eja: special subalgebra handling for Cartesian product EJAs.

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

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index afd0f55c103c885315e99bc90afe647262aadfbd..92a7df167a4596504c712cf2117e79568cf7eda9 100644 (file)
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -1,4 +1,4 @@
-"""
+r"""
 Representations and constructions for Euclidean Jordan algebras.
 
 A Euclidean Jordan algebra is a Jordan algebra that has some
@@ -34,12 +34,13 @@ for these simple algebras:
   * :class:`QuaternionHermitianEJA`
   * :class:`OctonionHermitianEJA`
 
-In addition to these, we provide two other example constructions,
+In addition to these, we provide a few other example constructions,
 
   * :class:`JordanSpinEJA`
   * :class:`HadamardEJA`
   * :class:`AlbertEJA`
   * :class:`TrivialEJA`
+  * :class:`ComplexSkewSymmetricEJA`
 
 The Jordan spin algebra is a bilinear form algebra where the bilinear
 form is the identity. The Hadamard EJA is simply a Cartesian product
@@ -1193,7 +1194,7 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
             sage: x = J.random_element()
             sage: J.one()*x == x and x*J.one() == x
             True
-            sage: A = x.subalgebra_generated_by()
+            sage: A = x.subalgebra_generated_by(orthonormalize=False)
             sage: y = A.random_element()
             sage: A.one()*y == y and y*A.one() == y
             True
@@ -1219,7 +1220,7 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
             sage: actual == expected
             True
             sage: x = J.random_element()
-            sage: A = x.subalgebra_generated_by()
+            sage: A = x.subalgebra_generated_by(orthonormalize=False)
             sage: actual = A.one().operator().matrix()
             sage: expected = matrix.identity(A.base_ring(), A.dimension())
             sage: actual == expected
@@ -1447,26 +1448,13 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
         # For a general base ring... maybe we can trust this to do the
         # right thing? Unlikely, but.
         V = self.vector_space()
-        v = V.random_element()
-
-        if self.base_ring() is AA:
-            # The "random element" method of the algebraic reals is
-            # stupid at the moment, and only returns integers between
-            # -2 and 2, inclusive:
-            #
-            #   https://trac.sagemath.org/ticket/30875
-            #
-            # Instead, we implement our own "random vector" method,
-            # and then coerce that into the algebra. We use the vector
-            # space degree here instead of the dimension because a
-            # subalgebra could (for example) be spanned by only two
-            # vectors, each with five coordinates.  We need to
-            # generate all five coordinates.
-            if thorough:
-                v *= QQbar.random_element().real()
-            else:
-                v *= QQ.random_element()
+        if self.base_ring() is AA and not thorough:
+            # Now that AA generates actually random random elements
+            # (post Trac 30875), we only need to de-thorough the
+            # randomness when asked to.
+            V = V.change_ring(QQ)
 
+        v = V.random_element()
         return self.from_vector(V.coordinate_vector(v))
 
     def random_elements(self, count, thorough=False):
@@ -1812,14 +1800,13 @@ class RationalBasisEJA(FiniteDimensionalEJA):
             # Bypass the hijinks if they won't benefit us.
             return super()._charpoly_coefficients()
 
-        # Do the computation over the rationals. The answer will be
-        # the same, because all we've done is a change of basis.
-        # Then, change back from QQ to our real base ring
+        # Do the computation over the rationals.
         a = ( a_i.change_ring(self.base_ring())
               for a_i in self.rational_algebra()._charpoly_coefficients() )
 
-        # Otherwise, convert the coordinate variables back to the
-        # deorthonormalized ones.
+        # Convert our coordinate variables into deorthonormalized ones
+        # and substitute them into the deorthonormalized charpoly
+        # coefficients.
         R = self.coordinate_polynomial_ring()
         from sage.modules.free_module_element import vector
         X = vector(R, R.gens())
@@ -2200,15 +2187,6 @@ class ComplexHermitianEJA(HermitianMatrixEJA, RationalBasisEJA, ConcreteEJA):
         ...
         TypeError: Illegal initializer for algebraic number
 
-    This causes the following error when we try to scale a matrix of
-    complex numbers by an inexact real number::
-
-        sage: ComplexHermitianEJA(2,field=RR)
-        Traceback (most recent call last):
-        ...
-        TypeError: Unable to coerce entries (=(1.00000000000000,
-        -0.000000000000000)) to coefficients in Algebraic Real Field
-
     TESTS:
 
     The dimension of this algebra is `n^2`::
@@ -3438,6 +3416,34 @@ class CartesianProductEJA(FiniteDimensionalEJA):
         return FiniteDimensionalEJAOperator(Ji,self,Ei.matrix())
 
 
+    def subalgebra(self, basis, **kwargs):
+        r"""
+        Create a subalgebra of this algebra from the given basis.
+
+        Only overridden to allow us to use a special Cartesian product
+        subalgebra class.
+
+        SETUP::
+
+            sage: from mjo.eja.eja_algebra import (HadamardEJA,
+            ....:                                  QuaternionHermitianEJA)
+
+        EXAMPLES:
+
+        Subalgebras of Cartesian product EJAs have a different class
+        than those of non-Cartesian-product EJAs::
+
+            sage: J1 = HadamardEJA(2,field=QQ,orthonormalize=False)
+            sage: J2 = QuaternionHermitianEJA(0,field=QQ,orthonormalize=False)
+            sage: J = cartesian_product([J1,J2])
+            sage: K1 = J1.subalgebra((J1.one(),), orthonormalize=False)
+            sage: K = J.subalgebra((J.one(),), orthonormalize=False)
+            sage: K1.__class__ is K.__class__
+            False
+
+        """
+        from mjo.eja.eja_subalgebra import FiniteDimensionalCartesianProductEJASubalgebra
+        return FiniteDimensionalCartesianProductEJASubalgebra(self, basis, **kwargs)
 
 FiniteDimensionalEJA.CartesianProduct = CartesianProductEJA