From 9a84e870b4ce8e107ae4ff5eb6b9ed0b251bc6cb Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Sun, 15 Feb 2026 11:50:39 -0500 Subject: [PATCH] mjo/clan/clan_element.py: composite det example for the Vinberg clan --- mjo/clan/clan_element.py | 20 +++++++++++++++++++- 1 file changed, 19 insertions(+), 1 deletion(-) diff --git a/mjo/clan/clan_element.py b/mjo/clan/clan_element.py index bd481ea..eedf481 100644 --- a/mjo/clan/clan_element.py +++ b/mjo/clan/clan_element.py @@ -260,7 +260,7 @@ class NormalDecompositionElement(ClanElement): SETUP:: - sage: from mjo.clan.unital_clan import SnClan + sage: from mjo.clan.unital_clan import SnClan, VinbergClan EXAMPLES: @@ -291,6 +291,24 @@ class NormalDecompositionElement(ClanElement): sage: phi(X).D(2) 8 + In the Vinberg clan (Ishi, p. 169) we see that the composite + determinant is the product of the determinants of the two + matrices that make up an element. Our results agree with + that:: + + sage: C = VinbergClan() + sage: A = matrix(QQ, [ [2, 1], + ....: [1, 4] ]) + sage: B = matrix(QQ, [ [2, 2], + ....: [2,-1] ]) + sage: A.det() + 7 + sage: B.det() + -6 + sage: x = C.from_matrices(A, B) + sage: x.D(C.rank() - 1) + -42 + """ # The sum() hijinks avoid needing to know what the third # coordinate is. -- 2.51.0