order of the remainder

[qwertyjl]

t = Taylor1(7)
sin(t) # ... + 𝒪(t⁸)

Shouldn't the remainder be 𝒪(t⁹)?
Is there any way to get the correct order of the remainder even if it is greater than the order of the previously defined variable t?

[lbenet]

I think the output is correct from your definition of t, which is of order 7.

Let me put it in this way: If you truncate a series to order $n$, you know a priori nothing of the term $n+1$, hence the notation $\mathcal{O}^{n+1}$. This holds for sin(t) but also for the t variable, since the latter is a Taylor1 object and therefore has a finite order expansion.

Mathematically, $t$ is known to infinite precision, so for "simple" functions such as $sin$ we know everything. Yet t is a finite representation of the mathematical $t$, and we try to be consequent.