eja: fix inclusions/projections with trivial algebras.

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

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index de12bb10604094e9b90ffb89a335514c4811d2aa..739bff334c5aa2069dbf09244e7a7fa39ceaccb3 100644 (file)
--- a/mjo/eja/eja_element.py
+++ b/mjo/eja/eja_element.py
@@ -1,5 +1,3 @@
-# -*- coding: utf-8 -*-
-

 from sage.matrix.constructor import matrix
 from sage.modules.free_module import VectorSpace
 from sage.modules.with_basis.indexed_element import IndexedFreeModuleElement
 from sage.matrix.constructor import matrix
 from sage.modules.free_module import VectorSpace
 from sage.modules.with_basis.indexed_element import IndexedFreeModuleElement


@@ -183,7 +181,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             True
 
         """
             True
 
         """

-        p = self.parent().characteristic_polynomial()
+        p = self.parent().characteristic_polynomial_of()

         return p(*self.to_vector())
 
 
         return p(*self.to_vector())
 
 


@@ -525,6 +523,11 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         whether or not the paren't algebra's zero element is a root
         of this element's minimal polynomial.
 
         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.
 
         Beware that we can't use the superclass method, because it
         relies on the algebra being associative.
 


@@ -555,6 +558,11 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             else:
                 return False
 
             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()
         # 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()


@@ -796,8 +804,9 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
 
             sage: set_random_seed()
             sage: J = JordanSpinEJA.random_instance()
 
             sage: set_random_seed()
             sage: J = JordanSpinEJA.random_instance()

+            sage: n = J.dimension()

             sage: x = J.random_element()
             sage: x = J.random_element()

-            sage: x == x.coefficient(0)*J.one() or x.degree() == 2
+            sage: x.degree() == min(n,2) or (x == x.coefficient(0)*J.one())

             True
 
         TESTS:
             True
 
         TESTS:


@@ -904,7 +913,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         two here so that said elements actually exist::
 
             sage: set_random_seed()
         two here so that said elements actually exist::
 
             sage: set_random_seed()

-            sage: n_max = max(2, JordanSpinEJA._max_test_case_size())
+            sage: n_max = max(2, JordanSpinEJA._max_random_instance_size())

             sage: n = ZZ.random_element(2, n_max)
             sage: J = JordanSpinEJA(n)
             sage: y = J.random_element()
             sage: n = ZZ.random_element(2, n_max)
             sage: J = JordanSpinEJA(n)
             sage: y = J.random_element()


@@ -930,7 +939,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         and in particular, a re-scaling of the basis::
 
             sage: set_random_seed()
         and in particular, a re-scaling of the basis::
 
             sage: set_random_seed()

-            sage: n_max = RealSymmetricEJA._max_test_case_size()
+            sage: n_max = RealSymmetricEJA._max_random_instance_size()

             sage: n = ZZ.random_element(1, n_max)
             sage: J1 = RealSymmetricEJA(n)
             sage: J2 = RealSymmetricEJA(n,normalize_basis=False)
             sage: n = ZZ.random_element(1, n_max)
             sage: J1 = RealSymmetricEJA(n)
             sage: J2 = RealSymmetricEJA(n,normalize_basis=False)


@@ -954,7 +963,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
                 # in the "normal" case without us having to think about it.
                 return self.operator().minimal_polynomial()
 
                 # in the "normal" case without us having to think about it.
                 return self.operator().minimal_polynomial()
 

-        A = self.subalgebra_generated_by()
+        A = self.subalgebra_generated_by(orthonormalize_basis=False)

         return A(self).operator().minimal_polynomial()
 
 
         return A(self).operator().minimal_polynomial()
 
 


@@ -1009,6 +1018,10 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         """
         B = self.parent().natural_basis()
         W = self.parent().natural_basis_space()
         """
         B = self.parent().natural_basis()
         W = self.parent().natural_basis_space()

+
+        # This is just a manual "from_vector()", but of course
+        # matrix spaces aren't vector spaces in sage, so they
+        # don't have a from_vector() method.

         return W.linear_combination(zip(B,self.to_vector()))
 
 
         return W.linear_combination(zip(B,self.to_vector()))
 
 


@@ -1085,16 +1098,18 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             sage: set_random_seed()
             sage: x = JordanSpinEJA.random_instance().random_element()
             sage: x_vec = x.to_vector()
             sage: set_random_seed()
             sage: x = JordanSpinEJA.random_instance().random_element()
             sage: x_vec = x.to_vector()

+            sage: Q = matrix.identity(x.base_ring(), 0)

             sage: n = x_vec.degree()
             sage: n = x_vec.degree()

-            sage: x0 = x_vec[0]
-            sage: x_bar = x_vec[1:]
-            sage: A = matrix(AA, 1, [x_vec.inner_product(x_vec)])
-            sage: B = 2*x0*x_bar.row()
-            sage: C = 2*x0*x_bar.column()
-            sage: D = matrix.identity(AA, n-1)
-            sage: D = (x0^2 - x_bar.inner_product(x_bar))*D
-            sage: D = D + 2*x_bar.tensor_product(x_bar)
-            sage: Q = matrix.block(2,2,[A,B,C,D])
+            sage: if n > 0:
+            ....:     x0 = x_vec[0]
+            ....:     x_bar = x_vec[1:]
+            ....:     A = matrix(x.base_ring(), 1, [x_vec.inner_product(x_vec)])
+            ....:     B = 2*x0*x_bar.row()
+            ....:     C = 2*x0*x_bar.column()
+            ....:     D = matrix.identity(x.base_ring(), n-1)
+            ....:     D = (x0^2 - x_bar.inner_product(x_bar))*D
+            ....:     D = D + 2*x_bar.tensor_product(x_bar)
+            ....:     Q = matrix.block(2,2,[A,B,C,D])

             sage: Q == x.quadratic_representation().matrix()
             True
 
             sage: Q == x.quadratic_representation().matrix()
             True
 


@@ -1252,7 +1267,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             sage: (J0, J5, J1) = J.peirce_decomposition(c1)
             sage: (f0, f1, f2) = J1.gens()
             sage: f0.spectral_decomposition()
             sage: (J0, J5, J1) = J.peirce_decomposition(c1)
             sage: (f0, f1, f2) = J1.gens()
             sage: f0.spectral_decomposition()

-            [(0, 1.000000000000000?*f2), (1, 1.000000000000000?*f0)]
+            [(0, f2), (1, f0)]

 
         """
         A = self.subalgebra_generated_by(orthonormalize_basis=True)
 
         """
         A = self.subalgebra_generated_by(orthonormalize_basis=True)