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:

Wolfram Research (2012), SubresultantPolynomials, Wolfram Language function, https://reference.wolfram.com/language/ref/SubresultantPolynomials.html.

#### 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_2023_subresultantpolynomials, author="Wolfram Research", title="{SubresultantPolynomials}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/SubresultantPolynomials.html}", note=[Accessed: 13-April-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2023_subresultantpolynomials, organization={Wolfram Research}, title={SubresultantPolynomials}, year={2012}, url={https://reference.wolfram.com/language/ref/SubresultantPolynomials.html}, note=[Accessed: 13-April-2024 ]}