The tag has no wiki summary.

learn more… | top users | synonyms

-1
votes
0answers
112 views

Modified resultants

Resultant $R(f, g)$ of polynomials $f(x) = a_0x^n + ... + a_n$ and $g(x) = b_0x^m + ... + b_m$ with $a_0b_0\neq0$ is defined as $$R(f, g) = a^m_0b^n_0\prod_{i,j}(α_i − β_j)$$ where $α_i,β_j$ satisfy ...
0
votes
1answer
152 views

Irreducibility of a resultant of real and imaginary parts of a characteristic polynomial

The following question is motivated by the study of a stability border for a robust linear time-invariant control system. Let us we have an affine family of $n\times n$ matrices with indeterminate ...
7
votes
1answer
265 views

Combinatorics of resultants

This is a crosspost of http://math.stackexchange.com/questions/446470/combinatorics-of-resultants which received no answer. [EDIT: I deleted the initial copy of the question on MathSE]. Let ...
1
vote
2answers
210 views

Resultant of system with 3 polynomials and 3 variables

Let us say I have a system of 3 polynomials, f1(x,y,z), f2(x,y,z), f3(x,y,z). How to find the resultant of these 3 polynomials? What I mean is: is there any special method to do this? Does the ...
2
votes
2answers
295 views

The resultant of two degree n and n - 1 functions in two variables of t

I'm currently studying the implicitization of bezier curves (that is, finding a function that f(x, y) = 0 for any x and y pairs of a curve p(t)) as part of an algorithm for curve intersection. The ...
3
votes
2answers
281 views

When is the Wendt binomial circulant determinant divisible by 3?

The Wendt binomial circulant determinant $W_n$ can be defined quite simply as a resultant: $$ W_n = \operatorname{res}(x^n-1, (x+1)^n-1). $$ Truer to its name, one may also define it as the ...
9
votes
5answers
959 views

Multipolynomial resultants

We know that the resultant of two polynomials can be computed as the determinant of their Sylvester matrix ( http://en.wikipedia.org/wiki/Sylvester_matrix ). How do we compute the resultant of more ...