From 6efdc5031a3ae89c16a3184750fb7cf7e26b5fb9 Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Fri, 23 Apr 2021 11:59:05 -0400 Subject: [PATCH] eja: factor out the operator polynomial-matrix construction. --- mjo/eja/eja_algebra.py | 67 +++++++++++++++++++++++++++++++++++++----- 1 file changed, 59 insertions(+), 8 deletions(-) diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py index c0dc408..dd1bcf2 100644 --- a/mjo/eja/eja_algebra.py +++ b/mjo/eja/eja_algebra.py @@ -1518,6 +1518,64 @@ class FiniteDimensionalEJA(CombinatorialFreeModule): for idx in range(count) ) + def operator_polynomial_matrix(self): + r""" + Return the matrix of polynomials (over this algebra's + :meth:`coordinate_polynomial_ring`) that, when evaluated at + the basis coordinates of an element `x`, produces the basis + representation of `L_{x}`. + + SETUP:: + + sage: from mjo.eja.eja_algebra import (HadamardEJA, + ....: JordanSpinEJA) + + EXAMPLES:: + + sage: J = HadamardEJA(4) + sage: L_x = J.operator_polynomial_matrix() + sage: L_x + [X0 0 0 0] + [ 0 X1 0 0] + [ 0 0 X2 0] + [ 0 0 0 X3] + sage: x = J.one() + sage: d = zip(J.coordinate_polynomial_ring().gens(), x.to_vector()) + sage: L_x.subs(dict(d)) + [1 0 0 0] + [0 1 0 0] + [0 0 1 0] + [0 0 0 1] + + :: + + sage: J = JordanSpinEJA(4) + sage: L_x = J.operator_polynomial_matrix() + sage: L_x + [X0 X1 X2 X3] + [X1 X0 0 0] + [X2 0 X0 0] + [X3 0 0 X0] + sage: x = J.one() + sage: d = zip(J.coordinate_polynomial_ring().gens(), x.to_vector()) + sage: L_x.subs(dict(d)) + [1 0 0 0] + [0 1 0 0] + [0 0 1 0] + [0 0 0 1] + + """ + R = self.coordinate_polynomial_ring() + + def L_x_i_j(i,j): + # From a result in my book, these are the entries of the + # basis representation of L_x. + return sum( v*self.monomial(k).operator().matrix()[i,j] + for (k,v) in enumerate(R.gens()) ) + + n = self.dimension() + return matrix(R, n, n, L_x_i_j) + @cached_method def _charpoly_coefficients(self): r""" @@ -1541,16 +1599,9 @@ class FiniteDimensionalEJA(CombinatorialFreeModule): """ n = self.dimension() R = self.coordinate_polynomial_ring() - vars = R.gens() F = R.fraction_field() - def L_x_i_j(i,j): - # From a result in my book, these are the entries of the - # basis representation of L_x. - return sum( vars[k]*self.monomial(k).operator().matrix()[i,j] - for k in range(n) ) - - L_x = matrix(F, n, n, L_x_i_j) + L_x = self.operator_polynomial_matrix() r = None if self.rank.is_in_cache(): -- 2.44.2