eja: drop a pointless "solve" in the EJA charpoly system.

[sage.d.git] / mjo / eja / eja_algebra.py

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index 39703dd1b65d416865af044f41164e6ac4c3ee48..c35bf256453cfa9a3758c034a47a043745eb0c2b 100644 (file)
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -1101,6 +1101,21 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
         r"""
         The `r` polynomial coefficients of the "characteristic polynomial
         of" function.
+
+        SETUP::
+
+            sage: from mjo.eja.eja_algebra import random_eja
+
+        TESTS:
+
+        The theory shows that these are all homogeneous polynomials of
+        a known degree::
+
+            sage: set_random_seed()
+            sage: J = random_eja()
+            sage: all(p.is_homogeneous() for p in J._charpoly_coefficients())
+            True
+
         """
         n = self.dimension()
         R = self.coordinate_polynomial_ring()
@@ -1136,10 +1151,17 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
 
         # The theory says that only the first "r" coefficients are
         # nonzero, and they actually live in the original polynomial
-        # ring and not the fraction field. We negate them because
-        # in the actual characteristic polynomial, they get moved
-        # to the other side where x^r lives.
-        return -A_rref.solve_right(E*b).change_ring(R)[:r]
+        # ring and not the fraction field. We negate them because in
+        # the actual characteristic polynomial, they get moved to the
+        # other side where x^r lives. We don't bother to trim A_rref
+        # down to a square matrix and solve the resulting system,
+        # because the upper-left r-by-r portion of A_rref is
+        # guaranteed to be the identity matrix, so e.g.
+        #
+        #   A_rref.solve_right(Y)
+        #
+        # would just be returning Y.
+        return (-E*b)[:r].change_ring(R)
 
     @cached_method
     def rank(self):
@@ -1200,7 +1222,7 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
 
             sage: set_random_seed()    # long time
             sage: J = random_eja()     # long time
-            sage: caches = J.rank()    # long time
+            sage: cached = J.rank()    # long time
             sage: J.rank.clear_cache() # long time
             sage: J.rank() == cached   # long time
             True