Fix display of tensors on free modules of finite rank (#22520)

Author: egourgoulhon

src/sage/tensor/modules/comp.py

@@ -1153,6 +1153,13 @@ def display(self, symbol, latex_symbol=None, index_positions=None,
             C_01 = 0.33
             C_21 = 0.29
 
+        Check that the bug reported in :trac:`22520` is fixed::
+
+            sage: c = Components(SR, [1, 2], 1)
+            sage: c[0] = SR.var('t', domain='real')
+            sage: c.display('c')
+            c_0 = t
+
         """
         from sage.misc.latex import latex
         from sage.tensor.modules.format_utilities import FormattedExpansion
@@ -1190,7 +1197,8 @@ def display(self, symbol, latex_symbol=None, index_positions=None,
         for ind in generator:
             ind_arg = ind + (format_spec,)
             val = self[ind_arg]
-            if val != 0 or not only_nonzero:
+            if not (val == 0) or not only_nonzero:  # val != 0 would not be
+                                                    # correct, see :trac:`22520`
                 indices = ''  # text indices
                 d_indices = '' # LaTeX down indices
                 u_indices = '' # LaTeX up indices
@@ -1336,7 +1344,7 @@ def is_zero(self):
         # In other words, the full method should be
         #   return self.comp == {}
         for val in itervalues(self._comp):
-            if val != 0:
+            if not (val == 0):
                 return False
         return True
 
@@ -3244,7 +3252,7 @@ def __setitem__(self, args, value):
         else:
             sign, ind = self._ordered_indices(indices)
             if sign == 0:
-                if value != 0:
+                if not (value == 0):
                     raise ValueError("by antisymmetry, the component cannot " +
                                      "have a nonzero value for the indices " +
                                      str(indices))

src/sage/tensor/modules/free_module_alt_form.py

@@ -484,6 +484,15 @@ def display(self, basis=None, format_spec=None):
             sage: b.display(format_spec=10)  # 10 bits of precision
             b = 0.33 e^1/\e^2 + 2.5 e^1/\e^3 + 4.0 e^2/\e^3
 
+        Check that the bug reported in :trac:`22520` is fixed::
+
+            sage: M = FiniteRankFreeModule(SR, 2, name='M')
+            sage: e = M.basis('e')
+            sage: a = M.alternating_form(2)
+            sage: a[0,1] = SR.var('t', domain='real')
+            sage: a.display()
+            t e^0/\e^1
+
         """
         from sage.misc.latex import latex
         from sage.tensor.modules.format_utilities import is_atomic, \
@@ -497,7 +506,9 @@ def display(self, basis=None, format_spec=None):
         for ind in comp.non_redundant_index_generator():
             ind_arg = ind + (format_spec,)
             coef = comp[ind_arg]
-            if coef != 0:
+            if not (coef == 0):   # NB: coef != 0 would return False for
+                                  # cases in which Sage cannot conclude
+                                  # see :trac:`22520`
                 bases_txt = []
                 bases_latex = []
                 for k in range(self._tensor_rank):

src/sage/tensor/modules/free_module_tensor.py

@@ -641,6 +641,14 @@ def display(self, basis=None, format_spec=None):
             sage: v.display(format_spec=10)  # 10 bits of precision
             v = 0.33 e_1 - 2.0 e_2
 
+        Check that the bug reported in :trac:`22520` is fixed::
+
+            sage: M = FiniteRankFreeModule(SR, 3, name='M')
+            sage: e = M.basis('e')
+            sage: t = SR.var('t', domain='real')
+            sage: (t*e[0]).display()
+            t e_0
+
         """
         from sage.misc.latex import latex
         from sage.tensor.modules.format_utilities import is_atomic, \
@@ -655,7 +663,9 @@ def display(self, basis=None, format_spec=None):
         for ind in comp.index_generator():
             ind_arg = ind + (format_spec,)
             coef = comp[ind_arg]
-            if coef != 0:
+            if not (coef == 0):   # NB: coef != 0 would return False for
+                                  # cases in which Sage cannot conclude
+                                  # see :trac:`22520`
                 bases_txt = []
                 bases_latex = []
                 for k in range(n_con):
@@ -2550,7 +2560,7 @@ def contract(self, *args):
         for pos in range(0,k2):
             if pos not in pos2:
                 nb_con_o += 1
-        if nb_cov_s != 0 and nb_con_o !=0:
+        if nb_cov_s != 0 and nb_con_o != 0:
             # some reodering is necessary:
             p2 = k1 + l1 - ncontr
             p1 = p2 - nb_cov_s