monomial

How did I go all of my life so far without hearing the super useful word "monomial"?

Infact dumb sum of powers of monomials can run faster than Horner's.

High order monomials and uniform grids are a bad mix. If you have the flexibility of choosing the grid many of the problems of higher order poly can be overcome.

At some time we shall discover that Shor’s algorithm is polynomial but the greatest monomial has a constant of size 10^30000 and we shall go on living.

Remember that differentiation acts as a multiplication by a monomial, in the frequency domain [2].

Then you create a divisor polynomial by multiplying monomial terms involving powers of the generator.

The idea is to use the Newton basis for intermediate computations: first perform a Newton interpolation, then perform a conversion from the Newton basis to the monomial basis.

You don't have to talk about integrating higher degree polynomials, because a polynomial is just a sum of monomials, and you just end up integrating monomials over and over again.

Another application of arbitrary-length sequences is storing sparse multivariable polynomials as maps from monomials to coefficients.