Despite the fact that the Hamming weight is large, because of the ease of representation and other improvements there are efficient implementations in areas such as coding theory and cryptography
The degree of a term in a polynomial is the sum of all of the exponents on the variables in that term, where a variable with no exponent is understood to have an exponent of 1.
In knot theory the Alexander polynomial, the Jones polynomial, and the HOMFLY polynomial are important knot invariants.
Technically, an Alexander polynomial is a generator of a principal Alexander ideal related to the homology of the infinitely cyclic cover of a knot complement—where all the emphasised phrases have particular mathematical meanings.
(this is an Alexander polynomial of the knot).
HOMFLYPT is a binary (two-variable) polynomial, with as with the predecessors.
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