X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_element.py;h=eee8f69bd76ddfba49e3cb4531f55d0e970ebd1d;hb=bbd6d4c6e39870b0936949b510e70af2b5358f9e;hp=5944c0779a8b7a63b1fa41897947cef4dbee83bb;hpb=5cbb93016e4b192d2a2d7be81014a55a33c9a8f9;p=sage.d.git diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py index 5944c07..eee8f69 100644 --- a/mjo/eja/eja_element.py +++ b/mjo/eja/eja_element.py @@ -1,3 +1,5 @@ +# -*- coding: utf-8 -*- + from itertools import izip from sage.matrix.constructor import matrix @@ -34,7 +36,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement): Return ``self`` raised to the power ``n``. Jordan algebras are always power-associative; see for - example Faraut and Koranyi, Proposition II.1.2 (ii). + example Faraut and Korányi, Proposition II.1.2 (ii). We have to override this because our superclass uses row vectors instead of column vectors! We, on the other hand, @@ -375,7 +377,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement): True Ensure that the determinant is multiplicative on an associative - subalgebra as in Faraut and Koranyi's Proposition II.2.2:: + subalgebra as in Faraut and Korányi's Proposition II.2.2:: sage: set_random_seed() sage: J = random_eja().random_element().subalgebra_generated_by() @@ -460,7 +462,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement): ... ValueError: element is not invertible - Proposition II.2.3 in Faraut and Koranyi says that the inverse + Proposition II.2.3 in Faraut and Korányi says that the inverse of an element is the inverse of its left-multiplication operator applied to the algebra's identity, when that inverse exists::