eja: don't use product_on_basis() implementation details.

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

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index 40b4bcac6583e75f6877260f633d752b6693d8d7..db1e63d1b56ade8d29a33d256ee7e1f2b5e97d31 100644 (file)
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -460,9 +460,7 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
         this algebra was constructed with ``check_axioms=False`` and
         passed an invalid multiplication table.
         """
-        return all( self.product_on_basis(i,j) == self.product_on_basis(i,j)
-                    for i in range(self.dimension())
-                    for j in range(self.dimension()) )
+        return all( x*y == y*x for x in self.gens() for y in self.gens() )
 
     def _is_jordanian(self):
         r"""
@@ -931,7 +929,7 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
 
         # And to each subsequent row, prepend an entry that belongs to
         # the left-side "header column."
-        M += [ [self.gens()[i]] + [ self.product_on_basis(i,j)
+        M += [ [self.gens()[i]] + [ self.gens()[i]*self.gens()[j]
                                     for j in range(n) ]
                for i in range(n) ]
 
@@ -1994,11 +1992,11 @@ class RealSymmetricEJA(ConcreteEJA, RealMatrixEJA):
         if n <= 1:
             associative = True
 
-        super(RealSymmetricEJA, self).__init__(self._denormalized_basis(n),
-                                               self.jordan_product,
-                                               self.trace_inner_product,
-                                               associative=associative,
-                                               **kwargs)
+        super().__init__(self._denormalized_basis(n),
+                         self.jordan_product,
+                         self.trace_inner_product,
+                         associative=associative,
+                         **kwargs)
 
         # TODO: this could be factored out somehow, but is left here
         # because the MatrixEJA is not presently a subclass of the
@@ -2088,7 +2086,7 @@ class ComplexMatrixEJA(MatrixEJA):
             True
 
         """
-        super(ComplexMatrixEJA,cls).real_embed(M)
+        super().real_embed(M)
         n = M.nrows()
 
         # We don't need any adjoined elements...
@@ -2135,7 +2133,7 @@ class ComplexMatrixEJA(MatrixEJA):
             True
 
         """
-        super(ComplexMatrixEJA,cls).real_unembed(M)
+        super().real_unembed(M)
         n = ZZ(M.nrows())
         d = cls.dimension_over_reals()
         F = cls.complex_extension(M.base_ring())
@@ -2287,11 +2285,11 @@ class ComplexHermitianEJA(ConcreteEJA, ComplexMatrixEJA):
         if n <= 1:
             associative = True
 
-        super(ComplexHermitianEJA, self).__init__(self._denormalized_basis(n),
-                                                  self.jordan_product,
-                                                  self.trace_inner_product,
-                                                  associative=associative,
-                                                  **kwargs)
+        super().__init__(self._denormalized_basis(n),
+                         self.jordan_product,
+                         self.trace_inner_product,
+                         associative=associative,
+                         **kwargs)
         # TODO: this could be factored out somehow, but is left here
         # because the MatrixEJA is not presently a subclass of the
         # FDEJA class that defines rank() and one().
@@ -2374,7 +2372,7 @@ class QuaternionMatrixEJA(MatrixEJA):
             True
 
         """
-        super(QuaternionMatrixEJA,cls).real_embed(M)
+        super().real_embed(M)
         quaternions = M.base_ring()
         n = M.nrows()
 
@@ -2429,7 +2427,7 @@ class QuaternionMatrixEJA(MatrixEJA):
             True
 
         """
-        super(QuaternionMatrixEJA,cls).real_unembed(M)
+        super().real_unembed(M)
         n = ZZ(M.nrows())
         d = cls.dimension_over_reals()
 
@@ -2598,11 +2596,11 @@ class QuaternionHermitianEJA(ConcreteEJA, QuaternionMatrixEJA):
         if n <= 1:
             associative = True
 
-        super(QuaternionHermitianEJA, self).__init__(self._denormalized_basis(n),
-                                                     self.jordan_product,
-                                                     self.trace_inner_product,
-                                                     associative=associative,
-                                                     **kwargs)
+        super().__init__(self._denormalized_basis(n),
+                         self.jordan_product,
+                         self.trace_inner_product,
+                         associative=associative,
+                         **kwargs)
 
         # TODO: this could be factored out somehow, but is left here
         # because the MatrixEJA is not presently a subclass of the
@@ -2835,11 +2833,11 @@ class BilinearFormEJA(ConcreteEJA):
         if n <= 2:
             associative = True
 
-        super(BilinearFormEJA, self).__init__(column_basis,
-                                              jordan_product,
-                                              inner_product,
-                                              associative=associative,
-                                              **kwargs)
+        super().__init__(column_basis,
+                         jordan_product,
+                         inner_product,
+                         associative=associative,
+                         **kwargs)
 
         # The rank of this algebra is two, unless we're in a
         # one-dimensional ambient space (because the rank is bounded
@@ -2944,7 +2942,7 @@ class JordanSpinEJA(BilinearFormEJA):
 
         # But also don't pass check_field=False here, because the user
         # can pass in a field!
-        super(JordanSpinEJA, self).__init__(B, **kwargs)
+        super().__init__(B, **kwargs)
 
     @staticmethod
     def _max_random_instance_size():
@@ -3002,11 +3000,11 @@ class TrivialEJA(ConcreteEJA):
         if "orthonormalize" not in kwargs: kwargs["orthonormalize"] = False
         if "check_axioms" not in kwargs: kwargs["check_axioms"] = False
 
-        super(TrivialEJA, self).__init__(basis,
-                                         jordan_product,
-                                         inner_product,
-                                         associative=True,
-                                         **kwargs)
+        super().__init__(basis,
+                         jordan_product,
+                         inner_product,
+                         associative=True,
+                         **kwargs)
 
         # The rank is zero using my definition, namely the dimension of the
         # largest subalgebra generated by any element.