From 2fa1ab68eb30ef4c25e935de9b55f1cd1a617b49 Mon Sep 17 00:00:00 2001 From: Jackson Walters Date: Fri, 5 Apr 2024 20:43:25 -0400 Subject: [PATCH] add commentary explaining the DFT in this case remove form from argument --- src/sage/combinat/symmetric_group_algebra.py | 5 ++++- 1 file changed, 4 insertions(+), 1 deletion(-) diff --git a/src/sage/combinat/symmetric_group_algebra.py b/src/sage/combinat/symmetric_group_algebra.py index 8cdeba4c474..c2549728256 100644 --- a/src/sage/combinat/symmetric_group_algebra.py +++ b/src/sage/combinat/symmetric_group_algebra.py @@ -1945,11 +1945,14 @@ def _dft_modular(self): """ Return the discrete Foruier transform when the characteristic divides the order of the group. See [Mur1983]_ for contrstruction of central primitive orthogonal idempotents. + For each idempotent e_i we have a projection v |--> v*e_i. This is a homomorphism. + We choose a basis for each submodule spanning by {\sigma*e_i | \sigma \in S_n}. + The change-of-basis from the standard basis {\sigma}_\sigma is returned. EXAMPLES:: sage: GF2S3 = SymmetricGroupAlgebra(GF(2),3) - sage: GF2S3.dft(form="modular") + sage: GF2S3.dft() [1 0 0 0 1 0] [0 1 0 0 0 1] [0 0 1 0 0 1]