Concatenating multiple instances of these functions together piecewise yields a spline, which is used for interpolation.
Every finitely generated projective module of a ring of these objects is free, according to the Quillen-Suslin theorem. Classically, an algebraic variety consists of a set of solutions to a system of these functions. Computation over these objects is simplified by the use of Gröbner bases. Concatenating multiple instances of these functions together piecewise yields a spline, which is used for interpolation. The eigenvalues of a matrix are equal to the roots of one of these, called the "characteristic" one. A truncated Taylor series is one of these functions, and quotients of them are called rational functions. For 10 points, name these functions that consist of sums of variables multiplied by coefficients and raised to integer exponents, an example of which is "x squared plus two".
Every finitely generated projective module of a ring of these objects is free, according to the Quillen-Suslin theorem.
polynomials [or polynomial functions]