Comment #21 on issue 2440 by smi...@gmail.com: Equal Integrals compare
different when using different variables
http://code.google.com/p/sympy/issues/detail?id=2440
This is a repost from PR 3775:
Something that I think would be useful for addressing this issue is
a "fold" or "fold_symbols" method that remaps symbols canonically as
```
def fold(i):
all = list(uniq(i.variables + list(ordered(i.free_symbols))))
reps = dict(zip(all, [Symbol('_%i' % i) for i in range(len(all))]))
return i.xreplace(reps)
...
fold(Integral(x+y, (x, 1, 2)))
Integral(_0 + _1, (_0, 1, 2))
fold(Integral(x+y, (y, 1, 2)))
Integral(_0 + _1, (_0, 1, 2))
fold(Integral(x+y/2, (x, 1, 2)))
Integral(_0 + _1/2, (_0, 1, 2))
fold(Integral(x+y/2, (y, 1, 2)))
Integral(_0/2 + _1, (_0, 1, 2))
fold(Integral(x+Symbol('_0'), (x, 1, 2))) # there will be no clash
Integral(_0 + _1, (_0, 1, 2))
```
So before computing the hashable content, a function could do `expr =
self.fold_symbols` and then compute the hash. The Basic.fold_symbols would
be
```
@property
def fold_symbols(self):
all = list(ordered(self.atoms(Symbol)))
reps = dict(zip(all, [Symbol('_%i' % i) for i in range(len(all))]))
return self.xreplace(reps)
```
Methods that have their own bound symbols (like Lambda, Integral, Sum,
Product, ...) would override this to put the bound symbols first in
whatever order made sense.
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