Status: NeedsDecision
Owner: ----
Labels: Type-Defect Priority-Medium Assumptions NonCommutative
New issue 3714 by [email protected]: as_real_imag (and friends) for
noncommutatives
http://code.google.com/p/sympy/issues/detail?id=3714
See the discussion at https://github.com/sympy/sympy/pull/1923. To quote:
Me: "If as_real_imag and friends never makes sense for non-commutative
objects, it should fail in Expr.as_real_imag."
Sergey: "I'm not sure if this never makes sense. Why not? E.g. for complex
matrices."
Me: "This requires some thought. Abuses of terms like "real" lead to
inconsistencies in the assumptions. For example, if re() works for
matrices, and re(A).is_real is always True, then the "real" assumption
doesn't really mean element of the real numbers. But then we can't assert
real**2 == nonnegative."
(by the way, "and friends" means expand_complex(), expand(complex=True),
re(), and im(), which all call as_real_imag() internally)
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