eja: use fuzzy equality test with inexact base rings.

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

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index 562797318646cb1dd837691f846fd114b44ec131..7f7b1f9f1c09703a2d8f48e295b203604fa5556c 100644 (file)
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -61,7 +61,10 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule):
         """
         SETUP::
 
-            sage: from mjo.eja.eja_algebra import (JordanSpinEJA, random_eja)
+            sage: from mjo.eja.eja_algebra import (
+            ....:   FiniteDimensionalEuclideanJordanAlgebra,
+            ....:   JordanSpinEJA,
+            ....:   random_eja)
 
         EXAMPLES:
 
@@ -75,13 +78,20 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule):
 
         TESTS:
 
-        The ``field`` we're given must be real::
+        The ``field`` we're given must be real with ``check=True``::
 
             sage: JordanSpinEJA(2,QQbar)
             Traceback (most recent call last):
             ...
             ValueError: field is not real
 
+        The multiplication table must be square with ``check=True``::
+
+            sage: FiniteDimensionalEuclideanJordanAlgebra(QQ,((),()))
+            Traceback (most recent call last):
+            ...
+            ValueError: multiplication table is not square
+
         """
         if check:
             if not field.is_subring(RR):
@@ -98,6 +108,9 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule):
 
         # The multiplication table had better be square
         n = len(mult_table)
+        if check:
+            if not all( len(l) == n for l in mult_table ):
+                raise ValueError("multiplication table is not square")
 
         fda = super(FiniteDimensionalEuclideanJordanAlgebra, self)
         fda.__init__(field,
@@ -283,14 +296,26 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule):
         this algebra was constructed with ``check=False`` and passed
         an invalid multiplication table.
         """
+
+        # Used to check whether or not something is zero in an inexact
+        # ring. This number is sufficient to allow the construction of
+        # QuaternionHermitianEJA(2, RDF) with check=True.
+        epsilon = 1e-16
+
         for i in range(self.dimension()):
             for j in range(self.dimension()):
                 for k in range(self.dimension()):
                     x = self.monomial(i)
                     y = self.monomial(j)
                     z = self.monomial(k)
-                    if (x*y).inner_product(z) != x.inner_product(y*z):
-                        return False
+                    diff = (x*y).inner_product(z) - x.inner_product(y*z)
+
+                    if self.base_ring().is_exact():
+                        if diff != 0:
+                            return False
+                    else:
+                        if diff.abs() > epsilon:
+                            return False
 
         return True