From a811b47129cc0e39d3cb4b5f24504426adff3a88 Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Thu, 25 Feb 2021 16:49:37 -0500 Subject: [PATCH] eja: add some more docs for FDEJA. --- mjo/eja/eja_algebra.py | 47 +++++++++++++++++++++++++----------------- 1 file changed, 28 insertions(+), 19 deletions(-) diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py index 631d695..c6a82ca 100644 --- a/mjo/eja/eja_algebra.py +++ b/mjo/eja/eja_algebra.py @@ -84,25 +84,34 @@ class FiniteDimensionalEJA(CombinatorialFreeModule): INPUT: - - basis -- a tuple of basis elements in "matrix form," which - must be the same form as the arguments to ``jordan_product`` - and ``inner_product``. In reality, "matrix form" can be either - vectors, matrices, or a Cartesian product (ordered tuple) - of vectors or matrices. All of these would ideally be vector - spaces in sage with no special-casing needed; but in reality - we turn vectors into column-matrices and Cartesian products - `(a,b)` into column matrices `(a,b)^{T}` after converting - `a` and `b` themselves. - - - jordan_product -- function of two ``basis`` elements (in - matrix form) that returns their jordan product, also in matrix - form; this will be applied to ``basis`` to compute a - multiplication table for the algebra. - - - inner_product -- function of two ``basis`` elements (in matrix - form) that returns their inner product. This will be applied - to ``basis`` to compute an inner-product table (basically a - matrix) for this algebra. + - ``basis`` -- a tuple; a tuple of basis elements in "matrix + form," which must be the same form as the arguments to + ``jordan_product`` and ``inner_product``. In reality, "matrix + form" can be either vectors, matrices, or a Cartesian product + (ordered tuple) of vectors or matrices. All of these would + ideally be vector spaces in sage with no special-casing + needed; but in reality we turn vectors into column-matrices + and Cartesian products `(a,b)` into column matrices + `(a,b)^{T}` after converting `a` and `b` themselves. + + - ``jordan_product`` -- a function; afunction of two ``basis`` + elements (in matrix form) that returns their jordan product, + also in matrix form; this will be applied to ``basis`` to + compute a multiplication table for the algebra. + + - ``inner_product`` -- a function; a function of two ``basis`` + elements (in matrix form) that returns their inner + product. This will be applied to ``basis`` to compute an + inner-product table (basically a matrix) for this algebra. + + - ``field`` -- a subfield of the reals (default: ``AA``); the scalar + field for the algebra. + + - ``orthonormalize`` -- boolean (default: ``True``); whether or + not to orthonormalize the basis. Doing so is expensive and + generally rules out using the rationals as your ``field``, but + is required for spectral decompositions. + """ Element = FiniteDimensionalEJAElement -- 2.43.2