Well, I was a bit surprised too, but the stats module apparently does so,
as shown in this example:
In [1]: from sympy.stats import *
In [2]: var('sigma', positive=True)
Out[2]: σ
In [3]: N = Normal('X', mu, sigma)
In [6]: P(N**2>1, evaluate=False)
Out[6]:
(-∞, -1) ∪ (1, ∞)
⌠
⎮ 2
⎮ -(z - μ)
⎮ ──────────
⎮ 2
⎮ ___ 2⋅σ
⎮ ╲╱ 2 ⋅ℯ
⎮ ───────────────── dz
⎮ ___
⎮ 2⋅╲╱ π ⋅σ
⌡
In [7]: srepr(P(N**2>1, evaluate=False))
Out[7]: "Integral(Mul(Rational(1, 2), Pow(Integer(2), Rational(1, 2)),
Pow(pi, Rational(-1, 2)), Pow(Symbol('sigma'), Integer(-1)),
exp(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('sigma'), Integer(-2)),
Pow(Add(Dummy('z'), Mul(Integer(-1), Symbol('mu'))), Integer(2))))),
Tuple(Dummy('z'), Union(Interval(-oo, Integer(-1), S.true, S.true),
Interval(Integer(1), oo, S.true, S.true))))"
Apart the fact that such an integral looks wrong to me, i.e. there is no
account for the random variable being squared (or am I missing something?),
it looks like SymPy is OK with intervals, but not with unions of intervals:
https://github.com/sympy/sympy/blob/9242d31f6d31a1d9c3464264a5a6e61eab8acfb8/sympy/concrete/expr_with_limits.py#L37
That's the point where an Interval gets parsed by the integration algorithm.
I think it's an easy fix to add the processing for unions of intervals.
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