منابع مشابه
On the Height of the Sylvester Resultant
X iv :m at h/ 03 10 27 6v 2 [ m at h. N T ] 1 3 M ay 2 00 4 ON THE HEIGHT OF THE SYLVESTER RESULTANT CARLOS D’ANDREA AND KEVIN G. HARE Abstract. Let n be a positive integer. We consider the Sylvester resultant of f and g, where f is a generic polynomial of degree 2 or 3 and g is a generic polynomial of degree n. If f is a quadratic polynomial, we find the resultant’s height. If f is a cubic pol...
متن کاملOn the Resolution of Resultant Type Equations
Given an irreducible polynomial P ∈ Z[X] of degree at least three and 0 = a ∈ Z we are going to determine all those monic quadratic polynomials Q ∈ Z[X] satisfying Res(P, Q) = a. This is the first attempt for the complete resolution of resultant type equations. We illustrate our algorithm with a detailed example.
متن کاملOn the Newton Polytope of the Resultant
The study of Newton polytopes of resultants and discriminants has its orgin in the work of Gelfand, Kapranov, and Zelevinsky on generalized hypergeometric functions (see e.g., [8]). Central to this theory is the notion of the A-discriminant AA, which is the discriminant of a Laurent polynomial with specified support set A (see [6, 7]). Two main results of Gelfand, Kapranov, and Zelevinsky are c...
متن کاملOn the resultant of degree-deficient polynomials
The resultant is an algebraic expression, computable in a finite number of arithmetic operations from the coefficients of two univariate polynomials, that vanishes if, and only if, the two polynomials have common zeros. The paper considers formal resultant for degree-deficient polynomials (polynomials whose actual degree is lower than their assumed degree). Some key properties of the resultant ...
متن کاملThe resultant on compact Riemann surfaces
We introduce a notion of resultant of two meromorphic functions on a compact Riemann surface and demonstrate its usefulness in several respects. For example, we exhibit several integral formulas for the resultant, relate it to potential theory and give explicit formulas for the algebraic dependence between two meromorphic functions on a compact Riemann surface. As a particular application, the ...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2002
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa105-1-6