eja: fix an implicit TODO by eliminating lazy_import.

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

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index a5880c4c4c3fc083726fbf2adcef6ee071e7cd63..120870b7fa08b1ee0fcb936b92c62a9470a27754 100644 (file)
--- a/mjo/eja/eja_element.py
+++ b/mjo/eja/eja_element.py
@@ -2,11 +2,6 @@ from sage.matrix.constructor import matrix
 from sage.modules.free_module import VectorSpace
 from sage.modules.with_basis.indexed_element import IndexedFreeModuleElement
 
-# TODO: make this unnecessary somehow.
-from sage.misc.lazy_import import lazy_import
-lazy_import('mjo.eja.eja_algebra', 'FiniteDimensionalEuclideanJordanAlgebra')
-lazy_import('mjo.eja.eja_element_subalgebra',
-            'FiniteDimensionalEuclideanJordanElementSubalgebra')
 from mjo.eja.eja_operator import FiniteDimensionalEuclideanJordanAlgebraOperator
 from mjo.eja.eja_utils import _mat2vec
 
@@ -507,6 +502,14 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         if not self.is_invertible():
             raise ValueError("element is not invertible")
 
+        if self.parent()._charpoly_coefficients.is_in_cache():
+            # We can invert using our charpoly if it will be fast to
+            # compute. If the coefficients are cached, our rank had
+            # better be too!
+            r = self.parent().rank()
+            a = self.characteristic_polynomial().coefficients(sparse=False)
+            return (-1)**(r+1)*sum(a[i+1]*self**i for i in range(r))/self.det()
+
         return (~self.quadratic_representation())(self)
 
 
@@ -523,6 +526,11 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         whether or not the paren't algebra's zero element is a root
         of this element's minimal polynomial.
 
+        That is... unless the coefficients of our algebra's
+        "characteristic polynomial of" function are already cached!
+        In that case, we just use the determinant (which will be fast
+        as a result).
+
         Beware that we can't use the superclass method, because it
         relies on the algebra being associative.
 
@@ -553,6 +561,11 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             else:
                 return False
 
+        if self.parent()._charpoly_coefficients.is_in_cache():
+            # The determinant will be quicker than computing the minimal
+            # polynomial from scratch, most likely.
+            return (not self.det().is_zero())
+
         # In fact, we only need to know if the constant term is non-zero,
         # so we can pass in the field's zero element instead.
         zero = self.base_ring().zero()
@@ -1313,6 +1326,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             True
 
         """
+        from mjo.eja.eja_element_subalgebra import FiniteDimensionalEuclideanJordanElementSubalgebra
         return FiniteDimensionalEuclideanJordanElementSubalgebra(self, orthonormalize_basis)