From: Michael Orlitzky <michael@orlitzky.com>
Date: Sun, 29 Jan 2023 21:38:45 +0000 (-0500)
Subject: eja: write the ALGORITHM block for the degree of an element.
X-Git-Url: http://gitweb.michael.orlitzky.com/?p=sage.d.git;a=commitdiff_plain;h=6957e7f70a89c4ddcc5d9148e1833188ccd7353d

eja: write the ALGORITHM block for the degree of an element.
---

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index e1ea609..ef63704 100644
--- a/mjo/eja/eja_element.py
+++ b/mjo/eja/eja_element.py
@@ -795,7 +795,23 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
 
         ALGORITHM:
 
-        .........
+        First we handle the special cases where the algebra is
+        trivial, this element is zero, or the dimension of the algebra
+        is one and this element is not zero. With those out of the
+        way, we may assume that ``self`` is nonzero, the algebra is
+        nontrivial, and that the dimension of the algebra is at least
+        two.
+
+        Beginning with the algebra's unit element (power zero), we add
+        successive (basis representations of) powers of this element
+        to a matrix, row-reducing at each step. After row-reducing, we
+        check the rank of the matrix. If adding a row and row-reducing
+        does not increase the rank of the matrix at any point, the row
+        we've just added lives in the span of the previous ones; thus
+        the corresponding power of ``self`` lives in the span of its
+        lesser powers. When that happens, the degree of the minimal
+        polynomial is the rank of the matrix; if it never happens, the
+        degree must be the dimension of the entire space.
 
         SETUP::
 
@@ -838,7 +854,6 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
             sage: x = random_eja().random_element()
             sage: x.degree() == x.minimal_polynomial().degree()
             True
-
         """
         n = self.parent().dimension()