From abf218ab52a3b2c644597309e59a9a723a5ab7e3 Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Mon, 24 Jun 2019 14:05:41 -0400 Subject: [PATCH] eja/euclidean_jordan_algebra.py: add subalgebra_generated_by() method. --- mjo/eja/euclidean_jordan_algebra.py | 32 +++++++++++++++++++++++++++++ 1 file changed, 32 insertions(+) diff --git a/mjo/eja/euclidean_jordan_algebra.py b/mjo/eja/euclidean_jordan_algebra.py index 8487e0e..097233f 100644 --- a/mjo/eja/euclidean_jordan_algebra.py +++ b/mjo/eja/euclidean_jordan_algebra.py @@ -108,6 +108,38 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra): return self.span_of_powers().dimension() + def subalgebra_generated_by(self): + """ + Return the subalgebra of the parent EJA generated by this element. + """ + # First get the subspace spanned by the powers of myself... + V = self.span_of_powers() + F = self.base_ring() + + # Now figure out the entries of the right-multiplication + # matrix for the successive basis elements b0, b1,... of + # that subspace. + mats = [] + for b_right in V.basis(): + eja_b_right = self.parent()(b_right) + b_right_rows = [] + # The first row of the right-multiplication matrix by + # b1 is what we get if we apply that matrix to b1. The + # second row of the right multiplication matrix by b1 + # is what we get when we apply that matrix to b2... + for b_left in V.basis(): + eja_b_left = self.parent()(b_left) + # Multiply in the original EJA, but then get the + # coordinates from the subalgebra in terms of its + # basis. + this_row = V.coordinates((eja_b_left*eja_b_right).vector()) + b_right_rows.append(this_row) + b_right_matrix = matrix(F, b_right_rows) + mats.append(b_right_matrix) + + return FiniteDimensionalEuclideanJordanAlgebra(F, mats) + + def minimal_polynomial(self): return self.matrix().minimal_polynomial() -- 2.44.2