From 6ae3f4f1ecf5707621b3fadf8ba586826014df27 Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Tue, 3 Mar 2026 22:10:16 -0500 Subject: [PATCH] mjo/clan/jordan_spin_clan.py: fix the clan product I forgot a "2", and now that it's there we can verify the homogeneous polynomials D(0) and D(1). --- mjo/clan/jordan_spin_clan.py | 17 ++++++++++++++++- 1 file changed, 16 insertions(+), 1 deletion(-) diff --git a/mjo/clan/jordan_spin_clan.py b/mjo/clan/jordan_spin_clan.py index 12282f9..5d836d0 100644 --- a/mjo/clan/jordan_spin_clan.py +++ b/mjo/clan/jordan_spin_clan.py @@ -18,6 +18,21 @@ class JordanSpinClan(NormalDecomposition): sage: from mjo.clan.jordan_spin_clan import JordanSpinClan + EXAMPLES: + + The ``D`` polynomials for this clan are given by Gindikin on page + 90. We verify them for one example:: + + sage: C = JordanSpinClan(7) + sage: x = C.from_vector(vector(QQ,[1,2,3,4,5,6,7])) + sage: x21 = x.to_vector()[1:-1] + sage: x22 = x.to_vector()[-1] + sage: x11 = x.to_vector()[0] + sage: x.D(0) == x11 + True + sage: x.D(1) == x11*x22 - x21.inner_product(x21) + True + TESTS: Verifying the axioms:: @@ -82,7 +97,7 @@ class JordanSpinClan(NormalDecomposition): V = x.parent() z11 = x11*y11 z21 = y_bar*(x11 + x22)/two + y11*x_bar - z22 = x22*y22 + x_bar.inner_product(y_bar) + z22 = x22*y22 + 2*x_bar.inner_product(y_bar) z_coords = [z11] + list(z21) + [z22] return RN.from_vector(V(z_coords)) -- 2.51.0