Gauss Numbers

GaussNumber(n, v) : RngIntElt, RngElt -> RngElt

Given an integer n and a ring element v, this function returns the Gauss number corresponding to n with parameter v, i.e., the element [n]_v = v^{n - 1} + v^{n - 3} + ... + v ^{- n + 3} + v ^{- n + 1}.

GaussianFactorial(n, v) : RngIntElt, RngElt -> RngElt

Given an integer n and a ring element v, this function returns the Gaussian factorial corresponding to n with parameter v, i.e., the element [n]_v! = [n]_v[n - 1]_v ... [1]_v.

GaussianBinomial(n, k, v) : RngIntElt, RngIntElt, RngElt -> RngElt

Given an integer n, an integer k and a ring element v, this function returns the Gaussian binomial n choose k with parameter v, i.e., the element [n]_v!/([k]_v![n - k]_v!).

> F<q>:= RationalFunctionField(Rationals());
> GaussianBinomial(5, 3, q^2);
(q^24 + q^20 + 2*q^16 + 2*q^12 + 2*q^8 + q^4 + 1)/q^12