From 884b2015690a50a12f99852ea82c399309164f22 Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Wed, 4 Nov 2020 10:14:34 -0500 Subject: [PATCH] eja: remove more vestigial charpoly stuff. --- mjo/eja/eja_algebra.py | 60 ------------------------------------------ 1 file changed, 60 deletions(-) diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py index 2b769ac..fc64510 100644 --- a/mjo/eja/eja_algebra.py +++ b/mjo/eja/eja_algebra.py @@ -235,66 +235,6 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule): def product_on_basis(self, i, j): return self._multiplication_table[i][j] - def _a_regular_element(self): - """ - Guess a regular element. Needed to compute the basis for our - characteristic polynomial coefficients. - - SETUP:: - - sage: from mjo.eja.eja_algebra import random_eja - - TESTS: - - Ensure that this hacky method succeeds for every algebra that we - know how to construct:: - - sage: set_random_seed() - sage: J = random_eja() - sage: J._a_regular_element().is_regular() - True - - """ - gs = self.gens() - z = self.sum( (i+1)*gs[i] for i in range(len(gs)) ) - if not z.is_regular(): - raise ValueError("don't know a regular element") - return z - - - @cached_method - def _charpoly_basis_space(self): - """ - Return the vector space spanned by the basis used in our - characteristic polynomial coefficients. This is used not only to - compute those coefficients, but also any time we need to - evaluate the coefficients (like when we compute the trace or - determinant). - """ - z = self._a_regular_element() - # Don't use the parent vector space directly here in case this - # happens to be a subalgebra. In that case, we would be e.g. - # two-dimensional but span_of_basis() would expect three - # coordinates. - V = VectorSpace(self.base_ring(), self.vector_space().dimension()) - basis = [ (z**k).to_vector() for k in range(self.rank()) ] - V1 = V.span_of_basis( basis ) - b = (V1.basis() + V1.complement().basis()) - return V.span_of_basis(b) - - - def _charpoly_coeff(self, i): - """ - Return the coefficient polynomial "a_{i}" of this algebra's - general characteristic polynomial. - - Having this be a separate cached method lets us compute and - store the trace/determinant (a_{r-1} and a_{0} respectively) - separate from the entire characteristic polynomial. - """ - return self._charpoly_coefficients()[i] - - @cached_method def characteristic_polynomial(self): """ -- 2.44.2