Derivative of O(x^0)

Consider a power series

R.<x> = PowerSeries(SR)
f = 1 + O(x^2)
f.derivative()

This gives us O(x^1) as we would expect. However, if we do

f = O(x^0)
f.derivative()

we get O(x^-1) instead of O(x^0) again. Is this a bug or am I missing something?

1 Answer

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This is indeed a bug! Thanks for reporting it! What version of Sage were you using?

I can reproduce the bug in Sage 7.4 using PowerSeriesRing instead of PowerSeries:

sage: R.<x> = PowerSeriesRing(SR)
sage: f = 1 + O(x^2)
sage: f.derivative()
O(x^1)
sage: g = O(x^0)
sage: g.derivative()
O(x^-1)

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Asked: 8 years ago

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Last updated: Jan 17 '17