[tc4v]

good article, but I am very bother by the "standard basis"... it's called canonical in math. I don't think standard is the right name in any context.

[LegionMammal978]

If you treat the ring of polynomials as a vector space in their coefficients, then the unit monomials 1, x, x^2, etc. form the standard basis of that vector space. Wikipedia has an example of "standard basis" in this sense [0].

[0] https://en.wikipedia.org/wiki/Standard_basis#Generalizations