# boolean with numpy

numpy.array([1/5]) == 0.2


is False but

numpy.array([1/5.]) == 0.2


is True. At 2nd line of code there is point after 5.
What should I do to get true at first line of code?
Thanks a lot.

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For Sage, 1/5 is a rational number, whereas 1/5. is a floating point number:

sage: (1/5).parent()
Rational Field
sage: (1/5.).parent()
Real Field with 53 bits of precision


Now, when you put them in a numpy array, they are converted to a type named numpy.float64:

sage: type(numpy.array([1/5]))
<type 'numpy.float64'>
sage: type(numpy.array([1/5.]))
<type 'numpy.float64'>


As you can see, this conversion do not lead to the same approximation for 1/5 and 1/5., they seem not rounded to the same direction:

sage: numpy.float64(1/5)
0.19999999999999998
sage: numpy.float64(1/5.)
0.20000000000000001
sage: numpy.float64(0.2)
0.20000000000000001


This explains your problem. There are various issues about the rounding direction in Sage and the tools its uses, and i agree there should be a general audit.

Now, if you want 1/5 to be rounded in the right direction, you can first round it using RealField() which seems more consistent than numpy.float64:

sage: numpy.array([RR(1/5)]) == 0.2
True

more

This has been fixed now (trac ticket #14416), so if you upgrade, you will now get:

sage: numpy.array([1/5]) == 0.2
True

sage: numpy.float64(1/5)
0.20000000000000001

more