fix in Jordan

Author: fchapoton

src/sage/algebras/jordan_algebra.py

@@ -9,12 +9,12 @@
   Jordan algebra
 """
 
-#*****************************************************************************
+# ***************************************************************************
 #  Copyright (C) 2014, 2023 Travis Scrimshaw <tscrim at ucdavis.edu>
 #
 #  Distributed under the terms of the GNU General Public License (GPL)
 #                  https://www.gnu.org/licenses/
-#*****************************************************************************
+# ***************************************************************************
 
 from sage.structure.parent import Parent
 from sage.structure.unique_representation import UniqueRepresentation
@@ -209,7 +209,7 @@ def __classcall_private__(self, arg0, arg1=None, names=None):
         if not arg1.is_symmetric():
             raise ValueError("the bilinear form is not symmetric")
 
-        arg1 = arg1.change_ring(arg0) # This makes a copy
+        arg1 = arg1.change_ring(arg0)  # This makes a copy
         arg1.set_immutable()
         return JordanAlgebraSymmetricBilinear(arg0, arg1, names=names)
 
@@ -344,8 +344,6 @@ def gens(self) -> Family:
             sage: F.<x,y,z> = FreeAlgebra(QQ)
             sage: J = JordanAlgebra(F)
             sage: J.gens()
-            Traceback (most recent call last):
-            ...
             Lazy family (Term map(i))_{i in Free monoid on 3 generators (x, y, z)}
         """
         return self.algebra_generators()
@@ -975,7 +973,7 @@ def _mul_(self, other):
             P = self.parent()
             return self.__class__(P,
                                   self._s * other._s
-                                   + (self._v * P._form * other._v.column())[0],
+                                  + (self._v * P._form * other._v.column())[0],
                                   other._s * self._v + self._s * other._v)
 
         def _lmul_(self, other):
@@ -1024,8 +1022,8 @@ def monomial_coefficients(self, copy=True):
                 {0: 1, 1: 2, 2: -1}
             """
             d = {0: self._s}
-            for i,c in enumerate(self._v):
-                d[i+1] = c
+            for i, c in enumerate(self._v):
+                d[i + 1] = c
             return d
 
         def trace(self):
@@ -1259,8 +1257,8 @@ def _test_multiplication_self_adjoint(self, **options):
                  [SD[3].conjugate(), SD[1], SD[5]],
                  [SD[4].conjugate(), SD[5].conjugate(), SD[2]]]
             Y = [[OD[0], OD[3], OD[4]],
-                  [OD[3].conjugate(), OD[1], OD[5]],
-                  [OD[4].conjugate(), OD[5].conjugate(), OD[2]]]
+                 [OD[3].conjugate(), OD[1], OD[5]],
+                 [OD[4].conjugate(), OD[5].conjugate(), OD[2]]]
             for r, c in data_pairs:
                 if r != c:
                     val = sum(X[r][i] * Y[i][c] + Y[r][i] * X[i][c] for i in range(3)) * self._half
@@ -1685,8 +1683,8 @@ def _mul_(self, other):
                  [SD[3].conjugate(), SD[1], SD[5]],
                  [SD[4].conjugate(), SD[5].conjugate(), SD[2]]]
             Y = [[OD[0], OD[3], OD[4]],
-                  [OD[3].conjugate(), OD[1], OD[5]],
-                  [OD[4].conjugate(), OD[5].conjugate(), OD[2]]]
+                 [OD[3].conjugate(), OD[1], OD[5]],
+                 [OD[4].conjugate(), OD[5].conjugate(), OD[2]]]
             # we do a simplified multiplication for the diagonal entries since
             # we have, e.g., \alpha * \alpha' + (x (x')^* + x' x^* + y (y')^* + y' y^*) / 2
             ret = [X[0][0] * Y[0][0] + (X[0][1] * Y[1][0]).real_part() + (X[0][2] * Y[2][0]).real_part(),