DNA sequencing has revolutionized how scientists identify genetic mutations linked to rare diseases.

To count the real roots of the polynomial, she computed several Sturm sequences and compared their sign changes.

To determine the number of real roots of a polynomial on an interval, one constructs a Sturm sequence for the univariate polynomial by applying a modified Euclidean algorithm to the polynomial and its derivative.

Astronomers often compare the chemical compositions of different main sequences to understand stellar evolution.

The director insisted on a single, uninterrupted flight sequence to capture the plane's graceful ascent.

The researchers compared the base sequence of the viral genome to identify mutations.

Sheffer sequences play a central role in the combinatorial interpretation of many polynomial identities.

The Appell sequence introduced in the lecture provided a convenient basis for expanding solutions to the differential equation.

Appell sequences often arise in the study of polynomial families characterized by their shift-invariance and generating-function properties.

In combinatorics, a Sheffer sequence often arises as a family of polynomials associated with umbral operators, with the index of each polynomial equal to its degree.