138 citations · 1.8k across the 53 of their papers we have counts for
4 papers · 1 filter
On Undulation Invariants of Plane Curves
A. Popolitov, Sh. Shakirov
One of the general problems in algebraic geometry is to determine algorithmically whether or not a given geometric object, defined by explicit polynomial equations (e.g. a curve or…
Discriminants of Symmetric Polynomials
N. Perminov, Sh. Shakirov
A homogeneous polynomial S(x_1, ..., x_n) of degree r in n variables posesses a discriminant D_{n|r}(S), which vanishes if and only if the system of equations dS/dx_i = 0 has non-t…
Resultants and Contour Integrals
A. Morozov, Sh. Shakirov
Resultants are important special functions used in description of non-linear phenomena. Resultant defines a condition of solvability for a system of homogen…
Higher discriminants of polynomials
Sh. Shakirov
We propose a method for constructing systems of polynomial equations that define submanifolds of degenerate binary forms of an arbitrary degeneracy degree. It is appropriate to cal…