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 2bad32c2f500193e4126b7c5e209c0acb3116ede..c0dc408df3a7160a94c7cadcba6a5e35d78ba4fb 100644 (file)
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -367,7 +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
@@ -871,7 +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
@@ -920,13 +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):
@@ -1771,7 +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