eja: renumber coordinate variables from zero.

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

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index 6fb4baa5f87ca09d3deef5bf3e4d9eb9a241188a..c0dc408df3a7160a94c7cadcba6a5e35d78ba4fb 100644 (file)
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -166,9 +166,10 @@ from sage.modules.free_module import FreeModule, VectorSpace
 from sage.rings.all import (ZZ, QQ, AA, QQbar, RR, RLF, CLF,
                             PolynomialRing,
                             QuadraticField)
-from mjo.eja.eja_element import FiniteDimensionalEJAElement
+from mjo.eja.eja_element import (CartesianProductEJAElement,
+                                 FiniteDimensionalEJAElement)
 from mjo.eja.eja_operator import FiniteDimensionalEJAOperator
-from mjo.eja.eja_utils import _all2list, _mat2vec
+from mjo.eja.eja_utils import _all2list
 
 def EuclideanJordanAlgebras(field):
     r"""
@@ -366,7 +367,7 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
 
         if orthonormalize:
             # Now "self._matrix_span" is the vector space of our
-            # algebra coordinates. The variables "X1", "X2",...  refer
+            # algebra coordinates. The variables "X0", "X1",...  refer
             # to the entries of vectors in self._matrix_span. Thus to
             # convert back and forth between the orthonormal
             # coordinates and the given ones, we need to stick the
@@ -870,7 +871,7 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
 
             sage: J = JordanSpinEJA(3)
             sage: p = J.characteristic_polynomial_of(); p
-            X1^2 - X2^2 - X3^2 + (-2*t)*X1 + t^2
+            X0^2 - X1^2 - X2^2 + (-2*t)*X0 + t^2
             sage: xvec = J.one().to_vector()
             sage: p(*xvec)
             t^2 - 2*t + 1
@@ -919,13 +920,13 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
 
             sage: J = HadamardEJA(2)
             sage: J.coordinate_polynomial_ring()
-            Multivariate Polynomial Ring in X1, X2...
+            Multivariate Polynomial Ring in X0, X1...
             sage: J = RealSymmetricEJA(3,field=QQ,orthonormalize=False)
             sage: J.coordinate_polynomial_ring()
-            Multivariate Polynomial Ring in X1, X2, X3, X4, X5, X6...
+            Multivariate Polynomial Ring in X0, X1, X2, X3, X4, X5...
 
         """
-        var_names = tuple( "X%d" % z for z in range(1, self.dimension()+1) )
+        var_names = tuple( "X%d" % z for z in range(self.dimension()) )
         return PolynomialRing(self.base_ring(), var_names)
 
     def inner_product(self, x, y):
@@ -1281,7 +1282,9 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
         #
         # Of course, matrices aren't vectors in sage, so we have to
         # appeal to the "long vectors" isometry.
-        oper_vecs = [ _mat2vec(g.operator().matrix()) for g in self.gens() ]
+
+        V = VectorSpace(self.base_ring(), self.dimension()**2)
+        oper_vecs = [ V(g.operator().matrix().list()) for g in self.gens() ]
 
         # Now we use basic linear algebra to find the coefficients,
         # of the matrices-as-vectors-linear-combination, which should
@@ -1291,7 +1294,7 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
         # We used the isometry on the left-hand side already, but we
         # still need to do it for the right-hand side. Recall that we
         # wanted something that summed to the identity matrix.
-        b = _mat2vec( matrix.identity(self.base_ring(), self.dimension()) )
+        b = V( matrix.identity(self.base_ring(), self.dimension()).list() )
 
         # Now if there's an identity element in the algebra, this
         # should work. We solve on the left to avoid having to
@@ -1768,7 +1771,7 @@ class RationalBasisEJA(FiniteDimensionalEJA):
 
             sage: J = JordanSpinEJA(3)
             sage: J._charpoly_coefficients()
-            (X1^2 - X2^2 - X3^2, -2*X1)
+            (X0^2 - X1^2 - X2^2, -2*X0)
             sage: a0 = J._charpoly_coefficients()[0]
             sage: J.base_ring()
             Algebraic Real Field
@@ -3087,6 +3090,7 @@ class CartesianProductEJA(FiniteDimensionalEJA):
         sage: actual == expected             # long time
         True
     """
+    Element = CartesianProductEJAElement
     def __init__(self, factors, **kwargs):
         m = len(factors)
         if m == 0:
@@ -3190,6 +3194,34 @@ class CartesianProductEJA(FiniteDimensionalEJA):
         ones = tuple(J.one().to_matrix() for J in factors)
         self.one.set_cache(self(ones))
 
+    def _sets_keys(self):
+        r"""
+
+        SETUP::
+
+            sage: from mjo.eja.eja_algebra import (ComplexHermitianEJA,
+            ....:                                  RealSymmetricEJA)
+
+        TESTS:
+
+        The superclass uses ``_sets_keys()`` to implement its
+        ``cartesian_factors()`` method::
+
+            sage: J1 = RealSymmetricEJA(2,
+            ....:                       field=QQ,
+            ....:                       orthonormalize=False,
+            ....:                       prefix="a")
+            sage: J2 = ComplexHermitianEJA(2,field=QQ,orthonormalize=False)
+            sage: J = cartesian_product([J1,J2])
+            sage: x = sum(i*J.gens()[i] for i in range(len(J.gens())))
+            sage: x.cartesian_factors()
+            (a1 + 2*a2, 3*b0 + 4*b1 + 5*b2 + 6*b3)
+
+        """
+        # Copy/pasted from CombinatorialFreeModule_CartesianProduct,
+        # but returning a tuple instead of a list.
+        return tuple(range(len(self.cartesian_factors())))
+
     def cartesian_factors(self):
         # Copy/pasted from CombinatorialFreeModule_CartesianProduct.
         return self._sets