Cannot determine truth value of Relational while simplifying expression

[clinssen]

For a moderately simple expression, sympy>=1.11 throws an exception when simplifying. Small (minimal?) reproducer:

import sympy
a, b, c = sympy.symbols("a b c")
sympy.powsimp(sympy.exp(a)/((c*a - c*b)*(sympy.Float(1.0)*c*a - sympy.Float(1.0)*c*b)))

[...snip...]
~/.local/lib/python3.9/site-packages/sympy/core/relational.py in __bool__(self)
    509 
    510     def __bool__(self):
--> 511         raise TypeError("cannot determine truth value of Relational")
    512 
    513     def _eval_as_set(self):

TypeError: cannot determine truth value of Relational

The offending subexpression is:

(Pdb) self
1.0*a*c - 1.0*b*c < a*c - b*c

This works fine on sympy<=1.10. The cause was tracked down props to @pnbabu: earlier sympy used sorted(d.keys()) whereas the current release uses sorted(d.items()) while sorting a dictionary d created internally by powsimp():

0ca399d#diff-18021242f0d8c835ef8fa3190d8379ab5cb7ca45c31a75fffbc65d1f0f36797fL296

[oscarbenjamin]

I think this is a bug in ordered. It tries to sort this:

In [15]: l = [(((10, 0, 'tuple'), (2, (((3, 1, 'Add'), (2, (((3, 0, 'Mul'), (2, (((2, 0, 'Symbol'), (1, (
    ...: 'a',)), ((1, 0, 'Number'), (0, ()), (), 1), 1), ((2, 0, 'Symbol'), (1, ('c',)), ((1, 0, 'Number'
    ...: ), (0, ()), (), 1), 1))), ((1, 0, 'Number'), (0, ()), (), 1), 1), ((3, 0, 'Mul'), (2, (((2, 0, '
    ...: Symbol'), (1, ('b',)), ((1, 0, 'Number'), (0, ()), (), 1), 1), ((2, 0, 'Symbol'), (1, ('c',)), (
    ...: (1, 0, 'Number'), (0, ()), (), 1), 1))), ((1, 0, 'Number'), (0, ()), (), 1), -1))), ((1, 0, 'Num
    ...: ber'), (0, ()), (), 1), 1), ((10, 0, 'list'), (1, (((1, 0, 'Number'), (0, ()), (), -1),)), ((1,
    ...: 0, 'Number'), (0, ()), (), 1), 1))), ((1, 0, 'Number'), (0, ()), (), 1), 1), [(a*c - b*c, [-1])]
    ...: ), (((10, 0, 'tuple'), (2, (((3, 1, 'Add'), (2, (((3, 0, 'Mul'), (2, (((2, 0, 'Symbol'), (1, ('a
    ...: ',)), ((1, 0, 'Number'), (0, ()), (), 1), 1), ((2, 0, 'Symbol'), (1, ('c',)), ((1, 0, 'Number'),
    ...:  (0, ()), (), 1), 1))), ((1, 0, 'Number'), (0, ()), (), 1), 1.00000000000000), ((3, 0, 'Mul'), (
    ...: 2, (((2, 0, 'Symbol'), (1, ('b',)), ((1, 0, 'Number'), (0, ()), (), 1), 1), ((2, 0, 'Symbol'), (
    ...: 1, ('c',)), ((1, 0, 'Number'), (0, ()), (), 1), 1))), ((1, 0, 'Number'), (0, ()), (), 1), -1.000
    ...: 00000000000))), ((1, 0, 'Number'), (0, ()), (), 1), 1), ((10, 0, 'list'), (1, (((1, 0, 'Number')
    ...: , (0, ()), (), -1),)), ((1, 0, 'Number'), (0, ()), (), 1), 1))), ((1, 0, 'Number'), (0, ()), (),
    ...:  1), 1), [(1.0*a*c - 1.0*b*c, [-1])])]
    ...: 

In [16]: sorted(l)
TypeError: cannot determine truth value of Relational

The two elements of this list should be orderable but the problem is that the floats and integers compare equal:

In [17]: l[0]
Out[17]: 
(((10, 0, 'tuple'),
  (2,
   (((3, 1, 'Add'),
     (2,
      (((3, 0, 'Mul'),
        (2,
         (((2, 0, 'Symbol'),
           (1, ('a',)),
           ((1, 0, 'Number'), (0, ()), (), 1),
           1),
          ((2, 0, 'Symbol'),
           (1, ('c',)),
           ((1, 0, 'Number'), (0, ()), (), 1),
           1))),
        ((1, 0, 'Number'), (0, ()), (), 1),
        1),
       ((3, 0, 'Mul'),
        (2,
         (((2, 0, 'Symbol'),
           (1, ('b',)),
           ((1, 0, 'Number'), (0, ()), (), 1),
           1),
          ((2, 0, 'Symbol'),
           (1, ('c',)),
           ((1, 0, 'Number'), (0, ()), (), 1),
           1))),
        ((1, 0, 'Number'), (0, ()), (), 1),
        -1))),
     ((1, 0, 'Number'), (0, ()), (), 1),
     1),
    ((10, 0, 'list'),
     (1, (((1, 0, 'Number'), (0, ()), (), -1),)),
     ((1, 0, 'Number'), (0, ()), (), 1),
     1))),
  ((1, 0, 'Number'), (0, ()), (), 1),
  1),
 [(a*c - b*c, [-1])])

In [18]: l[1]
Out[18]: 
(((10, 0, 'tuple'),
  (2,
   (((3, 1, 'Add'),
     (2,
      (((3, 0, 'Mul'),
        (2,
         (((2, 0, 'Symbol'),
           (1, ('a',)),
           ((1, 0, 'Number'), (0, ()), (), 1),
           1),
          ((2, 0, 'Symbol'),
           (1, ('c',)),
           ((1, 0, 'Number'), (0, ()), (), 1),
           1))),
        ((1, 0, 'Number'), (0, ()), (), 1),
        1.0),
       ((3, 0, 'Mul'),
        (2,
         (((2, 0, 'Symbol'),
           (1, ('b',)),
           ((1, 0, 'Number'), (0, ()), (), 1),
           1),
          ((2, 0, 'Symbol'),
           (1, ('c',)),
           ((1, 0, 'Number'), (0, ()), (), 1),
           1))),
        ((1, 0, 'Number'), (0, ()), (), 1),
        -1.0))),
     ((1, 0, 'Number'), (0, ()), (), 1),
     1),
    ((10, 0, 'list'),
     (1, (((1, 0, 'Number'), (0, ()), (), -1),)),
     ((1, 0, 'Number'), (0, ()), (), 1),
     1))),
  ((1, 0, 'Number'), (0, ()), (), 1),
  1),
 [(1.0*a*c - 1.0*b*c, [-1])])

Related to this:

In [19]: list(ordered([1, 1.0]))
Out[19]: [1, 1.0]

In [20]: list(ordered([1.0, 1]))
Out[20]: [1.0, 1]

The problem is that there is no tie-breaker rule to distinguish floats from rationals.