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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 = vn - 1 + vn - 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!).

Example AlgQEA_QGrpGauss (H102E1)

> 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

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Version: V2.19 of Mon Dec 17 14:40:36 EST 2012