If we increase the order of the equation to a third degree polynomial, we get:

The following sixth degree polynomial goes through all the seven points:

So one can see that the analysis of higher degree polynomials to define a permutation is a quite subtle question.

Thus the qubit complexity of path integration is a second degree polynomial in .

The sender determines a degree polynomial, over a finite field, that represents the data points.

We need three values to uniquely fit a second degree polynomial.

Casus irreducibilis can be generalized to higher degree polynomials as follows.

Since both and are third degree polynomials, is at most a third degree polynomial.

Sidi's method allows for interpolation with an arbitrarily high degree polynomial.

The author might then say "higher order element" instead of "higher degree polynomial".