eja: add "check" parameter to check if our field is real.

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

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index 515e25f9c97de0ae102e8dc6bd7b29db89e39dd0..7a65fabdcfcd4adf9c2369dd7d64da50e17b1bd3 100644 (file)
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -16,12 +16,9 @@ from sage.misc.cachefunc import cached_method
 from sage.misc.prandom import choice
 from sage.misc.table import table
 from sage.modules.free_module import FreeModule, VectorSpace
-from sage.rings.integer_ring import ZZ
-from sage.rings.number_field.number_field import QuadraticField
-from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
-from sage.rings.rational_field import QQ
-from sage.rings.real_lazy import CLF, RLF
-
+from sage.rings.all import (ZZ, QQ, RR, RLF, CLF,
+                            PolynomialRing,
+                            QuadraticField)
 from mjo.eja.eja_element import FiniteDimensionalEuclideanJordanAlgebraElement
 from mjo.eja.eja_utils import _mat2vec
 
@@ -40,11 +37,12 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule):
                  rank,
                  prefix='e',
                  category=None,
-                 natural_basis=None):
+                 natural_basis=None,
+                 check=True):
         """
         SETUP::
 
-            sage: from mjo.eja.eja_algebra import random_eja
+            sage: from mjo.eja.eja_algebra import (JordanSpinEJA, random_eja)
 
         EXAMPLES:
 
@@ -56,7 +54,23 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule):
             sage: x*y == y*x
             True
 
+        TESTS:
+
+        The ``field`` we're given must be real::
+
+            sage: JordanSpinEJA(2,QQbar)
+            Traceback (most recent call last):
+            ...
+            ValueError: field is not real
+
         """
+        if check:
+            if not field.is_subring(RR):
+                # Note: this does return true for the real algebraic
+                # field, and any quadratic field where we've specified
+                # a real embedding.
+                raise ValueError('field is not real')
+
         self._rank = rank
         self._natural_basis = natural_basis
 
@@ -1223,15 +1237,17 @@ class ComplexMatrixEuclideanJordanAlgebra(MatrixEuclideanJordanAlgebra):
         n = M.nrows()
         if M.ncols() != n:
             raise ValueError("the matrix 'M' must be square")
-        field = M.base_ring()
+
+        # We don't need any adjoined elements...
+        field = M.base_ring().base_ring()
+
         blocks = []
         for z in M.list():
-            a = z.vector()[0] # real part, I guess
-            b = z.vector()[1] # imag part, I guess
+            a = z.list()[0] # real part, I guess
+            b = z.list()[1] # imag part, I guess
             blocks.append(matrix(field, 2, [[a,b],[-b,a]]))
 
-        # We can drop the imaginaries here.
-        return matrix.block(field.base_ring(), n, blocks)
+        return matrix.block(field, n, blocks)
 
 
     @staticmethod
@@ -1338,6 +1354,16 @@ class ComplexHermitianEJA(ComplexMatrixEuclideanJordanAlgebra, KnownRankEJA):
 
         sage: from mjo.eja.eja_algebra import ComplexHermitianEJA
 
+    EXAMPLES:
+
+    In theory, our "field" can be any subfield of the reals::
+
+        sage: ComplexHermitianEJA(2, AA)
+        Euclidean Jordan algebra of dimension 4 over Algebraic Real Field
+        sage: ComplexHermitianEJA(2, RR)
+        Euclidean Jordan algebra of dimension 4 over Real Field with
+        53 bits of precision
+
     TESTS:
 
     The dimension of this algebra is `n^2`::
@@ -1623,6 +1649,16 @@ class QuaternionHermitianEJA(QuaternionMatrixEuclideanJordanAlgebra,
 
         sage: from mjo.eja.eja_algebra import QuaternionHermitianEJA
 
+    EXAMPLES:
+
+    In theory, our "field" can be any subfield of the reals::
+
+        sage: QuaternionHermitianEJA(2, AA)
+        Euclidean Jordan algebra of dimension 6 over Algebraic Real Field
+        sage: QuaternionHermitianEJA(2, RR)
+        Euclidean Jordan algebra of dimension 6 over Real Field with
+        53 bits of precision
+
     TESTS:
 
     The dimension of this algebra is `2*n^2 - n`::