# G-circulant matrices

Dear the community,

I wonder whether there is a built-in library/function for $G$-circulant matrices in SAGE? Here $G$ is a group and a matrix $A$ is called $G$-circulant if $A$ has the form $A=(a_{ \tau^{-1} \sigma})_{\tau, \sigma \in G}$. Please see [1] for further details.

When $G=\mathbb{Z}/n$, SAGE has a built-in library/function. Namely, given a vector $v$ of length $n$, we can generate a circulant matrix with the first row equal to $v$ using the following code

matrix.circulant(v)

Thank you for your help!

[1] Kanemitsu, Shigeru, and Michel Waldschmidt. "Matrices of finite abelian groups, finite Fourier transform and codes, Proc. 6th China-Japan Sem. Number Theory, World Sci. London-Singapore-New Jersey (2013): 90-106.