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 = vn - 1 + vn - 3 + ... + v - n + 3 + v - n + 1.
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.
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
V2.28, 13 July 2023