eja: use NumberField instead of QuadraticField everywhere.

This will be more extensible when we need a field containing both
sqrt(2) and sqrt(-1). QuadraticField can't handle that, so we have to
use NumberField anyway at that point. Might as well get it out of the
way.

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index 992174e45b763e95677588beee2787859c0e64b1..12166267cd34410e0a03616a4b2ad5c7f5b8c105 100644 (file)
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -15,9 +15,10 @@ 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.number_field.number_field import NumberField
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 from sage.rings.rational_field import QQ
+from sage.rings.real_lazy import CLF
 from sage.structure.element import is_Matrix
 
 from mjo.eja.eja_element import FiniteDimensionalEuclideanJordanAlgebraElement
@@ -851,7 +852,9 @@ def _complex_hermitian_basis(n, field):
         True
 
     """
-    F = QuadraticField(-1, 'I')
+    R = PolynomialRing(field, 'z')
+    z = R.gen()
+    F = NumberField(z**2 + 1, 'I', embedding=CLF(-1).sqrt())
     I = F.gen()
 
     # This is like the symmetric case, but we need to be careful:
@@ -965,7 +968,9 @@ def _embed_complex_matrix(M):
 
     EXAMPLES::
 
-        sage: F = QuadraticField(-1,'i')
+        sage: R = PolynomialRing(QQ, 'z')
+        sage: z = R.gen()
+        sage: F = NumberField(z**2 + 1, 'i', embedding=CLF(-1).sqrt())
         sage: x1 = F(4 - 2*i)
         sage: x2 = F(1 + 2*i)
         sage: x3 = F(-i)
@@ -984,7 +989,9 @@ def _embed_complex_matrix(M):
 
         sage: set_random_seed()
         sage: n = ZZ.random_element(5)
-        sage: F = QuadraticField(-1, 'i')
+        sage: R = PolynomialRing(QQ, 'z')
+        sage: z = R.gen()
+        sage: F = NumberField(z**2 + 1, 'i', embedding=CLF(-1).sqrt())
         sage: X = random_matrix(F, n)
         sage: Y = random_matrix(F, n)
         sage: actual = _embed_complex_matrix(X) * _embed_complex_matrix(Y)
@@ -1031,7 +1038,9 @@ def _unembed_complex_matrix(M):
     Unembedding is the inverse of embedding::
 
         sage: set_random_seed()
-        sage: F = QuadraticField(-1, 'i')
+        sage: R = PolynomialRing(QQ, 'z')
+        sage: z = R.gen()
+        sage: F = NumberField(z**2 + 1, 'i', embedding=CLF(-1).sqrt())
         sage: M = random_matrix(F, 3)
         sage: _unembed_complex_matrix(_embed_complex_matrix(M)) == M
         True
@@ -1043,7 +1052,9 @@ def _unembed_complex_matrix(M):
     if not n.mod(2).is_zero():
         raise ValueError("the matrix 'M' must be a complex embedding")
 
-    F = QuadraticField(-1, 'i')
+    R = PolynomialRing(QQ, 'z')
+    z = R.gen()
+    F = NumberField(z**2 + 1, 'i', embedding=CLF(-1).sqrt())
     i = F.gen()
 
     # Go top-left to bottom-right (reading order), converting every
@@ -1104,7 +1115,9 @@ def _embed_quaternion_matrix(M):
     if M.ncols() != n:
         raise ValueError("the matrix 'M' must be square")
 
-    F = QuadraticField(-1, 'i')
+    R = PolynomialRing(QQ, 'z')
+    z = R.gen()
+    F = NumberField(z**2 + 1, 'i', embedding=CLF(-1).sqrt())
     i = F.gen()
 
     blocks = []
@@ -1277,11 +1290,13 @@ class RealSymmetricEJA(FiniteDimensionalEuclideanJordanAlgebra):
 
     """
     def __init__(self, n, field=QQ, **kwargs):
-        if n > 1 and field is QQ:
+        if n > 1:
             # We'll need sqrt(2) to normalize the basis, and this
             # winds up in the multiplication table, so the whole
             # algebra needs to be over the field extension.
-            field = QuadraticField(2, 'sqrt2')
+            R = PolynomialRing(field, 'z')
+            z = R.gen()
+            field = NumberField(z**2 - 2, 'sqrt2')
 
         S = _real_symmetric_basis(n, field)
         Qs = _multiplication_table_from_matrix_basis(S)