eja: use "b" as the default prefix.

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

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index da008d0cf70249de27ac1a52b1d53ae4be9ef4f2..c55061e34fb2b7a4d04f127d74148984ce21f9fa 100644 (file)
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -141,7 +141,7 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
                  cartesian_product=False,
                  check_field=True,
                  check_axioms=True,
-                 prefix='e'):
+                 prefix="b"):
 
         n = len(basis)
 
@@ -210,7 +210,7 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
         # ambient vector space V that our (vectorized) basis lives in,
         # as well as a subspace W of V spanned by those (vectorized)
         # basis elements. The W-coordinates are the coefficients that
-        # we see in things like x = 1*e1 + 2*e2.
+        # we see in things like x = 1*b1 + 2*b2.
         vector_basis = basis
 
         degree = 0
@@ -337,16 +337,16 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
             sage: set_random_seed()
             sage: J = random_eja()
             sage: n = J.dimension()
-            sage: ei = J.zero()
-            sage: ej = J.zero()
-            sage: ei_ej = J.zero()*J.zero()
+            sage: bi = J.zero()
+            sage: bj = J.zero()
+            sage: bi_bj = J.zero()*J.zero()
             sage: if n > 0:
             ....:     i = ZZ.random_element(n)
             ....:     j = ZZ.random_element(n)
-            ....:     ei = J.monomial(i)
-            ....:     ej = J.monomial(j)
-            ....:     ei_ej = J.product_on_basis(i,j)
-            sage: ei*ej == ei_ej
+            ....:     bi = J.monomial(i)
+            ....:     bj = J.monomial(j)
+            ....:     bi_bj = J.product_on_basis(i,j)
+            sage: bi*bj == bi_bj
             True
 
         """
@@ -618,7 +618,7 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
             sage: J2 = RealSymmetricEJA(2)
             sage: J = cartesian_product([J1,J2])
             sage: J( (J1.matrix_basis()[1], J2.matrix_basis()[2]) )
-            e1 + e5
+            b1 + b5
 
         TESTS:
 
@@ -893,15 +893,15 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
             sage: J = JordanSpinEJA(4)
             sage: J.multiplication_table()
             +----++----+----+----+----+
-            | *  || e0 | e1 | e2 | e3 |
+            | *  || b0 | b1 | b2 | b3 |
             +====++====+====+====+====+
-            | e0 || e0 | e1 | e2 | e3 |
+            | b0 || b0 | b1 | b2 | b3 |
             +----++----+----+----+----+
-            | e1 || e1 | e0 | 0  | 0  |
+            | b1 || b1 | b0 | 0  | 0  |
             +----++----+----+----+----+
-            | e2 || e2 | 0  | e0 | 0  |
+            | b2 || b2 | 0  | b0 | 0  |
             +----++----+----+----+----+
-            | e3 || e3 | 0  | 0  | e0 |
+            | b3 || b3 | 0  | 0  | b0 |
             +----++----+----+----+----+
 
         """
@@ -955,7 +955,7 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
 
             sage: J = RealSymmetricEJA(2)
             sage: J.basis()
-            Finite family {0: e0, 1: e1, 2: e2}
+            Finite family {0: b0, 1: b1, 2: b2}
             sage: J.matrix_basis()
             (
             [1 0]  [                  0 0.7071067811865475?]  [0 0]
@@ -966,7 +966,7 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
 
             sage: J = JordanSpinEJA(2)
             sage: J.basis()
-            Finite family {0: e0, 1: e1}
+            Finite family {0: b0, 1: b1}
             sage: J.matrix_basis()
             (
             [1]  [0]
@@ -1048,20 +1048,20 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
 
             sage: J = HadamardEJA(5)
             sage: J.one()
-            e0 + e1 + e2 + e3 + e4
+            b0 + b1 + b2 + b3 + b4
 
         The unit element in the Hadamard EJA is inherited in the
         subalgebras generated by its elements::
 
             sage: J = HadamardEJA(5)
             sage: J.one()
-            e0 + e1 + e2 + e3 + e4
+            b0 + b1 + b2 + b3 + b4
             sage: x = sum(J.gens())
             sage: A = x.subalgebra_generated_by(orthonormalize=False)
             sage: A.one()
-            f0
+            c0
             sage: A.one().superalgebra_element()
-            e0 + e1 + e2 + e3 + e4
+            b0 + b1 + b2 + b3 + b4
 
         TESTS:
 
@@ -1864,13 +1864,13 @@ class RealSymmetricEJA(ConcreteEJA, RealMatrixEJA):
     EXAMPLES::
 
         sage: J = RealSymmetricEJA(2)
-        sage: e0, e1, e2 = J.gens()
-        sage: e0*e0
-        e0
-        sage: e1*e1
-        1/2*e0 + 1/2*e2
-        sage: e2*e2
-        e2
+        sage: b0, b1, b2 = J.gens()
+        sage: b0*b0
+        b0
+        sage: b1*b1
+        1/2*b0 + 1/2*b2
+        sage: b2*b2
+        b2
 
     In theory, our "field" can be any subfield of the reals::
 
@@ -2621,19 +2621,19 @@ class HadamardEJA(ConcreteEJA):
     This multiplication table can be verified by hand::
 
         sage: J = HadamardEJA(3)
-        sage: e0,e1,e2 = J.gens()
-        sage: e0*e0
-        e0
-        sage: e0*e1
+        sage: b0,b1,b2 = J.gens()
+        sage: b0*b0
+        b0
+        sage: b0*b1
         0
-        sage: e0*e2
+        sage: b0*b2
         0
-        sage: e1*e1
-        e1
-        sage: e1*e2
+        sage: b1*b1
+        b1
+        sage: b1*b2
         0
-        sage: e2*e2
-        e2
+        sage: b2*b2
+        b2
 
     TESTS:
 
@@ -2874,20 +2874,20 @@ class JordanSpinEJA(BilinearFormEJA):
     This multiplication table can be verified by hand::
 
         sage: J = JordanSpinEJA(4)
-        sage: e0,e1,e2,e3 = J.gens()
-        sage: e0*e0
-        e0
-        sage: e0*e1
-        e1
-        sage: e0*e2
-        e2
-        sage: e0*e3
-        e3
-        sage: e1*e2
+        sage: b0,b1,b2,b3 = J.gens()
+        sage: b0*b0
+        b0
+        sage: b0*b1
+        b1
+        sage: b0*b2
+        b2
+        sage: b0*b3
+        b3
+        sage: b1*b2
         0
-        sage: e1*e3
+        sage: b1*b3
         0
-        sage: e2*e3
+        sage: b2*b3
         0
 
     We can change the generator prefix::
@@ -3099,23 +3099,23 @@ class CartesianProductEJA(FiniteDimensionalEJA):
         sage: J = cartesian_product([J1,cartesian_product([J2,J3])])
         sage: J.multiplication_table()
         +----++----+----+----+
-        | *  || e0 | e1 | e2 |
+        | *  || b0 | b1 | b2 |
         +====++====+====+====+
-        | e0 || e0 | 0  | 0  |
+        | b0 || b0 | 0  | 0  |
         +----++----+----+----+
-        | e1 || 0  | e1 | 0  |
+        | b1 || 0  | b1 | 0  |
         +----++----+----+----+
-        | e2 || 0  | 0  | e2 |
+        | b2 || 0  | 0  | b2 |
         +----++----+----+----+
         sage: HadamardEJA(3).multiplication_table()
         +----++----+----+----+
-        | *  || e0 | e1 | e2 |
+        | *  || b0 | b1 | b2 |
         +====++====+====+====+
-        | e0 || e0 | 0  | 0  |
+        | b0 || b0 | 0  | 0  |
         +----++----+----+----+
-        | e1 || 0  | e1 | 0  |
+        | b1 || 0  | b1 | 0  |
         +----++----+----+----+
-        | e2 || 0  | 0  | e2 |
+        | b2 || 0  | 0  | b2 |
         +----++----+----+----+
 
     TESTS: