Fix is_real for trigonometric and hyperbolic functions #13678
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| if self.args[0].is_real: | ||
| return True | ||
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| def _eval_is_positive(self): |
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In your branch:
>>> sinh(1 + I).is_positive
None
>>> sinh(1 + I).evalf().is_positive
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You probably want sinh(1 + I).is_real to be False instead of None (making is_positive False too), but I'm not sure it's worth it.
It would be easy to call self.as_real_imag() and then .is_zero, but even if we pass deep=False nested evaluation will lead to runtime exponential in the depth of the expression: 8 seconds for building (sinh^9)(1 + I) (^ in the sense of nested application) and 24 seconds for .is_real, instead of 3 milliseconds total with the current PR.
Slowing down to return True instead of None could have been worthwhile because proving something is real often leads to simplifications, but is it worth the slowdown to return False instead of None?
Food for thought: in the current implementation, (a+b).is_real only returns True when both a and b are real.
>>> (exp(2*I*pi/3) + exp(4*I*pi/3)).is_real
None
| if self.args[0].is_real: | ||
| return self.args[0].is_positive | ||
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| def _eval_is_negative(self): |
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This looks good to me. It fixes a bug even though it does not completely resolve all cases. Thanks! |
Fixes #13677