eja: fix ComplexHermitianEJA over AA and RR.

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

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index c131c5f6b612a6ffcae8e1d3357264e5f016176e..359b7404a6fe5d003151e1e82d6c78090b0ea9f6 100644 (file)
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -17,7 +17,7 @@ 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 NumberField, QuadraticField
+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
@@ -910,7 +910,7 @@ class MatrixEuclideanJordanAlgebra(FiniteDimensionalEuclideanJordanAlgebra):
             z = R.gen()
             p = z**2 - 2
             if p.is_irreducible():
-                field = NumberField(p, 'sqrt2', embedding=RLF(2).sqrt())
+                field = field.extension(p, 'sqrt2', embedding=RLF(2).sqrt())
                 basis = tuple( s.change_ring(field) for s in basis )
             self._basis_normalizers = tuple(
                 ~(self.natural_inner_product(s,s).sqrt()) for s in basis )
@@ -1020,6 +1020,7 @@ class MatrixEuclideanJordanAlgebra(FiniteDimensionalEuclideanJordanAlgebra):
         Xu = cls.real_unembed(X)
         Yu = cls.real_unembed(Y)
         tr = (Xu*Yu).trace()
+
         if tr in RLF:
             # It's real already.
             return tr
@@ -1074,6 +1075,14 @@ class RealSymmetricEJA(RealMatrixEuclideanJordanAlgebra, KnownRankEJA):
         sage: e2*e2
         e2
 
+    In theory, our "field" can be any subfield of the reals::
+
+        sage: RealSymmetricEJA(2, AA)
+        Euclidean Jordan algebra of dimension 3 over Algebraic Real Field
+        sage: RealSymmetricEJA(2, RR)
+        Euclidean Jordan algebra of dimension 3 over Real Field with
+        53 bits of precision
+
     TESTS:
 
     The dimension of this algebra is `(n^2 + n) / 2`::
@@ -1214,15 +1223,17 @@ 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
@@ -1263,10 +1274,12 @@ class ComplexMatrixEuclideanJordanAlgebra(MatrixEuclideanJordanAlgebra):
         if not n.mod(2).is_zero():
             raise ValueError("the matrix 'M' must be a complex embedding")
 
-        field = QQ
+        # If "M" was normalized, its base ring might have roots
+        # adjoined and they can stick around after unembedding.
+        field = M.base_ring()
         R = PolynomialRing(field, 'z')
         z = R.gen()
-        F = NumberField(z**2 + 1,'i', embedding=CLF(-1).sqrt())
+        F = field.extension(z**2 + 1, 'i', embedding=CLF(-1).sqrt())
         i = F.gen()
 
         # Go top-left to bottom-right (reading order), converting every
@@ -1327,6 +1340,16 @@ 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`::
@@ -1403,9 +1426,9 @@ class ComplexHermitianEJA(ComplexMatrixEuclideanJordanAlgebra, KnownRankEJA):
             True
 
         """
-        R = PolynomialRing(QQ, 'z')
+        R = PolynomialRing(field, 'z')
         z = R.gen()
-        F = NumberField(z**2 + 1, 'I', embedding=CLF(-1).sqrt())
+        F = field.extension(z**2 + 1, 'I')
         I = F.gen()
 
         # This is like the symmetric case, but we need to be careful:
@@ -1540,7 +1563,7 @@ class QuaternionMatrixEuclideanJordanAlgebra(MatrixEuclideanJordanAlgebra):
         if M.ncols() != n:
             raise ValueError("the matrix 'M' must be square")
         if not n.mod(4).is_zero():
-            raise ValueError("the matrix 'M' must be a complex embedding")
+            raise ValueError("the matrix 'M' must be a quaternion embedding")
 
         # Use the base ring of the matrix to ensure that its entries can be
         # multiplied by elements of the quaternion algebra.