polynomial basis

Definitions

1. 1

   A basis of a polynomial ring (said ring being viewed either as a vector space over the…

   A basis of a polynomial ring (said ring being viewed either as a vector space over the field of coefficients or as a free module over the ring of coefficients).

2. 2

   Specifically, a basis, of the form {1, α, ..., αⁿ⁻¹}, of a finite extension F_(qⁿ) of a…

   Specifically, a basis, of the form {1, α, ..., αⁿ⁻¹}, of a finite extension F_(qⁿ) of a Galois field F_q, where α is a primitive element of F_(qⁿ) (i.e., a root of a degree-n primitive polynomial over F_q).

   • When using polynomial bases, the first stage in computing the product of two elements of #92;mathbbF#95;#123;2ⁿ#125; is the multiplication of two polynomials of degree at most n-1 in #92;mathbbF#95;2#91;x#93;.

The neighborhood

• neighborBernstein basis polynomial
• neighbordual basis
• neighbormonomial
• neighbornormal basis