eja: use QuadraticField selectively to simplify tests.

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index f7983c857d8fdceffac3dbdfeaa6bf70fd7e811e..05dea56e6c389a25713b0f99d95663c8d2998a0d 100644 (file)
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -15,7 +15,7 @@ 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
+from sage.rings.number_field.number_field import NumberField, 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
@@ -853,9 +853,7 @@ def _complex_hermitian_basis(n, field):
 
         sage: set_random_seed()
         sage: n = ZZ.random_element(1,5)
-        sage: R = PolynomialRing(QQ, 'z')
-        sage: z = R.gen()
-        sage: field = NumberField(z**2 - 2, 'sqrt2', embedding=RLF(2).sqrt())
+        sage: field = QuadraticField(2, 'sqrt2')
         sage: B = _complex_hermitian_basis(n, field)
         sage: all( M.is_symmetric() for M in  B)
         True
@@ -989,9 +987,7 @@ def _embed_complex_matrix(M):
 
     EXAMPLES::
 
-        sage: R = PolynomialRing(QQ, 'z')
-        sage: z = R.gen()
-        sage: F = NumberField(z**2 + 1, 'i', embedding=CLF(-1).sqrt())
+        sage: F = QuadraticField(-1, 'i')
         sage: x1 = F(4 - 2*i)
         sage: x2 = F(1 + 2*i)
         sage: x3 = F(-i)
@@ -1010,9 +1006,7 @@ def _embed_complex_matrix(M):
 
         sage: set_random_seed()
         sage: n = ZZ.random_element(5)
-        sage: R = PolynomialRing(QQ, 'z')
-        sage: z = R.gen()
-        sage: F = NumberField(z**2 + 1, 'i', embedding=CLF(-1).sqrt())
+        sage: F = QuadraticField(-1, 'i')
         sage: X = random_matrix(F, n)
         sage: Y = random_matrix(F, n)
         sage: actual = _embed_complex_matrix(X) * _embed_complex_matrix(Y)
@@ -1059,9 +1053,7 @@ def _unembed_complex_matrix(M):
     Unembedding is the inverse of embedding::
 
         sage: set_random_seed()
-        sage: R = PolynomialRing(QQ, 'z')
-        sage: z = R.gen()
-        sage: F = NumberField(z**2 + 1, 'i', embedding=CLF(-1).sqrt())
+        sage: F = QuadraticField(-1, 'i')
         sage: M = random_matrix(F, 3)
         sage: _unembed_complex_matrix(_embed_complex_matrix(M)) == M
         True
@@ -1137,9 +1129,7 @@ def _embed_quaternion_matrix(M):
     if M.ncols() != n:
         raise ValueError("the matrix 'M' must be square")
 
-    R = PolynomialRing(QQ, 'z')
-    z = R.gen()
-    F = NumberField(z**2 + 1, 'i', embedding=CLF(-1).sqrt())
+    F = QuadraticField(-1, 'i')
     i = F.gen()
 
     blocks = []