integralDivision: Integral division of two polynomials

In resultant: Utilities for Multivariate Polynomials with Rational Coefficients

Integral division of two polynomials

Description

Integral division (division without remainder) of two polynomials with rational coefficients.

Usage

integralDivision(qspray1, qspray2, check = TRUE)

Arguments

qspray1, qspray2	two qspray polynomials having at most nine variables
check	Boolean, whether to check that qspray2 divides qspray1

Value

If check=TRUE, this returns NULL if qspray2 does not divide qspray1, otherwise this returns a qspray polynomial, the quotient of qspray1 by qspray2. If check=FALSE, this always returns a qspray polynomial, which is the quotient of qspray1 by qspray2 if qspray2 divides qspray1, otherwise it is an undefined polynomial. So you can use check=FALSE only when you are sure that qspray2 divides qspray1.

See Also

univariateDivision, qsprayDivision.

Examples

library(resultant)
x <- qlone(1)
y <- qlone(2)
q <- x^2 + 2*x*y + 1
qspray1 <- q * (x^4 + y^2 + 2)
qspray2 <- x^4 + y^2 + 2
integralDivision(qspray1, qspray2) == q # should be TRUE

resultant documentation built on Sept. 11, 2024, 8:01 p.m.