eja: renumber coordinate variables from zero.

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

diff --git a/mjo/eja/eja_cache.py b/mjo/eja/eja_cache.py
index b5743ec94892a74f0d3914cf8dc639993008505e..81ea398a5060220e557ac1620f1a4c0de91a9772 100644 (file)
--- a/mjo/eja/eja_cache.py
+++ b/mjo/eja/eja_cache.py
@@ -5,8 +5,10 @@ sense to cache them and then only test that the cached values are
 correct every once in a while. And they're in this separate file
 because they are visually horrific.
 
-The function used to turn SageMath's output into the appropriate input
-can be found in the eja_utils module.
+SageMath's output can be converted back into "input form" using a sed
+script, for example:
+
+    $ sed -e 's/\^/\*\*/g' -e 's/X\([0-9][0-9]*\)/X\[\1\]/g' <input>
 
 The simple algebras _not_ represented here all have rank two or less,
 and are "easy" to compute even over the algebraic reals.

diff --git a/mjo/eja/eja_utils.py b/mjo/eja/eja_utils.py
index 79d8ecfce61c555375deffd40501b2fb100c0379..1e10943e6ee686a015b45f2f1592efca3323e705 100644 (file)
--- a/mjo/eja/eja_utils.py
+++ b/mjo/eja/eja_utils.py
@@ -1,41 +1,5 @@
 from sage.structure.element import is_Matrix
 
-def _charpoly_sage_input(s):
-    r"""
-    Helper function that you can use on the string output from sage
-    to convert a charpoly coefficient into the corresponding input
-    to be cached.
-
-    SETUP::
-
-        sage: from mjo.eja.eja_algebra import JordanSpinEJA
-        sage: from mjo.eja.eja_utils import _charpoly_sage_input
-
-    EXAMPLES::
-
-        sage: J = JordanSpinEJA(4,QQ)
-        sage: a = J._charpoly_coefficients()
-        sage: a[0]
-        X1^2 - X2^2 - X3^2 - X4^2
-        sage: _charpoly_sage_input(str(a[0]))
-        'X[0]**2 - X[1]**2 - X[2]**2 - X[3]**2'
-
-    """
-    import re
-
-    exponent_out = r"\^"
-    exponent_in = r"**"
-
-    digit_out = r"X([0-9]+)"
-
-    def replace_digit(m):
-        # m is a match object
-        return "X[" + str(int(m.group(1)) - 1) + "]"
-
-    s = re.sub(exponent_out, exponent_in, s)
-    return re.sub(digit_out, replace_digit, s)
-
-
 def _scale(x, alpha):
     r"""
     Scale the vector, matrix, or cartesian-product-of-those-things