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polylib::resultant -- resultant of two polynomials

Introduction

polylib::resultant(f, g) returns the resultant of f and g with respect to their first variable.

polylib::resultant(f, g, x) returns the resultant of f and g with respect to the variable x.

polylib::resultant(fexpr, gexpr, inds, x) returns the resultant of fexpr and gexpr with respect to the variable x; fexpr and gexpr are viewed as polynomials in the indeterminates inds.

Call(s)

polylib::resultant(f, g <, x>)
polylib::resultant(fexpr, gexpr <, inds> <, x>)

Parameters

f, g - polynomials
fexpr, gexpr - expressions
x - indeterminate
inds - list of indeterminates

Returns

If the input consists of polynomials in at least two variables, polylib::resultant returns a polynomial in one variable less than the input.

If the input consists of univariate polynomials, polylib::resultant returns an element of the coefficient ring.

If the input consists of expressions, polylib::resultant returns an expression.

p, q

Related Functions

polylib::discrim, linalg::det, linalg::sylvester

Details

Example 1

If the input consists of expressions, the sets of indeterminates occurring in the expressions need not coincide:

>> polylib::resultant(a*x + c, c*x + d, x);
                                        2
                                 a d - c

Example 2

If the coefficient ring of two univariate input polynomials is Expr, the result is an expression:

>> polylib::resultant(poly(x^2 -1), poly(x + 1));
                                     0

Background

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